The truck coasting up the hill with its engine turned off is obeying the principle of conservation of mechanical energy because the kinetic energy is converted into gravitational potential energy without external work, while the sports car with the running engine is not conserving mechanical energy since it is adding energy to the system.
Explanation:The principle of conservation of mechanical energy states that the total mechanical energy in a system remains constant if only conservative forces are doing work. When friction and air resistance are ignored, as requested, the truck that coasts up the hill with the engine turned off obeys this principle because its initial kinetic energy is converted into gravitational potential energy without any external work being done on or by the system. On the other hand, the sports car with its engine running is continually adding energy to the system to maintain a constant speed up the hill, which means it is not conserving mechanical energy as in the first case.
Your on-board GPS-based FMS/RNAV unit is IFR certified under TSO-C129() or TSO-C196(). Your destination is below minimums for the GPS RNAV approach and you proceed to your filed alternate. You know that:________.A. GPS units certified under TSO-C129() or TSO-C196() are not authorized for alternate approach requirements; subsequently, you must use an approach procedure based on ground-based NAVAIDsB. Once diverted to the alternate airport, you may fly a GPS-based approach as long as there is an operational ground-based NAVAID and appropriate airborne receiver for use as a backupC. If your air-craft is equipped with a second TSO-C129() certified GPS as a backup in place of a ground-based NAVAID receiver, you may complete the approach even if the IAP is based on ground-based NAVAIDs
Answer:
B. Once diverted to the alternate airport,you may fly a GPS-based approach as long as there is an operational ground-based NAVAID and appropriate airborne receiver for use as a backup.
Explanation:
As stated in the question, If someone is on-board GPS-based FMS/RNAV unit, and the destination is the minimum target, it is obvious that once diverted to the alternate airport,you may fly a GPS-based approach as long as there is an operational ground-based NAVAID and appropriate airborne receiver for use as a backup. The correct answer is option B.
GPS-based FMS/RNAV units can be used for approach procedures at the alternate airport, as long as there is a ground-based NAVAID and an appropriate airborne receiver available.
The subject of this question is Computers and Technology. The question is about the requirements for using a GPS-based FMS/RNAV unit for approach procedures.
The correct answer is B. Once diverted to the alternate airport, you may fly a GPS-based approach as long as there is an operational ground-based NAVAID and appropriate airborne receiver for use as a backup.
Therefore, as long as there is a ground-based NAVAID available and an appropriate backup receiver, you can use the GPS-based approach at the alternate airport.
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When making a turn, do not have the steering wheel turned in the direction of the turn before beginning the turning maneuver.a) True b) False
Answer:
a) True.
Explanation:
If you turn the wheel in the direction of the turn before beginning the turning maneuver then it's possible that there might be not enough space available for turning and also if you are waiting for the traffic to get clear with rear ended then it will get pushed forward onto the coming traffic.
IN this Turning in a Car question, The steering wheel of a car must be turned in the direction of the desired turn. The feeling of being flung away from the center during a turn is due to the 'centrifugal force', a result of the body's inertia.
The statement 'When making a turn, do not have the steering wheel turned in the direction of the turn before beginning the turning maneuver.' is False. When making a turn in a car, you indeed must turn the steering wheel in the direction you wish to go.
This causes the car to change its direction, following a circular path or curve. The change in direction is due to the force that you apply to the steering wheel and subsequently to the car's tires that are in contact with the road.
The force applied to the tires creates an acceleration, changing the car's velocity from straight-line motion to a curved path.
Relatedly, the sensation of being pulled or flung away from the center of the turn as you make it is described by a concept in physics called the centrifugal force.
This is not an actual force. Instead, it's a result of your body's tendency to continue in straight-line motion (according to Newton's first law of motion), while the car is changing direction.
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The eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. If it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning
Answer:
[tex]v=\frac{28\pi R}{\sqrt{2} }[/tex] m/sec
Explanation:
According to the question
[tex]\frac{1}{2}I\omega^2=\frac{1}{2} mv^2[/tex]
\omega= angular velocity = 14 spins per sec
I= MOI of the spinning eel= 0.5mR^2
m= mass of eel
v= linear velocity of eel.
[tex]\frac{1}{2}0.5mR^2\omega^2=\frac{1}{2} mv^2[/tex]
solving for v in the above equation we get
[tex]v=\sqrt{\frac{R^2\omega^2}{2} }[/tex]
now \omega in radians = 14 rev/sec×2π radian/rev= 28π radian/sec
value of radius is not provided in the question
therefore we get
[tex]v=\frac{28\pi R}{\sqrt{2} }[/tex]
An object is lifted from the surface of aspherical planet to an altitude equal to the radius of the planet.As a result, what happens to the mass and wieght of the object?a) massincreases; weight decreasesb) massdecreases; weight decreasesc) massincreases; weight increasesd) massincreases; weight remains the samee) mass remainsthe same; weight decreasesf) mass remainsthe same; weight increasesg) mass remainsthe same; weight remains the same
Answer: Mass remains the same and weight decrease
Explanation: mass is always constant but weight varies. Weight is affected by height. The higher you go the lesser your weight because you are moving away from gravity
Which of the following energy systems is used most when running a 10-second sprint?
Answer:
Adenosine Triphosphate - Phosphocreatine (ATP-PC)
Explanation:
The name ATP-PC in full means Adenosine Triphosphate - Phosphocreatine (ATP-PC). ATP-PC system is made up Adenosine Triphosphate (ATP) and Phosphocreatine (PC). This system is otherwise known as the Phosphogen system. Energy coming from the breakdown of the ATP stores within the muscles supplies energy during the first few seconds of any activity after which the breakdown of PC provides energy for another 5-8 seconds of the activity until another energy is required. ATP-PC system is not oxygenated and it is and instant energy which allows ±12 seconds of maximum effort approximately. Examples of activities where ATP-PC is used: a short sprint, pitching a baseball or lifting a heavy weight.
Would the frequency of the angular simple harmonic motion (SHM) of the balance wheel increase or decrease if the dimensions of the balance wheel were changed as described?
Answer:
Yes the frequency of the angular simple harmonic motion (SHM) of the balance wheel increases three times if the dimensions of the balance wheel reduced to one-third of original dimensions.
Explanation:
Considering the complete question attached in figure below.
Time period for balance wheel is:
[tex]T=2\pi\sqrt{\frac{I}{K}}[/tex]
[tex]I=mR^{2}[/tex]
m = mass of balance wheel
R = radius of balance wheel.
Angular frequency is related to Time period as:
[tex]\omega=\frac{2\pi}{T}\\\omega=\sqrt{\frac{K}{I}} \\\omega=\sqrt{\frac{K}{mR^{2}}[/tex]
As dimensions of new balance wheel are one-third of their original values
[tex]R_{new}=\frac{R}{3}[/tex]
[tex]\omega_{new}=\sqrt{\frac{K}{mR_{new}^{2}}}\\\\\omega_{new}=\sqrt{\frac{K}{m(\frac{R}{3})^{2}}}\\\\\omega_{new}={3}\sqrt{\frac{K}{mR^{2}}}\\\\\omega_{new}={3}\omega[/tex]
What is the advantage of D-step tuning on 2020 Pathfinder’s Xtronic CVT at cruising speed?
Explanation:
The transmission stimulates shifts at higher rotation per minutes and providing stepped acceleration at with linear acceleration feel.
D-Step Logic Control is found in other Nissan CVT equipped models such as 2020 Altima, 2020 Pathfinder, 2020 Murano and the sporty 2020 Maxima.
A player hits a ball with a bat. The action force is the impact of the bat against the ball. The reaction to this force is the
Answer:
Force of the ball against the bat
Explanation:
Newton's third law of motion states that for every action, there is an equal and opposite reaction. When a player hits a ball with a bat, the force the player exerted on the ball through the bat gave the ball a push force in the forward direction. This is an action force. Now that an action has been initiated, there must be a reaction according to Newton's third law of motion. The magnitude of the force on the ball equals the magnitude of the force on the bat. The direction of the force on the ball is opposite to the direction of the force on the ball. The ball will give the bat an equal and opposite force trying to push the bat backward by resisting the impact of the bat. This is the reaction. The ball will only move if the applied force is able to overcome the resisting force by the bat.
[tex]F_{A} = - F_{B}[/tex]
Where;
[tex]F_{A}[/tex] is the action force of the bat against the ball.
[tex]F_{B}[/tex] is the equal and opposite reaction force of the ball towards the ball.
If a player hit a ball with a bat the ore that which the ball is coming towards the player and the force with which the player is moving the bat will impact the ball which will have an equal and opposite reaction.
Thus the reaction of the force will be the force of the ball against the bat.Hence the newtons law of motion will be applied.
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A block of copper was heated to 55oC and dropped into a beaker of 55 mL of water at 22oC. After the water reached thermal equilibrium, the temperature was 28oC. What was the mass of the copper block? Assume no heat is lost by the beaker.Cs, Cu= 0.385 J/gKCs, H2O= 4.18 J/gK
Answer:
132.70kg
Explanation:
Given:
Temperature of copper block = 55°C
Temperature of water = 22°C
Mass of copper block, m₁ = ?
Mass of water, m₂ = 55 mL = 5.5 × 10⁻⁵m³
Density of water [tex]= \frac{mass}{volume}[/tex]
m₂ = Density of water × volume
m₂ = 1000kg/m³ × (5.5 × 10⁻⁵m³)
m₂ = 0.055 kg
m₂ = 55g
Quantity of heat lost by the copper block = m₁cΔT
= m₁ × 0.385 × (55 - 28)
= m₁ × 0.385 × 27
= 10.395 × m₁ J
Quantity of heat gained by the water = m₂cΔT
= 55 × 4.18 × (28-22)
= 55 × 4.18 × 6
= 1379.4 J
Heat lost by copper block = Heat gained by water
10.395m₁ = 1379.4
[tex]m_{1} =\frac{1379.4}{10.395}[/tex]
m₁ = 132.6984kg
m₁ = 132.70kg
The mass of the copper block is 132.70kg
The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C(mass 2.34×10−26kg) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted at right angles to each other. The electron (mass 9.11×10−31kg) has a speed of 3.40×107 m/s and the neutrino has a momentum of 6.70×10−24 kg⋅m/s .
What is the recoil speed of the nucleus?
The answer is not 1900 or 1600 m/s...
The recoil speed of the nucleus in the beta decay process is gotten as; 1354.27 m/s
What is the recoil speed?From principle of conservation of momentum, we will have;
Recoil momentum of nucleus = Recoil momentum of emitted particle
We are given;
Mass of electron; m_e = 9.11 × 10⁻³¹ kg
speed of electron; v_e = 3.4 × 10⁷ m/s
Momentum of electron; P = 6.7 × 10⁻²⁴ kg.m/s
Thus;
Momentum of electron ignoring relativistic effect is;
P_f = m_e * v_e
P_f = 9.11 × 10⁻³¹ × 3.4 × 10⁷
P_f = 3.0974 × 10⁻²³ kg.m/s
Resultant momentum is gotten from;
R = √[(3.0974 × 10⁻²³)² + (6.7 × 10⁻²⁴)²]
R = 3.169 × 10⁻²³ kg.m/s
The formula for the recoil speed of the nucleus is;
v = R/m_n
where m_n is mass of neutrino = 2.34 × 10⁻²⁶ kg
v = (3.169 × 10⁻²³)/(2.34 × 10⁻²⁶)
v = 1354.27 m/s
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Final answer:
The recoil speed of the carbon nucleus after beta decay can be determined using the conservation of momentum and is found to be approximately 1381 m/s.
Explanation:
The recoil speed of the nucleus can be calculated using the principle of conservation of momentum, which states that the total momentum of a closed system is constant if no external forces are acting on it. In this case of beta decay, the initial momentum of the stationary carbon nucleus is zero. After decay, the sum of momenta of the electron, neutrino, and recoiling nucleus must also be zero, as momentum is conserved.
The momentum of the electron is given by its mass times its velocity (pe = me x ve), and the momentum of the neutrino is given (pν = 6.70 x 10-24 kg·m/s). The nucleus will recoil with momentum equal in magnitude but opposite in direction to the vector sum of the electron and neutrino momenta. Given that the electron and neutrino are emitted at right angles, we can use the Pythagorean theorem to find the magnitude of the resultant momentum that the nucleus must have:
Calculate the momentum of the electron: pe = me x veUse the Pythagorean theorem to calculate the magnitude of the vector sum of the electron and neutrino momenta: ptotal = √(pe2 + pν2)Since the nucleus must recoil with this magnitude of momentum to conserve momentum, we can find its speed using the recoil momentum and the mass of the carbon nucleus: vnucleus = ptotal / mnucleusFollowing through the calculations:
pe = (9.11 x 10-31 kg) x (3.40 x 107 m/s) = 3.0974 x 10-23 kg·m/sptotal = √((3.0974 x 10-23 kg·m/s)2 + (6.70 x 10-24 kg·m/s)2)ptotal = √(9.59577 x 10-46 + 4.489 x 10-47) kg·m/sptotal = √(1.044577 x 10-45) kg·m/sptotal = 3.23082 x 10-23 kg·m/svnucleus = (3.23082 x 10-23 kg·m/s) / (2.34 x 10-26 kg) = 1.38112 x 103 m/sTherefore, the recoil speed of the nucleus is approximately 1381 m/s.
A tuning fork with a frequency of 512 Hz is used to tune a violin. When played together, beats are heard with a frequency of 4 Hz. The string on the violin is tightened and when played again, the beats have a frequency of 2 Hz. The original frequency of the violin was ______.
The original frequency of the violin was 508 Hz. This is based on the principle of beats, where the beat frequency is the absolute difference in frequency between the two sources - in this case, the tuning fork and the violin string.
Explanation:The original frequency of the violin string can be found using the principle of beats. The frequency of the beats is equal to the absolute difference in frequency between the two sources - in this case, the tuning fork and the violin string.
Initially, the beat frequency was heard as 4 Hz. This indicates that the original frequency of the violin was either 512 Hz + 4 Hz = 516 Hz, or 512 Hz - 4 Hz = 508 Hz. However, when the violin string was tightened, the beat frequency decreased to 2 Hz, which means the frequency of the note it was producing increased.
Therefore, the violin must have initially been producing a note with lower frequency (508 Hz), and even after tightening the string, the note it now produces (510 Hz) remains lower than that of the tuning fork.
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In a ballistics test, a 28-g bullet pierces a sand bag that is thick. If the initial bullet velocity was and it emerged from the sandbag moving at what was the magnitude of the friction force (assuming it to be constant) that the bullet experienced while it traveled through the bag?
A. 130 N
B. 1.3 N
C. 1.4 N
D. 38 N
E. 13 N
Answer:
A) 130N
Explanation:
We know that:
[tex]E_i -E_f = W_f[/tex]
where [tex]E_i[/tex] is the initial energy, [tex]E_f[/tex] is the final energy and [tex]W_f[/tex] is the work of the friction force.
so:
[tex]\frac{1}{2}MV_i^2 -\frac{1}{2}MV_f^2 = Fd[/tex]
where M is the mass, [tex]V_i[/tex] is the initial velocity, [tex]V_f[/tex] is the final velocity, F the force and d the distance.
Replacing values, we get:
[tex]\frac{1}{2}(0.028)(55m/s)^2 -\frac{1}{2}(0.028)(18m/s)^2 = F(0.3m)[/tex]
solving for F:
F= 126N
the closest answer is A. 130 N
A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?A. 1000B. 1250C. 1300D. 1600E. 1625
Answer:
E
Explanation:
Let the total capacity of the pool be x
Let the initial volume of water in the pool be y
then;
300 + y =80% of x
300 + y = (80/100) * x
300 + y = 0.8x ...........................equation 1
300 gallons of water increased the volume by 30x
y +300 = y +30% of y
300 = 0.3y
y= (300/0.3)
y= 1000
substitute y into equation 1 to get x
300 + y = 0.8x
300 + 1000 = 0.8x
1300 =0.8x
x= (1300/0.8)
x= 1625 gallons
A security review has flagged this architecture as vulnerable, and a Security Engineer has been asked to make this design more secure. The company has a short deadline and a second VPN connection to the Aurora account is not possible.
How can a Security Engineer securely set up the bastion host?
A. Move the bastion host to the VPC and VPN connectivity. Create a VPC peering relationship between the bastion host VPC and Aurora VPC.
B. Create a SSH port forwarding tunnel on the Developer's workstation to the bastion host to ensure that only authorized SSH clients can access the bastion host.
C. Move the bastion host to the VPC with VPN connectivity. Create a cross-account trust relationship between the bastion VPC and Aurora VPC, and update the Aurora security group for the relationship.
D. Create an AWS Direct Connect connection between the corporate network and the Aurora account, and adjust the Aurora security group for this connection.
Answer:
Complete Question:
A company has two AWS accounts, each containing one VPC. The first VPC has a VPN connection with its corporate network. The second VPC, without a VPN, hosts an Amazon Aurora database cluster in private subnets. Developers manage the Aurora database from a bastion host in a public subnet as shown in the image.
A security review has flagged this architecture as vulnerable, and a Security Engineer has been asked to make this design more secure. The company has a short deadline and a second VPN connection to the Aurora account is not possible.
How can a Security Engineer securely set up the bastion host?
A. Move the bastion host to the VPC and VPN connectivity. Create a VPC peering relationship between the bastion host VPC and Aurora VPC.
B. Create a SSH port forwarding tunnel on the Developer's workstation to the bastion host to ensure that only authorized SSH clients can access the bastion host.
C. Move the bastion host to the VPC with VPN connectivity. Create a cross-account trust relationship between the bastion VPC and Aurora VPC, and update the Aurora security group for the relationship.
D. Create an AWS Direct Connect connection between the corporate network and the Aurora account, and adjust the Aurora security group for this connection.
Answer:
B. Create an SSH port forwarding tunnel on the Developer's workstation to the bastion host to ensure that only authorized SSH clients can access the bastion host.
Explanation:
To gain a better understanding of why the option selected in the answer to the question let first explain some terms.
AWS:
According to techtarget,
AWS (Amazon Web Services) is a comprehensive, evolving cloud computing platform provided by Amazon that includes a mixture of (1) infrastructure as a service (IaaS),(2) platform as a service (PaaS) and (3)packaged software as a service (SaaS) offerings.
An AWS account is a container for your AWS resources
A bastion host is a server whose purpose is to provide access to a private network from an external network, such as the Internet. Because of its exposure to potential attacks, a bastion host must minimize the chances of penetration to the private network.
SSH port forwarding, or TCP/IP connection tunneling, is a process whereby a TCP/IP connection that would otherwise be insecure is tunneled through a secure SSH(Secure Shell (SSH) is a cryptographic network protocol for operating network services securely over an unsecured network.) link, thus protecting the tunneled connection from network attacks.
So the Bastion protects the private network while the SSH prevent unauthorized access to the bastion
To securely set up the bastion host, it should be moved to the VPC with VPN connectivity. Subsequently, a cross-account trust relationship should be created between the bastion VPC and Aurora VPC, followed by updating the Aurora security group.
Explanation:Considering the context and options given, one of the best ways to securely set up the bastion host is to follow the path described in Option C. This involves moving the bastion host to the VPC (Virtual Private Cloud) with VPN (Virtual Private Network) connectivity. Subsequently, create a cross-account trust relationship between the bastion VPC and Aurora VPC. Once this relationship is established, proceed by updating the Aurora security group for the relationship.
This setup aids in restricting access to only trusted entities and thus fortifies security. An important point to note is that the assurance of security provided by this method is largely based on proper configuration and stringent maintenance of the trust relationship and security groups.
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A diode is reversed biased when the ? is connected to the negative side of the external voltage source and the ? is connected to the positive side.
Answer:
Diode is reverse biased when its negative us connected with positive terminal and positive is connected with negative terminal
Explanation:
A diode is reverse biased when the positive side of the diode is connected with the negative terminal of the voltage source
And negative side of he diode is connected with positive terminal of the diode
When diode is reverse bias there is no flow of current, as it makes barrier to the flow of current
A diode is reverse biased when the cathode is connected to the negative side and the anode to the positive side of the voltage source, preventing current flow by widening the depletion layer.
Explanation:A diode is reverse biased when the cathode is connected to the negative side of the external voltage source and the anode is connected to the positive side. In this configuration, the depletion layer at the p-n junction within the diode becomes wider, which increases its resistance and allows very little to no current to flow through. This is because the electrons in the n-type material and holes in the p-type material move away from the junction, reinforcing the built-in potential barrier. Therefore, in reverse bias, the diode blocks current flow rather than allowing it.
In contrast, when the diode is forward biased, the anode is connected to the positive side and the cathode to the negative side, allowing current to flow easily through the diode. This is because the positive voltage applied to the p-type material and the negative voltage on the n-type material cause the depletion layer to narrow and the potential barrier to decrease, enabling charge carriers to flow across the junction.
When does the most significant drop in physical activity typically occur in people's lives?
Answer:
Later high school years and freshman year of college
Explanation:
The transition from high school to college is an important developmental milestone that holds the potential for personal growth and behavioral change. A cohort of 2,025 students was recruited during the summer before they matriculated into college and completed Internet-based surveys about their participation in a variety of behavioral risks during the last three months of high school and throughout the first year of college. Alcohol use, marijuana use, and sex with multiple partners increased during the transition from high school to college, whereas driving after drinking, aggression, and property crimes decreased. Those from rural high schools and those who elected to live in private dormitories in college were at highest risk for heavy drinking and driving after drinking.
A golfer starts with the club over her head and swings it to reach maximum speed as it contacts the ball. Halfway through her swing, when the golf club is parallel to the ground, does the acceleration vector of the club head point straight down, parallel to the ground, approximately toward the golfer's shoulders, approximately toward the golfer's feet, or toward a point above the golfer's head? Explain.
Answer:
approximately toward the golfer's feet
Explanation:
The golf club experiences two accelerations. when the club is horizontal, centripetal acceleration acts on it toward the center parallel to the ground. The tangential acceleration acts towards the ground in downward direction. So when the golf club is horizontal, the acceleration vector is given by the combination of tangential and centripetal acceleration. the acceleration vector thus points in between horizontal and vertical direction . hence towards the golfer's feet.
Answer:
approximately toward the golfer's feet
Explanation:
The club head undergoes circular motion so it has a centripetal acceleration. As the speed of the club head is increasing, it also has an acceleration component pointed vertically down. Thus, the acceleration vector is pointed as described in (c)
A diver rises quickly to the surface from a 5.0 m depth. If she did not exhale the gas from her lunds before rising, by what factor would her lungs expand? Assume the temperature to be constant and the pressure in the lungs to match the pressure outside the diver's body. The density of seawater is 1.03x!0^3 kg.
Answer:
1.5 times
Explanation:
[tex]h[/tex] = depth of the diver initially = 5 m
[tex]\rho[/tex] = density of seawater = 1030 kg m⁻³
[tex]P_{i}[/tex] = Initial pressure at the depth
[tex]P_{f}[/tex] = final pressure after rising = 101325 Pa
Initial pressure at the depth is given as
[tex]P_{i} = P_{f} + \rho gh\\P_{i} = 101325 + (1030) (9.8) (5)\\P_{i} = 151795 Pa[/tex]
[tex]V_{i}[/tex] = Initial volume at the depth
[tex]V_{f}[/tex] = Final volume after rising
Since the temperature remains constant, we have
[tex]P_{f} V_{f} = P_{i} V_{i}\\(101325) V_{f} = (151795) V_{i}\\V_{f} = 1.5 V_{i}[/tex]
Using Boyle's law, the volume of gas in the diver's lungs would expand by a factor of 1.5 when a diver quickly rises to the surface from a 5m depth. This implies the lungs could potentially double in size if the diver does not exhale gas while ascending.
Explanation:In this scenario, we can use Boyle's law to answer the question accurately, which is an important principle in Physics that states that the pressure and volume of a gas have an inverse relationship when the temperature is held constant. To be specific, if a diver is at 5m below the sea level, he or she is under 1.5 atmospheres of pressure, including the sea pressure and atmospheric pressure (1 ATA). When the diver rises to the surface, there's only 1 ATA of pressure left, which is the atmospheric pressure.
The volume of gas in the diver's lungs would thus double by a factor of (1.5/1) = 1.5 when he or she ascends quickly to the surface from a 5m depth, according to Boyle's law. This is a simplified explanation without considering the temperature changes or the gas involved, always remember to exhale while rising to the surface to avoid potential lung damage.
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A man plans to make a rectangular garden with one side adjoining a neighbor’s yard. The garden is to be 675 ft2. If the neighbor agrees to pay half of the dividing fence, what should the dimensions of the garden be to ensure a minimum cost for the man?
Answer:
L = W = 26 ft.
Explanation:
Let the length of the garden is L and the width is W.
area of garden , A = L x W
675 = L x W ... (1)
Costing is minimum when the perimeter is minimum.
Perimeter, P = 2 ( L + W)
[tex]P=2\left ( L+\frac{675}{L} \right )[/tex]
For maxima and minima, differentiate perimeter with respect to L.
[tex]\frac{dP}{dL}=2\left ( 1-\frac{675}{L^{2}} \right )[/tex]
It should be zero for maxima and minima
L² = 675
L = 26 ft
W = 675/26 = 26 ft
Now, [tex]\frac{d^{2}P}{dL^{2}}=4\frac{675}{L^{3}}[/tex]
It is positive, so the costing is minimum.
So, length and width of the garden is 26 ft.
A child does 5.0 J of work on a spring while loading a ball into a spring-loaded toy gun. If mechanical energy is conserved, what will be the kinetic energy of the ball when it leaves the gun?
A 0 J
B 3.7 J
C 2.5 J
D 5.0 J
Explanation:
Here mechanical energy is conserved.
Kinetic energy + Potential energy = Constant.
First the child does 5.0 J of work on a spring while loading a ball into a spring-loaded toy gun.
That is potential energy = 5 J
Kinetic energy = 0 J
Kinetic energy + Potential energy = 0 + 5 = 5 J
Secondly the spring is released.
That is potential energy = 0 J
Kinetic energy = ?
Kinetic energy + Potential energy = Constant = 5 J
Kinetic energy + 0 = 5 J
Kinetic energy is 5 J
Option D is the correct answer.
The kinetic energy of the ball when it leaves the spring-loaded toy gun is 5.0 J. This is because the work done on the spring is entirely converted into the kinetic energy of the ball, according to the law of conservation of energy.
Explanation:The subject of this question is based on the conservation of mechanical energy, which is a principle of physics. The principle states that the total mechanical energy in a closed system—meaning one that does not have any external forces, like air resistance, acting on it—remains constant. In this case, the child does 5.0 J of work on the toy gun's spring. This work is converted into potential energy that is stored in the compressed spring.
When the spring launches the ball, the potential energy of the spring is then converted into the kinetic energy of the ball, as there's no friction or air resistance to cause energy loss. So, according to the law of conservation of energy, all of the initial energy (5.0 J) used to compress the spring will be transferred to the ball as kinetic energy. Therefore, the kinetic energy of the ball as it leaves the gun is 5.0 J (Option D).
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A certain piece of metal (density 9.45 grams per cubic centimeter) has the shape of a hockey puck with a diameter of 13 cm and a height of 2.8 cm. If this puck is placed into a bowl of mercury (density 13.6 grams per cubic centimeter), it floats. How deep below the surface of the mercury is the bottom of the metal puck?
Answer:
0.0195 m
Explanation:
[tex]\rho _{p}[/tex] = density of hockey puck = 9.45 gcm⁻³ = 9450 kgm³
[tex]d_{p}[/tex] = diameter of hockey puck = 13 cm = 0.13 m
[tex]h_{p}[/tex] = height of hockey puck = 2.8 cm = 0.028 m
[tex]\rho _{m}[/tex] = density of mercury = 13.6 gcm⁻³ = 13600 kgm³
[tex]d[/tex] = depth of puck below surface of mercury
According to Archimedes principle, the weight of puck is balanced by the weight of mercury displaced by puck
Weight of mercury displaced = Weight of puck
[tex]\rho _{m} (0.25)(\pi d_{p}^{2} d ) g = \rho _{p} (0.25)(\pi d_{p}^{2} h_{p} ) g\\\rho _{m} ( d ) = \rho _{p} ( h_{p} )\\(13600) d = (9450) (0.028)\\d = 0.0195 m[/tex]
Summers in Phoenix Arizona are hot (125 F is not uncommon), and dry. If you hop into an outdoor swimming pool on a summer day in Phoenix, you will find that the water is too warm to be very refreshing. However, when you get out of the pool and let the sun dry you off, you find that you are quite cold for a few minutes.
Answer:
Explanation:
when we get out of the water we feel quite cold due to the latent heat of evaporation of water.
Water at our body gets converted into gas and leaves behind the cooling effect which makes us feel cold.
While when we are inside the pool we are in constant touch of water, therefore, we get the warmth of the water and it becomes difficult to bear it.
A positive charge is placed at rest at the center of a region of space in which there is a uniform electric field. (A uniform field is one whose strength and direction are the same at all points within the region.) What happens to the electric potential energy of the positive charge, after the charge is released from rest in the uniform electric field?A. It will remain constant because the electric field is uniform.B.It will decrease because the charge will move in the opposite direction of the electric field.C.It will remain constant because the charge remains at rest.D.It will decrease because the charge will move in the direction of the electric field.E.It will increase because the charge will move in the direction of the electric field.
Answer:
.D.It will decrease because the charge will move in the direction of the electric field
Explanation:
which there is a uniform electric field. (A uniform field is one whose strength and direction are the same at all points within the region.) What happens to the electric potential energy of the positive charge, after the charge is released from rest in the uniform electric field?A. It will remain constant because the electric field is uniform.B.It will decrease because the charge will move in the opposite direction of the electric field.C.It will remain constant because the charge remains at rest.D.It will decrease because the charge will move in the direction of the electric field.E.It will increase because the charge will move in the direction of the electric field.
solution
The potential energy decreases, converted to kinetic energy
The charge will feel a force in the direction of the electric field (F=Eq) and thus it will accelerate with
a constant acceleration. (Just like releasing an object above the earth's surface - constant acceleration,
at least until it hits something.)
tus te answer will be
.D.It will decrease because the charge will move in the direction of the electric field
A radio receiver has an effective resistance of 300 Ω to the input signal on the antenna downlead. The signal voltage is 700 µV. What is the signal current flow in the antenna downlead?
Answer:
I = 2.33 µA
Explanation:
given,
Effective resistance (R)= 300 Ω
Voltage of signal (V)= 700 µV
current flow in the antenna = ?
Using ohm's law
V = I R
where I is the current flow
[tex]I = \dfrac{V}{R}[/tex]
[tex]I = \dfrac{700\times 10^{-6}}{300}[/tex]
I = 2.33 x 10⁻⁶ A
I = 2.33 µA
Hence, the current flow in the antenna downloaded is equal to I = 2.33 µA
Answer:I = 2.33 µA
Explanation:
A 1200-N crate rests on the floor. How much work is required to move it at constant speed (a) 5.0 m along the floor against a friction force of 230 N, and (b) 5.0 m vertically?
The work required to move a 1200-N crate 5.0 m along the floor against a friction force of 230 N is 1150 Joules. The work required to move it 5.0 m vertically is 6000 Joules.
Explanation:The work required to move an object can be calculated using the formula Work = Force x Distance. Force is the total force acting on an object, and distance is the distance the force moves the object.
(a) To move a box on the ground with a friction force of 230 N, the work done can be calculated as follows:
work = friction force x distance = 230 N x 5.0 m = 1150 joules
(b) To lift the box vertically, the force required is equal to the weight of the box, i.e. H. its mass multiplied by the acceleration due to gravity. The problem, however, is the weight of the box. When the box is lifted vertically, the force is equal to the weight, i.e. 1,200 N. The work done is then calculated as follows:
work = weight x height = 1200 N x 5.0 m = 6000 joules.
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Water has a high heat capacity. What does this term mean? a) Water is relatively resistant to an increase in temperature. b) Water heats up or cools down readily c) Water provides a useful source of stored kilocalories. d) Water provides excellent insulation for the body.
Answer:a) Water is relatively resistant to an increase in temperature
Explanation:
Water has relatively high heat capacity i.e. it requires high amount of heat to raise a little increase in temperature.
Heat capacity is defined as ability of molecule to absorb heat . Mathematically heat capacity is defined as
[tex]C=\frac{Q}{\Delta T}[/tex]
where [tex]C=heat\ capacity[/tex]
[tex]Q=heat\ interaction[/tex]
[tex]\Delta T=change\ in\ Temperature[/tex]
When the moving sidewalk at the airport is broken, as it often seems to be, it takes you 44 s to walk from your gate to baggage claim. When it is working and you stand on the moving sidewalk the entire way, without walking, it takes 90 s to travel the same distance
Answer:
a) 29.55 sec
Explanation:
Let the total distance be s feet.
Speed while walking = s/44 ft/sec.
Speed on sidewalk = s/90 ft/sec.
Total speed while walking on moving sidewalk
= s/44+s/90 = (90s+44s)/44×90
=(134x)/3960 ft/sec
= x/29.55 ft per sec.
Hence your travel time will be 29.55 secs.
A toy cork gun contains a spring whose spring constant is 10.0N/m. The spring is compressed 5.00cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:A. 1.02m/s
B. 1.41m/s
C. 2.00m/s
D. 2.04m/s
E. 4.00m/s
Answer:
The muzzle velocity of this cork is 2 m/s.
Explanation:
It is given that,
Spring constant of the spring, k = 10 N/m
Mass of the cork, m = 6 g = 0.006 kg
Initial position of the spring, x = 5 cm = 0.05 m
Final position of the spring, x' = 1 cm = 0.01 m
According to the law of conservation of energy, the initial potential energy of the spring is equal to the sum of final spring potential energy and the kinetic energy of cork such that,
[tex]\dfrac{1}{2}kx^2=\dfrac{1}{2}kx'^2+\dfrac{1}{2}mv^2[/tex]
v is the muzzle velocity of this cork.
[tex]kx^2=kx'^2+mv^2[/tex]
[tex]v=\sqrt{\dfrac{k(x^2-x'^2)}{m}}[/tex]
[tex]v=\sqrt{\dfrac{10\times ((0.05)^2-(0.01)^2)}{0.006}}[/tex]
v = 2 m/s
So, the muzzle velocity of this cork is 2 m/s. Hence, this is the required solution.
Answer:
2 m/s
Explanation:
Spring constant, k = 10 N/m
Mass of the cork, m = 6 g = 0.006 kg
Initial position of the spring, x = 5 cm = 0.05 m
Final position of the spring, x' = 1 cm = 0.01 m
Let v be the muzzle speed of the cork.
According to the law of conservation of energy,
Initial potential energy = final potential energy + kinetic energy
0.5 x 10 x 0.05 x 0.05 = 0.5 x 10 x 0.01 x 0.01 + 0.5 x 0.006 x v²
0.0125 = 0.0005 + 0.003v²
v = 2 m/s
Thus, the muzzle speed of the cork is 2 m/s.
Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 x 103 N. What is the largest mass that Tarzan can have and still make it safely across the river?
Answer:61.72 kg
Explanation:
Given
Length of rope [tex]L=10 m[/tex]
Speed at bottom of swing [tex]v=8 m/s[/tex]
Breaking strength of string [tex]T=1000 N[/tex]
At bottom Point
weight is acting downward and Tension is opposing it
Thus [tex]T-mg=\frac{mv^2}{L}[/tex]
[tex]T=mg+\frac{mv^2}{L}[/tex]
[tex]1000=m(9.8+\frac{8^2}{10})[/tex]
[tex]1000=m\cdot 16.2[/tex]
[tex]m=61.72 kg[/tex]
maximum mass Tarzan can have is [tex]61.72 kg[/tex]
The largest mass that Tarzan can have and still make it safely across the river is of 61.72 kg.
Given data:
The length of rope is, L = 10 m.
Speed at the bottom of swing is, v = 8 m/s.
Breaking strength of string is, T = 1000 N.
At the bottom point, the weight is acting downward and tension force on the string is acting upward. So, the balanced equilibrium condition is,
[tex]T - mg =\dfrac{mv^{2}}{L} \\\\T =mg+\dfrac{mv^{2}}{L} \\\\T =m(g+\dfrac{v^{2}}{L})\\\\1000 =m\times(9.8+\dfrac{8^{2}}{10})\\\\m=61.72 \;\rm kg[/tex]
Thus, we can conclude that the largest mass that Tarzan can have and still make it safely across the river is of 61.72 kg.
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Marcel is helping his two children, Jacques and Gilles, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child, Jacques, simply sinking to the ground. Given that Jacques, whose weight is W, is sitting at distance L to the left of the pivot, at what distance L₁ should Marcel place Gilles, whose weight is w, to the right of the pivot to balance the seesaw?
Express your answer in terms of L, W and ω.
Answer:
Explanation:
Given
Jacques weight is W and is at distance of L to the left
Gilles weight is [tex]\omega [/tex] and should be Placed at right at a distance of [tex]L_1[/tex] from pivot
Distance should be such that the torque of Jacques and Gilles is same in magnitude but opposite in direction.
[tex]W\times L-\omega \times L_1=0[/tex]
such that net torque is zero.
[tex]L_1=\frac{W}{\omega }\times L[/tex]
To balance the seesaw, the product of the weight of Jacques and the distance he is sitting from the pivot must be equal to the product of the weight of Gilles and the distance he should sit from the pivot.
Explanation:To balance the seesaw, the product of the weight of Jacques and the distance he is sitting from the pivot must be equal to the product of the weight of Gilles and the distance he should sit from the pivot.
So, we can write the equation as:
W * L = w * L₁
To find L₁, we can rearrange the equation:
L₁ = (W * L) / w
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