Explanation:
Given that
[tex]rA(t)=(3.00 m/s)t\hat{i}+ (1.00 m/s^2)t^2\hat{j}\texttt{ and }rB(t)=(4.00 m/s)t\hat{i}+ (-1.00 m/s^2)t^2\hat{j}[/tex]
We need to find distance when t = 3 s
Substituting t = 3 s
[tex]rA(t)=(3.00 m/s)\times 3\hat{i}+ (1.00 m/s^2)\times 3^2\hat{j}=9\hat{i}+9\hat{j}\\\\rB(t)=(4.00 m/s)\times 3\hat{i}+ (-1.00 m/s^2)\times 3^2\hat{j}=12\hat{i}-9\hat{j}[/tex]
[tex]\texttt{Displacement = }12\hat{i}-9\hat{j}-(9\hat{i}+9\hat{j})=3\hat{i}-18\hat{j}[/tex]
[tex]\texttt{Magnitude = }\sqrt{3^2+(-18)^2}=18.3m[/tex]
Option C is the correct answer.
The distance between object A and object B is approximately 18.248 meters. (Choice C)
How to calculate the distance between two objects
In this question we must apply the concepts of vector difference, dot product and norm to determine the distance between objects A and B, in meters:
[tex]r_{B/A} = \sqrt{(\vec r_{B}-\vec r_{A})\,\bullet\,(\vec r_{B}-\vec r_{A})}[/tex] (1)
Where:
[tex]\vec r_{A}[/tex] - Vector distance of object A, in meters.[tex]\vec r_{B}[/tex] - Vector distance of object B, in meters. [tex]r_{B/A}[/tex] - Distance of B relative to A, in meters.If we know that [tex]\vec r_{A} = (3\cdot t, t^{2})\,\left[m\right][/tex], [tex]\vec r_{B} = (4\cdot t,-t^{2})\,\left[m\right][/tex] and [tex]t = 3\,s[/tex], then the distance of B relative to A is:
[tex]r_{B/A}=\sqrt{t^{2}+4\cdot t^{4}}[/tex]
[tex]r_{B/A} = t\cdot \sqrt{1+4\cdot t^{2}}[/tex]
[tex]r_{B/A} = 3\cdot \sqrt{1+4\cdot 3^{2}}[/tex]
[tex]r_{B/A} \approx 18.248\,m[/tex]
The distance between object A and object B is approximately 18.248 meters. (Choice C) [tex]\blacksquare[/tex]
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What would happen to Earth if ocean floor were created at divergent boundaries at a faster rate than it is destroyed at convergent boundaries?
Answer:
The Earth would increase in volume
Explanation:
What would happen to Earth if ocean floor were created at divergent boundaries at a faster rate than it is destroyed at convergent boundaries?
Divergent boundaries are boundaries where plates pull away from each other, forming mild earthquakes and volcanoes as magma comes to the surface. Earthquakes are as a result of vibrations travelling within the earth or ocean floors . Volcanoes occur as a result of the eruption of molten magma from the ocean floor
In divergent boundaries, the plates pull away and and the weakened crust in between collapse leaving more space thereby increasing in volume.
Convergent boundaries are boundaries that pull into each other. mountain chains are formed as the two plates push into each other if they are of the same density.
What is the specific fuel requirement for flight under VFR at night in an airplane?
A) Enough to fly to the first point of intended landing and to fly after that for 45 minutes at normal cruising speed.
B) Enough to complete the flight at normal cruising speed with adverse wind conditions.
C) Enough to fly to the first point of intended landing and to fly after that for 30 minutes at normal cruising speed.
Answer:
A). Enough to fly to the first point of intended landing and to fly after that for 45 minutes at normal cruising speed
Explanation:
Here are Fuel requirements for flight in VFR conditions
No person may begin a flight in an airplane under VFR conditions unless there is enough fuel to fly to the first point of intended landing and, assuming normal cruising speed -
During the day, to fly after that for at least 30 minutes; or At night, to fly after that for at least 45 minutes.why doesnt the moon get pulled into the sun
Answer:
The moon does not get pulled into the sun because of gravitational pull.
Explanation:
Gravitational pull is a force that pulls things down or into i guess you can say. Like are orbit, all of the planets (even the dwarf planet "pluto") are circling around are sun but we have things called moons that circle are planets. Are moon is orbiting us like we (are earth) are orbiting the sun. So to get into a little more detail, i will add that we circle the sun or the moon circles us because the action of earth pulling away from the suns gravitational pull is causing it to either rotate or revolve.So we are stuck in the gravitational force of the sun and the moon is stuck in ares. But as someone who LOVES astronamy will say that i watched a video about are earth, sun, and moon and it said that each year are moon is slowly pulling away from the earth. sooner or later we might not have a solar or lunar eclipse anymore.
Answer:
But the path of the Moon is always concave towards the Sun; the gravitational force exerted by the Sun on the Moon is always greater than the pull of the Earth on the Moon
Explanation:
A horse draws a sled horizontally across a snow-covered field. The coefficient of friction between the sled and the snow is 0.135, and the mass of the sled, including the load, is 195.9kg. If the horse moves the sled at a constant speed of 1.785m/s, what is the power needed to accomplish this?
Answer:
P = 462.62 watts
Explanation:
The power needed to accomplish this can be calculated how
P = Fv
Where F: The force exerted by the horse
v: velocity
The force exerted by the horse is against friction force; how the movement is with constant velocity these forces must be equals, then
Fr = μN
=μmg
= (0.135)(195.9)(9.8)
= 259.17 N
And the power is
P = (259.17)(1.785)
P = 462.62 watts
The power needed to accomplish this is 462.62 watts.
What is the coefficient of friction?It is defined as the numerical value that indicates the amount of friction present between the surfaces of two bodies. The lower the coefficient of friction the lower the friction between the surfaces and the higher coefficient of friction the higher the friction force between them.
We know the:
P = F×v
Where P is the power needed to accomplish this.
F = force exerted by the horse
v = velocity of the horse.
For F = [tex]\rm \mu N[/tex]
[tex]\mu = 0.135[/tex]
N = mg ⇒ 195.9×9.8 ( m= 195.9 kg and g = 9.8 [tex]\rm m/sec^2[/tex])
N = 1919.82 Newtons
F = 0.135×1919.82 ⇒ 259.1757 Newtons
Now P = F×v ⇒259.1757×1.785
P = 462.62 Watts
Thus, the power needed to accomplish this is 462.62 watts.
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Julie runs 2 miles every day after school because it reduces the stress she feels from schoolwork. Julie's running habit is maintained by a ________ reinforcer.
Answer:
negative
Explanation:
The term reinforce means to strengthen, and is used in psychology to refer to any stimulus which strengthens or increases the probability of a specific response.
Negative Reinforcement can be seen as the act of taking something negative away in order to increase a response.
Julie runs 2 miles every day after school because it reduces the stress (negative) she feels from school work (in order to increase her response in her school work).
You have purchased a new 20-pin power supply to replace one that failed. However, the motherboard only has a 24-pin connector. What should you do?
This question is incorrect.The correct question is here
You have purchased a new 24-pin power supply to replace one that failed. However, the motherboard only has a 20-pin connector. What should you do?
Answer:
To solve this problem you should plug the 24-pin power supply into the motherboard, as your mother board has 20 pin you leave pins 11, 12, 23, and 24 on the motherboard unconnected.
I have attached a picture from which you can see that there are pins for same working
A metal ball at 30°C is dropped from a height of 6.2 km. The ball is heated due to the air resistance and it completely melts just before reaching the ground. The molten substance falls slowly on the ground. If the specific heat of lead = 126 Jkg−1^o C^{-1} and melting point of lead = 130^oC and suppose that any mechanical energy lost is used to heat the ball, then the latent heat of fusion of lead is:__________.
Answer:
Explanation:
Given
height [tex]h=6.2 km[/tex]
Initial temperature [tex]T_1=30^{\circ}C[/tex]
Specific heat of lead [tex]c=126 J/kg-^{\circ}C[/tex]
Melting Point of Lead [tex]T_m=130^{\circ}C[/tex]
Here Potential Energy is converted to heat energy to melt the lead ball
Sphere ball will first will be heated to [tex]130^{\circ}C[/tex] then it starts melting
thus
[tex]mgh=mc\Delta T+mL[/tex]
where [tex]L=latent\ heat\ of\ fusion[/tex]
[tex]\Delta T=[/tex]change in Temperature
[tex]gh=c\Delta T+L[/tex]
[tex]9.8\times 6.2\times 1000=126\times (130-30)+L[/tex]
[tex]L=48,160\ J/kg [/tex]
[tex]L=48.16\ kJ/kg[/tex]
As a way of determining the inductance of a coil used in a research project, a student first connects the coil to a 9.7 V battery and measures a current of 0.742 A. The student then connects the coil to a 27.3 V(rms), 51.1 Hz generator and measures an rms current of 0.429 A. What is the inductance?
Answer:
L = 0.194 H
Explanation:
given,
Voltage = 9.7 V
current = 0.742 A
R = 9.7 V / 0.742 A
R = 13.07 Ohms.
the A.C. impedance of the inductor, like this:
Z = V / I
Z = 27.3 V / 0.429 A
Z = 63.64 Ohms.
now,
inductive reactance, X_L
[tex]X_L = \sqrt{Z^2 - R^2}[/tex]
[tex]X_L = \sqrt{63.64^2 - 13.07^2}[/tex]
[tex]X_L =62.28\ \Omega[/tex]
[tex]X_L = 2\pi f \times L[/tex]
[tex]L = \dfrac{X_L}{2\pi f}[/tex]
[tex]L = \dfrac{62.28}{2\pi \times 51.1}[/tex]
L = 0.194 H
A falling object of weight 10 N encounters 10 N of air resistance. The net force on the object is____________.
An object of weight 10 N that is falling on the ground, and it experiences a 10 N air resistance, then the net force on the object will be 0 N.
What is Force?A force in physics is an input that has the power to change an object's motion.
A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe forces. Being such a vector quantity, a force does have magnitude and direction. The SI unit metric newton is used to measure it (N). The letter F stands for force.
According to Newton's second law's original formulation, an object's net force is equal to the speed that its momentum is changing over time.
As per the given information in the question,
Weight of the object = 10 N
Friction due to air resistance = 10 N
Then, the net force will be,
10 N - 10 N = 0 N
Therefore, the net force will be 0 N.
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The net force on the object is zero.
When an object is falling, it experiences two main forces: gravity (its weight) pulling it downward and air resistance pushing upward. In this case, the object has a weight of 10 N (newtons), which is a force acting downward due to gravity, and it encounters 10 N of air resistance, which is a force acting upward against the motion of the falling object.
To find the net force on the object, you need to calculate the difference between the two forces:
Net Force = Weight - Air Resistance
Net Force = 10 N - 10 N
Net Force = 0 N
So, the net force on the object is 0 N. This means that the forces of gravity and air resistance are equal in magnitude and opposite in direction, resulting in a net force of zero. In this situation, the object is in a state of dynamic equilibrium, and its velocity remains constant (it doesn't accelerate further).
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Scientists who wished to study the metabolic function of cells with balanced translocations while preventing cell replication would be best served by arresting the cells during which phase of the cell cycle?
Answer:
Interphase.
Explanation:
interphase
When scientists were to prevent cell duplication, they would have to interrupt the division of cells (mitosis). Interphase is the stage of the cell life cycle that occur in between cell dividing stages.
It is during this phase that preventing cell replication would be best served by arresting the cells.
Two speakers are spaced 15 m apart and are both producing an identical sound wave. You are standing at a spot as pictured. What would be the frequency produced by the speakers to create perfectly constructive interference? Assume n = 1 and v = 343 m/s
213.04 Hz
256.70 Hz
186.68 Hz
233.14 Hz
Answer:
213.04
Explanation:
Answer:
The correct answer is option 213.04 Hz
Explanation:
Hello!
Let's solve this!
In this link we will find the image of the problem.
https://smart-answers.com/physics/question14138735
Regarding that image, we will first calculate the distance from my position to S1 and then to S2. Then the difference between these results.
We will use pitagoras.
S1 = [tex]\sqrt{10^{2}+22^{2} }[/tex]
S1 = 24.17
S2 = [tex]\sqrt{5^{2}+22^{2} }[/tex]
S2 = 22.56
The difference will be:
24.17-22.56 = 1.61 m
Constructive interference:
Δr=n*λ
λ=1.61 m (for n = 1)
Then we will calculate the frequency:
f = v / λ
f = (343m / s) /1.61m
f = 213.04 Hz
So the correct answer is option 213.04 Hz
When driving through standing water at high speed water may build up beneath the wheels and cause the vehicle to skid is commonly referred to as:________
Answer: Hydroplaning
Explanation: Hydroplaning is the skiding of a high speed vehicle when water builds beneath the wheels when driving through standing water.
It is usually caused by factors such as High speed,Standing water,deflated tyres. It is strongly recommended that when driving in standing water a driver should drive at a slow and steady speed and always to ensure that the vehicle tyres are adequately inflated with air,this is one of the causes of vehicular accidents during rainy season or flood.
Two neutral metal spheres on wood stands are touching. A negatively charged rod is held directly above the top of the left sphere, not quite touching it. While the rod is there, the right sphere is moved so that the spheres no longer touch. Then the rod is withdrawn. Afterward, what is the charge state of each sphere? Use charge diagrams to explain your answer.
A. Both the spheres are neutral.
B. The left sphere is negatively charged, the right sphere is charged positively.
C. The right sphere is negatively charged, the left sphere is charged positively.
D. Both the spheres are charged positively.
E. Both the spheres are charged negatively.
Answer:
The right sphere is negatively charged, the left sphere is charged positively.
Explanation:
When a negatively charged rod is held above the top of left sphere, the rod will attract positive charges and repel negative charges. As the sphere are initially touching each other so positive charges from the both spheres will moves toward the rod. When we separate the spheres positive charges from right sphere have already moved toward the rod i.e. left sphere, creating a deficiency of positive charges in the right sphere and excessiveness of positive charges in left sphere , hence the right sphere will remain negatively charged and left sphere will remain positively charged.
What is a geologist’s role in the petroleum industry? stay with the drillers to examine rock and fossils brought to the surface chart information on a well log calculate the distance and direction of movement of the lost vein of ore locate environments in which petroleum forms
Answer:what is the role of of geologist in the petroleum industry
A. Stay with the drillers to examine rocks and fossils brought to the surface.
B. Chart information on a well log
C. Calculate the distance and direction of movement of the lost vein of ore
D. locate environment in which the petroleum forms
Correct option. Is D locate environment in which petroleum forms
Explanation:
Petroleum geologists are usually linked to the actual discovery of oil and the identification of possible oil deposits or leads. It can be a very labor-intensive task involving several different fields of science and elaborate equipment. Petroleum
geologists look at the structural and
sedimentary aspects of the stratum/strata to identify possible oil traps
Answer: D locate environment in which the petroleum forms
Explanation:
If an astronaut landed on a planet that had the same radius as Earth but 4 times its mass, then the astronaut's weight on the planet would be:
Answer:
4 times
Explanation:
[tex]M[/tex] = mass of the earth
[tex]R[/tex] = radius of the earth
[tex]g_{e}[/tex] = acceleration due to gravity on earth
acceleration due to gravity on the earth is given as
[tex]g_{e} =\frac{GM}{R^{2}}[/tex]
[tex]w_{e}[/tex] = weight of the astronaut on earth
weight of the astronaut on earth is given as
[tex]w_{e} = m g_{e} = \frac{GMm}{R^{2}}[/tex]
[tex]M_{p}[/tex] = mass of the planet = [tex]4 M[/tex]
[tex]R_{p}[/tex] = radius of the planet = R
[tex]g_{p}[/tex] = acceleration due to gravity on earth
acceleration due to gravity on the planet is given as
[tex]g_{p} =\frac{GM_{p}}{R_{p}^{2}}\\g_{p} = \frac{4GM}{R^{2}}\\g_{p} = 4 g_{e}[/tex]
[tex]w_{p}[/tex] = weight of the astronaut on planet
weight of the astronaut on planet is given as
[tex]w_{p} = m g_{p}\\w_{p} = m (4) g_{e}\\w_{p} = 4 w_{e}[/tex]
hence the weight of the astronaut on the planet is four times.
Final answer:
An astronaut would weigh 4 times more on a planet with the same radius as Earth but 4 times its mass, due to the direct relationship between mass and gravitational force.
Explanation:
To understand how an astronaut's weight would change on a planet with the same radius as Earth but 4 times its mass, we need to consider the universal law of gravitation. The formula to calculate gravitational force (which determines weight) is F = G (m1m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two masses (the radius of the planet, in this case).
Since the planet has 4 times the mass of Earth but the same radius, applying these values to the formula shows that the astronaut's weight would be 4 times greater on this new planet compared to Earth. The increase in mass directly increases the gravitational force, while the radius remains constant, leading to an increase in weight.
The Kepler Space Telescope is searching for extrasolar planets by the transit method. It is necessary for Kepler to photometrically monitor a large number of stars because ____.
Answer:
The Kepler Space Telescope is searching for extrasolar planets by the transit method. It is necessary for Kepler to photometrically monitor a large number of stars because increase the probability to see a transit.
Explanation:
Photometry is the study of the intensivity of light radiated from a particular object.
In the other hand, the transit method consists in the measured of the dimming on the brightness of a star when a planet is passing in front of it, as long as the star, the planet and the detector (in this case the Kepler Telescope) are in the same line of sign.
However, that transit has a short duration. So it is necessary that the Kepler Telescope monitorates the brightness of several stars each thirty minutes in order to increase the probability of detection of a transit.
A 15,000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.040-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car? Group of answer choices
Answer:
[tex]F_{piston} = 600 N[/tex]
Explanation:
[tex]F_{car}[/tex] = weight of the car = Force on the larger piston = 15000 N
[tex]r_{1}[/tex] = radius of the larger piston = 0.20 m
[tex]F_{piston}[/tex] = force on the smaller piston
[tex]r_{2}[/tex] = radius of the smaller piston = 0.040 m
Using pascal's law, Pressure must be equal on each piston, hence
[tex]\frac{F_{car}}{\pi r_{1}^{2} } = \frac{F_{piston}}{\pi r_{2}^{2} } \\\\\frac{15000}{0.20^{2} } = \frac{F_{piston}}{0.040^{2} }\\\\F_{piston} = 600 N[/tex]
600 N force must be applied to this smaller piston in order to lift the car.
Let's solve the question:
Pascal's Law:It states that if some pressure is applied at any point of incompressible liquid then the same pressure is transmitted to all the points of liquid and on the walls of the container.
Given:
Force on car, F= 15,000 N
Radius of larger piston, r₁ = 0.20m
Radius of larger piston, r₂ = 0.040m
To find:
Force on piston, F=?
Using Pascal's law:
[tex]\frac{F_{car}}{\pi r_1^2} =\frac{F_{piston}}{\pir_2^2}\\\\ \frac{15000}{0.20^2}=\frac{F_{piston}}{0.40^2}\\\\F_{piston}=600N[/tex]
600 N force must be applied to this smaller piston in order to lift the car.
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The multi-link mechanism in the Variable Compression Turbo Engine _____, thus varying the compression ratio.
A. Adjusts how far down the piston travels
B. Can change one individual piston's operation independent of the other three
C. Acts like a fixed-length connecting rod
Answer:
A. Adjusts how far down the piston travels
Explanation:
This type of engine changes the possition of the piston in order to modify the compression chamber volume and therefore the compression ratio of the engine. The volume of the chamber is proportional to the run of the piston (how far down the piston travels)
This engine is used to achive the optimal compression rate in each individual stage.
The multi-link mechanism in a Variable Compression Turbo Engine adjusts the piston travel to vary the compression ratio, providing efficient operation under different conditions but does not change individual pistons independently.
The multi-link mechanism in the Variable Compression Turbo Engine adjusts the angle of the connecting rods, which in turn adjusts how far down the piston travels in the cylinder. This adjustment changes the volume of the cylinder when the piston is at the top of its stroke, thus varying the compression ratio. The multi-link mechanism does not act like a fixed-length connecting rod nor can it change one individual piston's operation independent of the others, as all pistons in a multi-cylinder engine are generally interconnected and move synchronously.
By varying the compression ratio, the engine can operate efficiently under a variety of conditions, offering more power when needed or improving fuel efficiency when less power is required. This mechanism is a sophisticated mechanical linkage that transforms the linear motion of the pistons into the rotary motion of the crankshaft, similar to the operation of conventional connecting rods, but with the added capability of adjusting the compression ratio.
Suppose that a person riding on the top of a freight car shines a searchlight beam in the direction in which the train is traveling.
How does the speed of the light beam relative to the ground compare to the speed of beam when the train is at rest?
Answer:
same
Explanation:
Acc. to Einstien's postulate of special theory of
Relativity , Velocity of the light beam is same in all frames of references
(a) If the freight car is at rest
The frame we can assumed as Non - inertial frame of reference s
In the inertial frame of reference , velocity of the light beam has its own value as : 3 x 10^8 m/s
(b) If the freight car is moving , the frame we can assumed as Non -inertial frame of reference
In thus case also , The velocity of the light beam will also have the same value as ; 3 x 108 m/s
Suppose we imagine the Sun to be about the size of a grapefruit. How big an area would the orbits of the nine planets of the Solar System cover?
Answer:
size at this scale of the solar system is 10⁸ m²
Explanation:
For this exercise we can use a direct proportions rule or rule of three.
If the radius of the Sun is 7 10⁸ m is equal to the radius of a grapefruit is on average about 5 cm, the radius of the orbit of the plant is x
Mercury
r1 = 5.8 10¹⁰m
x = r1 / r_Sum 5
x = 5.8 10¹⁰/7 10⁸
x = 82 m
We repeat the same formula with all the radii of the orbit, the results in the table
Numb name r_orbit (m) x (m) A (m2)
0 Sun 7 10⁸ 1 3.14
1 mercury 5.8 10¹⁰ 8.2 10¹ 2.0 10⁴
2 venus 1 10¹¹ 1.4 10² 6.2 10⁴
3 Earth 1.5 10¹¹ 2.1 10² 1.4 10⁵
4 Mars 2.3 10¹¹ 3.2 10² 3.2 10⁵
5 Jupiter 7.8 10¹¹ 1.1 10³ 3.8 10⁶
6 Saturn 1.4 10¹² 2 10³ 1.3 10⁷
7 Uranus 2.9 10¹² 4.1 10³ 5.3 10⁷
8 Neptune 4.5 10¹² 6.4 10³ 1.3 10⁸
9 Pluto 5.9 10¹² 8.4 10³ 2.2 10⁸
The area of a circle is
A = π R²
Mercury
A = π 80²
A = 2.0 14 m²
The other values are in the table
The size at this scale of the solar system is 10⁸ m²
A 60.0-kg ball of clay is tossed vertically in the air with an initial speed of 4.60 m/s. Ignoring air resistance, what is the change in its potential energy when it reaches its highest point?
Answer:
the change in potential energy when it reaches the highest height = 634.8 J
Explanation:
Potential Energy: This is the energy a body posses due to position.
From the law of conservation of energy,
At the highest point and lowest points, potential energy is converted to kinetic energy
I.e
Ek = Ek
Where Ek = potential energy, Ep = potential energy
Ep₁ = 1/2mu² (potential energy at the lowest point)................ Equation 1
Ep₂ = 1/2mv² (potential energy at the highest point)............. Equation 2
ΔEp = Ep₂ - Ep₁ = 1/2mu² - 1/2mv²........................ Equation 3
Where ΔEp = change in potential energy, m = mass of the ball of clay, v = final velocity of the ball of clay, u = initial velocity of the ball of clay
Given: m= 60 kg, u = 4.6 m/s v = 0 ( velocity at the maximum height)
Substituting these values into equation 3
ΔEp = 1/2×60×4.6 - 1/2×60×0²
ΔEp = 30×21.16 - 0
ΔEp = 634.8 J.
Therefore the change in potential energy when it reaches the highest height = 634.8 J
Final answer:
The change in potential energy of the 60.0-kg ball of clay when it reaches its highest point, ignoring air resistance, is 636.0 J.
Explanation:
To calculate the change in potential energy of the 60.0-kg ball of clay at its highest point, we use the formula for gravitational potential energy ([tex]PE_{g}[/tex]):
[tex]PE_{g}[/tex] = m × g × h
where m is the mass of the object, g is the acceleration due to gravity (9.81 m/s² on Earth), and h is the height reached.
First, determine the maximum height h the ball reaches using the conservation of energy principle, where the initial kinetic energy (KE) is fully converted to potential energy (PE) at the highest point:
[tex]KE_{initial}[/tex] = [tex]PE_{g,max}[/tex]
To find [tex]KE_{initial}[/tex], we use the kinetic energy formula:
KE = 1/2 × m × v²
[tex]KE_{initial}[/tex] = 1/2 × 60.0 kg × (4.60 m/s)²
[tex]KE_{initial}[/tex] = 1/2 × 60 kg × 21.16 m²/s²
[tex]KE_{initial}[/tex] = 636.0 J
Since [tex]KE_{initial}[/tex] = [tex]PE_{g,max}[/tex], the ball's change in potential energy is also 636.0 J.
Suppose a 52 N sled runs on packed snow. The coefficient of friction is only 0.11. If a person weighing 700 N sits on the sled, what force is needed to pull the sled across the snow at constant speed?
Answer:
A force of 83 N is needed to pull the sled with constant speed.
Explanation:
Hi there!
Please, see the attached figure for a graphical description of the problem.
We have the following horizontal forces applied on the sled:
F = applied force.
Fr = friction force.
And the following vertical forces:
N = normal force.
W = weight of the sled + weight of the person
According to the Newton´s second law:
∑F = m · a
Where "m" is the mass of the object and "a" is its acceleration
So, in the horizontal direction:
F - Fr = m · a
We have to find what force, F, is needed so that the sled moves with constant speed (acceleration = 0). Then:
F - Fr = 0
F = Fr
The applied force has to be equal in magnitude to the friction force.
The friction force is calculated as follows:
Fr = μ · N
Where μ is the coefficient of friction and N is the normal force.
To find the normal force, let´s apply Newton´s second law in the vertical direction:
∑F = N - W = m · a
Notice that the sled is not accelerated in the vertical direction so that a = 0:
N - W = 0
N = W
The normal force is equal to the weight and the weight is the sum of the weight of the sled plus the weight of the person:
W = 52 N + 700 N = 752 N
Then:
N = 752 N
Fr = 0.11 · 752 N
Fr = 83 N
Then
F = 83 N
A force of 83 N is needed to pull the sled with constant speed.
A force of 83 N is needed to pull the sled with constant speed.
We have the following horizontal forces applied on the sled:
F = applied force.
Fr = friction force.
And the following vertical forces:
N = normal force.
W = weight of the sled + weight of the person
According to the Newton´s second law:
F = m * a
Where "m" is the mass of the object and "a" is its acceleration
So, in the horizontal direction:
F - Fr = m *a
To find what force, F, is needed so that the sled moves with constant speed (acceleration = 0). Then,
F - Fr = 0
F = Fr
The applied force has to be equal in magnitude to the friction force.
The friction force is calculated as follows:
Fr = μ · N
Where μ is the coefficient of friction and N is the normal force.
To find the normal force, let´s apply Newton´s second law in the vertical direction:
F = N - W = m · a
Notice that the sled is not accelerated in the vertical direction so that a = 0:
N - W = 0
N = W
The normal force is equal to the weight and the weight is the sum of the weight of the sled plus the weight of the person:
W = 52 N + 700 N = 752 N
Then:
N = 752 N
Fr = 0.11 · 752 N
Fr = 83 N
Then
F = 83 N
A force of 83 N is needed to pull the sled with constant speed.
Lean more:
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A day has 86,400 second (s). Notice that the decimal point is to the far right of the number. The first part of scientific notation is a number between 1 and 10. Move the decimal point to the left to obtain 8.64, which equals m in our traditional notation. The value for n is given by the number of places the decimal point was moved from its location in 86,400 to 8.64. Thus, 86,400 s = 8.64×104 s. Because the decimal was moved four places to the left (and the value is larger than 1), the exponent is a positive integer. If you had a very precise clock, you could write this as 8.640×104 s, or 8.6400×104 s. The number of digits you keep in the first part of the notation describes the precision of your value and determines the number of significant digits.
Answer:
There are 2 number of significant figures.
Explanation:
Significant figures include a zero at the start or between the digits after the decimal. But do not include a zero at the end. There are two zeros . It is 6400 but these zeros are at the end so they will not be counted in the significant figures. If they were present at the start or between any two non zero digits they would be included in significant figured
In which one of the following circumstances could mechanical energy not possibly be conserved, even if friction and air resistance are absent?
A car moves down a hill, its velocity continually increasing alongthe way.
A car moves up a hill at a constant velocity.
A car moves along level ground at a constant velocity.
A car moves up a hill, its velocity continually decreasing alongthe way.
Answer:
A car moves up a hill at a constant velocity
Explanation:
Since the velocity is constant, the speed is also constant and so is the kinetic energy. However, total mechanical energy is sum of gravitational potential energy and kinetic energy, and the car is moving up the hill so its potential energy rises.
Thus, in the circumstances described the mechanical energy cannot be conserved.
The correct answer is A car moving up the hill with constant velocity.
You throw a ball straight up, it peaks out, and then cones back down to you. During this motion, the velocity and acceleration
a) always point in the same direction
b) always point in opposite direction
c) sometimes point in the same direction, and other times point in opposite to each other.
d) depends on the way the ball is thrown
e) depends in the mass of the ball
Answer:
The answer is C sometimes point in the same direction, and other times point in opposite to each other.
Explanation:
When you throw a ball straight up velocity direction head up to up side but the acceleration points opposite direction due to gravitation of earth. Gr aviation slows down the ball when it goes up, when it reaches the summit and starts to fall down both velocity and acceleration points the same way. The ball speeds up and drops down.
The velocity and acceleration of a ball thrown straight up sometimes point in the same direction and sometimes in opposite directions. On the way up, they are opposite, but when the ball peaks and begins falling, they align in the same direction (downward). Therefore, the correct answer is that they sometimes point in the same direction and other times in opposite directions.
Explanation:When you throw a ball straight up, it follows a parabolic trajectory due to the influence of gravity. Let's examine the ball's velocity and acceleration throughout its motion:
The ball's velocity is initially positive as it travels upwards after being thrown. When the ball reaches its highest point, its velocity becomes zero as it changes direction.From the moment the ball is released until it hits the ground, the acceleration due to gravity is a constant negative value, directed downward toward the center of the Earth.On the way up, the direction of the ball's velocity (upward) and the direction of acceleration (downward) are opposite. When the ball reaches its peak and starts to fall back down, the velocity (now downward) and the constant acceleration due to gravity (also downward) will be in the same direction.Therefore, during the motion of the ball, the acceleration does not always point in the same direction as the ball's motion. Instead, the direction of velocity and acceleration are opposite on the ascent and the same on the descent. Hence, our answer to the question is that the velocity and acceleration sometimes point in the same direction, and other times point in opposite to each other.
A novice skier, starting from rest, slides down a frictionless 29.0∘ incline whose vertical height is 185 mm. How fast is she going when she reaches the bottom?
Answer:
Her speed when she reaches the bottom of the incline is 1.90 m/s.
Explanation:
Hi there!
To solve this problem, let´s use the energy conservation theorem:
Initially, the skier is at rest at a height of 0.185 m. Since she is at rest, her kinetic energy will be zero and her gravitational potential energy (PE) will be:
PE = m · g · h
Where
m = mass of the skier.
g = acceleration due to gravity.
h = height.
When she reaches the bottom, the height is zero and then the potential energy will be zero. Since there is no friction, the initial potential energy had to be converted into kinetic energy because the total energy of the skier remains constant, i.e., it is conserved.
Then, the final kinetic energy (KE) of the skier has to be equal to the initial potential energy:
PE = KE
The equation of kinetic energy is the following:
KE = 1/2 · m · v²
Then:
KE = PE
1/2 · m · v² = m · g · h
1/2 · m · v² = m · 9.8 m/s² · 0.185 m
v² = 2 · 9.8 m/s² · 0.185 m
v = 1.90 m/s
Her speed when she reaches the bottom of the incline is 1.90 m/s.
An adult generates 72 W of power as she pulls a sled forward across a flat snowy surface with a force of 80 N. The adult pulls with this force for 4.5 minutes. What distance does the sled move?
130 m
280 m
240 m
180 m
Answer:
240 m
Explanation:
Gradpoint
Final answer:
To calculate the distance the sled moves, use the formula Work = Force x Distance and substitute the given values to find the answer as 240 meters.
Explanation:
Power is a physical quantity that represents the rate at which work is done or energy is transferred or converted. Mathematically, power is defined as the amount of energy transferred or converted per unit time. It is typically measured in watts (W), where 1 watt is equivalent to 1 joule per second. In other words, power indicates how quickly work is done or energy is transferred.
To find the distance the sled moves, we can use the formula:
Work = Force x Distance
Given: Power = 72 W, Force = 80 N, Time = 4.5 minutes = 270 seconds
Work = Power x Time = 72 W x 270 s = 19440 J
Distance = Work / Force = 19440 J / 80 N = 243 m
Therefore, the sled moves a distance of 240 meters.
A sound system is being set up in a gazebo in a park. It needs to produce music so that everyone can hear it. How much power would the speakers need to produce in order for the intensity at 5 meters away to be 1 x 10^-8 W/m^2? (assume the shape of the propagation of the sound wave is a hemisphere)
1.87 x 10^-7 W
1.57 x 10^-6 W
1.14 x 10^-6 W
2.46 x 10^-7 W
Answer:
Power, P=1.57×[tex]10^{-6}[/tex] Watt
Explanation:
Given
Intensity, I=1×[tex]10^{-8}[/tex] W/m²
Distance, r=5 meter
Considering the hemispherical space with radius 5 meter centered on the speaker. Speaker emits sound wave continuously with Power P. Intensity I is constant throughout the space and defined as power per unit area.
I=[tex]\frac{P}{A}[/tex]
so, P=I×A
where A is the area of shape of propagation.
since ,shape of propagation is hemispherical
so, A=2×p×r²=2×3.14×5×5=157 m²
P=1×[tex]10^{-8}[/tex]×157
P=1.57×[tex]10^{-6}[/tex] Watt
A ski jumper has 1.2 x 10 4 J of potential energy at the top of the ski jump. The friction on the jump slope is small, but not negligible. What can you conclude about the ski jumpers kinetic energy at the bottom of the jump?
Answer
kinetic energy will be less than 1.2×10^4 J
Explanation:
as some of this potential energy will be used to over come force of friction , hence by law of conservation of energy , kinetic energy will be less than potential energy at top and will be less than 1.2×10^4 J
Final answer:
The ski jumper's kinetic energy at the bottom of the ski jump will be slightly less than the initial potential energy of 1.2 x 10⁴ J due to the small but non-negligible work done by friction, which converts some of the mechanical energy into other forms like heat and sound.
Explanation:
If a ski jumper has 1.2 x 10⁴ J of potential energy at the top of the ski jump and we take into account that friction is small but not negligible, we can conclude that the ski jumper's kinetic energy at the bottom will be slightly less than 1.2 x 10⁴ J. According to the conservation of energy principle, the sum of potential and kinetic energy in a system should be constant if there is no external work done. However, friction does perform negative work (it removes energy from the system), converting some mechanical energy into heat and sound, and therefore the actual kinetic energy at the bottom will be the initial potential energy minus the energy lost due to friction.
For example, in the given scenario where a ski jumper starts from rest, their initial kinetic energy is zero, and all the energy is in the form of potential energy. As they descend, potential energy is converted into kinetic energy. When friction is present, it will do negative work on the system, represented by a slight decrease in the total mechanical energy by the time the skier reaches the bottom. The kinetic energy of the ski jumper at the bottom would be the initial potential energy minus the work done by friction during the descent.
In a theoretical scenario without friction, the skier's kinetic energy at the bottom would equal their initial potential energy minus zero (since no work is done by friction), resulting in the skier having kinetic energy equal to 1.2 x 10⁴ J at the bottom.
The basal metabolic rate is the rate at which energy is produced in the body when a person is at rest. A 71 kg ( 157 lb ) person of height 1.75 m (5.7 ft ) would have a body surface area of approximately 1.90 m².
What is the net amount of heat this person could radiate per second into a room at 19.0 °C (about 66.2 °F) if his skin's surface temperature is 30.0 °C? (At such temperatures, nearly all the heat is infrared radiation, for which the body's emissivity is 1.0, regardless of the amount of pigment.)
Answer:
125.04181 W
Explanation:
[tex]\sigma[/tex] = Stefan-Boltzmann constant = [tex]5.67\times 10^{-8}\ W/m^2K^4[/tex]
A = Surface area = 1.9 m²
[tex]T_b[/tex] = Skin surface temperature = 19°C
[tex]T_s[/tex] = Room temperature = 30°C
[tex]\epsilon[/tex] = Emissivity = 1
Radiated thermal energy is given by
[tex]P=\epsilon A\sigma (T_b^4-T_s^4)\\\Rightarrow P=1\times 1.9\times 5.67\times 10^{-8}((273.15+30)^4-(273.15+19)^4)\\\Rightarrow P=125.04181\ W[/tex]
The net amount of heat this person could radiate per second into the room is 125.04181 W