Answer:
A) first laser
B) 0.08m
C) 0.64m
Explanation:
To find the position of the maximum you use the following formula:
[tex]y=\frac{m\lambda D}{d}[/tex]
m: order of the maximum
λ: wavelength
D: distance to the screen = 4.80m
d: distance between slits
A) for the first laser you use:
[tex]y_1=\frac{(1)(d/20)(4.80m)}{d}=0.24m\\[/tex]
for the second laser:
[tex]y_2=\frac{(1)(d/15)(4.80m)}{d}=0.32m[/tex]
hence, the first maximum of the first laser is closer to the central maximum.
B) The difference between the first maximum:
[tex]\Delta y=y_2-y_1=0.32m-0.24m=0.08m=8cm[/tex]
hence, the distance between the first maximum is 0.08m
C) you calculate the second maximum of laser 1:
[tex]y_{m=2}=\frac{(2)(d/20)(4.80m)}{d}=0.48m[/tex]
and for the third minimum of laser 2:
[tex]y_{minimum}=\frac{(m+\frac{1}{2})(\lambda)(D)}{d}\\\\y_{m=3}=\frac{(3+\frac{1}{2})(d/15)(4.80m)}{d}=1.12m[/tex]
Finally, you take the difference:
[tex]1.12m-0.48m=0.64m[/tex]
hence, the distance is 0.64m
To understand how to use the principle of superposition in conjunction with the Biot-Savart (or Ampere's) law. From the Biot-Savart law, it can be calculated that the magnitude of the magnetic field due to a long straight wire is given by Bwire=μ0I2πd , where μ0 (=4π×10−7T⋅m/A) is the permeability constant, I is the current in the wire, and d is the distance from the wire to the location at which the magnitude of the magnetic field is being calculated. The same result can be obtained from Ampere's law as well.
The principle of superposition can be used in conjunction with the Biot-Savart (or Ampere's) law to calculate the magnetic field due to a combination of current-carrying wires. Ampere's law is a more general law that relates the magnetic field to the total current passing through a closed loop.
Explanation:The principle of superposition can be used in conjunction with the Biot-Savart (or Ampere's) law to calculate the magnetic field due to a combination of current-carrying wires. The Biot-Savart law allows us to calculate the magnetic field at any point due to an element of current in a wire. By integrating this law over the entire length of the wires and applying the principle of superposition, we can determine the total magnetic field produced by multiple wires.
For example, if we have two parallel wires carrying currents I1 and I2, the total magnetic field at a point due to both wires can be found by summing the individual magnetic fields produced by each wire using the Biot-Savart law.
It is important to note that Ampere's law can also be used to determine the magnetic field produced by current-carrying wires. It is a more general law that relates the magnetic field to the total current passing through a closed loop. The results obtained from Ampere's law are consistent with the Biot-Savart law.
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A pursuit spacecraft from the planet Tatooine is attempting to catch up with a Trade Federation cruiser. As measured by an observer on Tatooine, the cruiser is traveling away from the planet with a speed of 0.600c. The pursuit ship is traveling at a speed of 0.800c relative to Tatooine, in the same direction as the cruiser. (a) For the pursuit ship to catch the cruiser, should the velocity of the cruiser relative to the pursuit ship be directed toward or away from the pursuit ship? (b) What is the speed of the cruiser relative to the pursuit ship?
Answer:
a) toward the pursuit
b) 0.384c
Explanation:
a) The velocity of the cruiser relative to the pursuit should be toward the pursuit.
b) To find the speed of the cruiser relative to the pursuit ship you use the following formula:
[tex]u'=\frac{u-v}{1-\frac{uv}{c^2}}[/tex]
v: velocity of the cruiser as seen by Tatooine
u: velocity of the pursuit ship as seen by Tatooine
c: speed of light
By replacing the values of the parameters you obtain:
[tex]u'=\frac{0.800c-0.600c}{1-\frac{(0.800)(0.600)c^2}{c^2}}=0.384c[/tex]
When accounting for relativistic velocity addition, the velocity of the cruiser relative to the pursuit ship should be directed towards the pursuit ship for it to be 'caught up' with. The cruiser's relative speed is about -0.429c from the perspective of the pursuit ship.
Explanation:From the perspective of the observer on Tatooine, the cruiser is moving away from the planet at a speed of 0.600c and the pursuit ship is moving in the same direction at a speed of 0.800c. To figure out these velocities in a relative sense, we must use the theory of relativity, specifically the concept of relativistic velocity addition. In classical physics, velocities simply add or subtract, but this isn't the case when dealing with speeds close to the speed of light.
(a) For the pursuit ship to catch up with the cruiser, the velocity of the cruiser relative to the pursuit ship should be directed towards the pursuit ship.
(b) When solving for the relative speed of the cruiser from the perspective of the pursuit ship, we use the formula for relativistic velocity addition: V'=(v-u)/(1-(uv/c^2)). In this case, v is the speed of the cruiser (0.600c), u is the speed of the pursuit spacecraft (0.800c), and c is the speed of light. Plugging in the values, you will find that the speed of the cruiser relative to the pursuit ship is approximately -0.429c (where the minus sign indicates the cruiser is moving towards the pursuit ship relative to the pursuit ship's frame of reference).
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A current of 4.0 A is maintained in a single circular loop having a circumference of 80 cm. An external magnetic field of 2.0 T is directed so that the angle between the field and the plane of the loop is 20°. Determine the magnitude of the torque exerted on the loop by the magnetic forces acting upon it. Group of answer choices 0.27 N ⋅ m 0.41 N ⋅ m 0.38 N ⋅ m 0.77 N ⋅ m 0.14 N ⋅ m
The torque on a single circular loop in an external magnetic field can be calculated using the formula T = NIAB sin 0. We need to find the area of the loop using the given circumference and then substitute the values of the current, magnetic field strength, area, and angle into the formula to find the torque.
Explanation:To calculate the magnitude of the torque exerted on the circular loop by the magnetic forces, we need to use the formula for torque on a current-carrying loop in a uniform magnetic field, which is T = NIAB sin 0, where N represents the number of turns in the loop, I represents the current, A represents the area of the loop, B represents the magnetic field strength, and 0 represents the angle between the field and the plane of the loop.
In this case, since there is only a single loop, N is equal to 1. The current I is given as 4.0 A. The magnetic field strength B is given as 2.0 T. The angle 0 is 20°. The area of the loop A can be calculated from the circumference given as 80 cm or 0.8 m. Recall that the circumference of a circle is given by the formula 2πr. If the circumference C is given by 80 cm or 0.8 m, the radius r can be found by dividing the circumference by 2π. Once you've found the radius r, the area of the circle is πr².
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The correct answer is "0.14 N.m". The final torque value is 0.14 N·m on the loop.
To determine the torque exerted on the loop, we use the formula:
Torque (τ) = nIBA sin(θ)
First, find the area (A) of the loop. The circumference (C) of the loop is given by 80 cm, which is 0.80 m. From the circumference, we can find the radius (r):
C = 2πr -> r = C / 2π = 0.80 m / 2π ≈ 0.127 m
Now, calculate the area (A) of the loop:
A = πr² = π(0.127 m)² ≈ 0.0507 m²
Next, calculate the torque:
τ = nIBA sin(θ) = 1 × 4.0 A × 2.0 T × 0.0507 m² × sin(20°)
Using the value of sin(20°) ≈ 0.342:
τ ≈ 1 × 4.0 A × 2.0 T × 0.0507 m² × 0.342 ≈ 0.14 N · m
Therefore, the magnitude of the torque exerted on the loop is 0.14 N·m.
A mother is helping her children, of unequal weight, to balance on a seesaw so that they will be able to make it tilt back and forth without the heavier child simply sinking to the ground. Given that her heavier child of weight WWW is sitting a distance LLL to the left of the pivot, at what distance L1L1L_1 must she place her second child of weight www on the right side of the pivot to balance the seesaw? Express your answer in terms of LLL, WWW, and www.
Answer:
L1L1L_1 = ( LLL × WWW)/ www.
Explanation:
From the question we are given that the children's weight are not equal, thus, there will be a need to balance the seesaw "so that they will be able to make it tilt back and forth without the heavier child simply sinking to the ground''.
Also, From the question, we are gven that the weight of the heavier child = WWW, the heavier child's is sitting a distance = LLL, the weight of the second child= www.
Therefore, in order to balance the seesaw, she will need to place her second child of weight www on the right side of the pivot to balance the seesaw at a distance of;
L1L1L_1 = ( LLL × WWW)/ www.
If the temperature of this balloon were to decrease suddenly, how would the balloon change?
A. Its mass would increase.
B. Its mass would decrease.
C. Its volume would increase.
D. Its volume would decrease.
Final answer:
The volume of a balloon decreases when its temperature is suddenly lowered, in accordance with Charles's Law, because the gas particles inside the balloon move less vigorously due to a decrease in their average kinetic energy.
Explanation:
When the temperature of a balloon decreases suddenly, according to Charles's Law, the volume of the gas inside the balloon also decreases, assuming that all other conditions, such as pressure and the amount of gas, remain constant. This occurs because a decrease in temperature leads to a decrease in the average kinetic energy of the gas particles, meaning they move less vigorously and occupy less space. Therefore, the correct answer to the question would be D. Its volume would decrease.
A hydrogen atom can be in the 1S state, whose energy we'll call 0, the 2S state, or any of 3 2P states. The 2S and 2P states have energies of 10.2 eV. There are other states with higher energy but we'll ignore them for simplicity. The 2P states have distinctive optical properties, so we're interested in how many are present even when it's a small fraction of the total. 1) What fraction of the H is in 2P states at T=5900 K, a typical Sun surface temperature?
Final answer:
The fraction of hydrogen atoms in the 2P states at T=5900 K is calculated using the Boltzmann distribution. The energy of the 2S and 2P states is 10.2 eV, and their degeneracies are factored into the Boltzmann factor to determine the relative populations of these states.
Explanation:
The fraction of hydrogen atoms in the 2P states at a temperature of 5900 K can be calculated using the Boltzmann distribution. According to quantum mechanics, the energy levels of a hydrogen atom involve principal quantum numbers, with the ground state being 1s and higher energy excited states being designated by higher quantum numbers and corresponding letters (s, p, d, f, etc.) for their angular momentum quantum numbers. Since we are given that the energy of 2S and 2P states are the same at 10.2 eV and the ground state (1S) has an energy we'll call 0, we can use the Boltzmann factor to find the relative populations of these states.
To calculate the fraction of hydrogen atoms in the 2P state, use the following Boltzmann factor equation: fraction = (g2P / gTotal) * exp(-E2/kT), where g2P is the degeneracy of the 2P state, gTotal is the total degeneracy of all states considered, E2 is the energy of the 2P state, k is the Boltzmann constant, and T is the temperature. The degeneracy of the 2P state is 3 (since there are three 2P states) and the only other state considered here is the 2S state, which has degeneracy 1, making gTotal = 4. Plugging in the energy of 10.2 eV for E2 and converting it to joules (multiply by 1.602 x 10-19 J/eV), using k = 1.38 x 10-23 J/K, and T = 5900 K, we can calculate the fraction of hydrogen in the 2P state.
In deserts the temperatures can reach extreme values in deep of summer and winter. A steel bridge is being constructed and it is supposed to be 1234.567 m long at 233.15 K in the coldest possible winter. What will be the possible length of this bridge when the temperature rises to a possible extreme of +140.0°F in hottest part of summer? The average coefficient of linear expansion of the steel is 11.0123 × 10-6 K-1.
Answer:
The length of the bridge during the hottest part of summer is [tex]L_s = 1235.925 m[/tex]
Explanation:
From the question we are told that
The length of the steel bridge is [tex]L = 1234.567m[/tex]
The temperature for this length is [tex]T_1 = 233.15K[/tex]
The temperature at summer [tex]T_2 = + 140.0F = \frac{140 - 32}{180} *100 + 273= 333 K[/tex]
The coefficient of linear expansion is [tex]\alpha = 11.0123*10^{-6} K^{-1}[/tex]
Generally the change in length of the steel bridge is mathematically represented as
[tex]\Delta L = \alpha L \Delta T[/tex]
Substituting value
[tex]\Delta L = 11.0123*10^{-6} * 1234.567 (333-233.15)[/tex]
[tex]\Delta L = 1.3575 \ m[/tex]
The length of the bridge in summer is mathematically evaluated as
[tex]L_s = L + \Delta L[/tex]
Substituting values
[tex]L_s = 1234.567 + 1.3575[/tex]
[tex]L_s = 1235.925 m[/tex]
A horizontal rope is tied to a 57.0 kg kg box on frictionless ice. What is the tension in the rope if: You may want to review (Pages 135 - 137) . Part A The box is at rest? Express your answer as an integer and include the appropriate units. T T = nothing nothing SubmitRequest Answer Part B The box moves at a steady v x vxv_x = 4.20 m/s m/s ? Express your answer as an integer and include the appropriate units. T T = nothing nothing SubmitRequest Answer Part C The box v x vxv_x = 4.20 m/s m/s and a x axa_x = 5.80 m/ s 2 m/s2 ?
Answer:
Explanation:
A ) The surface is frictionless . If the box is at rest , there will be no tension in the rope.
B ) In this case , the box is moving with steady rate of 4.20 m /s . In this case also no force is acting on the box so tension in the rope will be nil.
C ) In this case the box is moving with acceleration of 5.8 m /s² so force on the box = mass x acceleration
= 57 x 5.8
= 330.6 N .
So tension in the rope will be equal to force acting on the rope . Hence tension = 330.6 N .
Final answer:
The tension in the rope tied to a 57.0 kg box on frictionless ice is 0 N when the box is at rest, 0 N when moving at a steady velocity of 4.20 m/s, and 331 N when the box is accelerating at 5.80 m/s².
Explanation:
When considering the tension in the rope connected to the 57.0 kg box on frictionless ice, different scenarios will result in different tensions:
Part A: Box at Rest
In the first scenario where the box is at rest, the tension in the rope will be zero Newtons (0 N). This is because, on frictionless ice, there is no other force opposing the box's motion that the rope would need to counteract.
Part B: Box Moving at Steady Velocity
For the second part, where the box is moving at a constant velocity (4.20 m/s), the tension is still zero Newtons. Even if the box is in motion, the lack of frictional forces on the ice means no net force is required to maintain the box's constant velocity.
Part C: Box Accelerating
In the third case, where the box is moving at 4.20 m/s and also accelerating at 5.80 m/s², we need to apply Newton's second law, F = ma. The tension (T) in the rope is calculated as the product of the mass (m) of the box and its acceleration (a). Thus:
T = m × a = 57.0 kg × 5.80 m/s² = 330.6 N
Therefore, the tension in the rope would be 331 N (rounded to the nearest integer).
A 50 mm diameter steel shaft and a 100 mm long steel cylindrical bushing with an outer diameter of 70 mm have been incorrectly shrink fit together and have to be separated. What axial force, Pa, is needed for this if the diametral interference is 0.005 mm and the coefficient of friction is 0.2? E (steel) = 207 x 103 MPa (N/mm2)
Answer:
The axial force is [tex]P = 15.93 k N[/tex]
Explanation:
From the question we are told that
The diameter of the shaft steel is [tex]d = 50mm[/tex]
The length of the cylindrical bushing [tex]L =100mm[/tex]
The outer diameter of the cylindrical bushing is [tex]D = 70 \ mm[/tex]
The diametral interference is [tex]\delta _d = 0.005 mm[/tex]
The coefficient of friction is [tex]\mu = 0.2[/tex]
The Young modulus of steel is [tex]207 *10^{3} MPa (N/mm^2)[/tex]
The diametral interference is mathematically represented as
[tex]\delta_d = \frac{2 *d * P_B * D^2}{E (D^2 -d^2)}[/tex]
Where [tex]P_B[/tex] is the pressure (stress) on the two object held together
So making [tex]P_B[/tex] the subject
[tex]P_B = \frac{\delta _d E (D^2 - d^2)}{2 * d* D^2}[/tex]
Substituting values
[tex]P_B = \frac{(0.005) (207 *10^{3} ) * (70^2 - 50^2))}{2 * (50) (70) ^2 }[/tex]
[tex]P_B = 5.069 MPa[/tex]
Now he axial force required is
[tex]P = \mu * P_B * A[/tex]
Where A is the area which is mathematically evaluated as
[tex]\pi d l[/tex]
So [tex]P = \mu P_B \pi d l[/tex]
Substituting values
[tex]P = 0.2 * 5.069 * 3.142 * 50 * 100[/tex]
[tex]P = 15.93 k N[/tex]
Compared to the current in the 10.-ohm resistance in the circuit shown at the right, the current in the 5.0-ohm resistance is
a. one-half as great
b. one-fourth as great
c. the same
d. twice as great
Answer:
The answer is d. Twice as great.
Explanation:
The German physicist and mathematician Georg Simon Ohm says in his basic law of electrical circuits or Ohm's law that the potential difference V that is applied at the ends of a conductor is proportional to the intensity I of the current that circulates and that the electrical resistance R is the ratio factor between I and V.
The equation would be I = V / R
If by any chance R is reduced because it is inversely proportional, the current would increase.
So if the current goes from 10 to half 5, its current would double.
Calculate the induced electric field (in V/m) in a 52-turn coil with a diameter of 12 cm that is placed in a spatially uniform magnetic field of magnitude 0.30 T so that the face of the coil and the magnetic field are perpendicular. This magnetic field is reduced to zero in 0.10 seconds. Assume that the magnetic field is cylindrically symmetric with respect to the central axis of the coil. (Enter the magnitude.)
Given Information:
Number of turns = N = 52
Diameter of coil = d = 12 cm = 0.12 m
Time = t = 0.10 seconds
Magnetic field = B = 0.30 T
Required Information:
Induced electric field = E = ?
Answer:
Induced electric field = E = 4.68 V/m
Explanation:
The Maxwell's third equation can be used to find out the induced electric field,
∫E.dl = -dΦ/dt
Where E is the induced electric field, dl is the circumference of the loop and dΦ/dt is the rate of change of magnetic flux and is given by
Φ = NABcos(θ)
Where N is the number of turns, A is the area of coil and B is the magnetic field and cos(θ) = 1
Φ = NAB
∫E.dl = -dΦ/dt
E(2πr) = -d(NAB)/dt
E =1/(2πr)*-d(NAB)/dt
E =NA/(2πr)*-dB/dt
Area is given by
A = πr²
E =Nπr²/(2πr)*-dB/dt
E =Nr/2*-dB/dt
The magnetic field reduce from 0.30 to zero in 0.10 seconds
E =Nr/2*-(0.30 - 0)/(0 - 0.10)
E =Nr/2*-(0.30)/(-0.10)
E = Nr/2*-(-3)
The radius r is given by
r = d/2 = 0.12/2 = 0.06 m
E = (52*0.06)/2*(3)
E = 1.56*3
E = 1.56*3
E = 4.68 V/m
Therefore, the induced electric field in the coil is 4.68 V/m
A rod of 2.0-m length and a square (2.0 mm X 2.0 mm) cross section is made of a material with a resistivity of 6.0 E–8 Ohm meter. If a potential difference of 0.50 V is placed across the ends of the rod, at what rate is heat generated in the rod? *
Answer:
8.33*10^-16 Watt
Explanation:
Given that
Length of the rod, l = 2 m,
Area of the rod, A = 2 x 2 mm² = 4*10^-6 m²
resistivity of the rod, p = 6*10^-8 ohm metre,
Potential difference of the rod, V = 0.5 V
Let R be the resistance of the rod, then
R = p * l / A
R = (6*10^-8 * 2) / (4*10^-6)
R = 3*10^14 ohm
Heat generated per second = V² / R Heat = (0.5)² / (3*10^14)
Heat = 0.25 / 3*10^14
Heat = 8.33*10^-16 Watt
Therefore, the rate at which heat is generated is 8.33*10^-16 Watt
Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 600 cm3, the pressure is 150 kPa, and the pressure is increasing at a rate of 40 kPa/min. At what rate is the volume decreasing at this instant?
Answer:
The volume is decreasing at 160 cm³/min
Explanation:
Given;
Boyle's law, PV = C
where;
P is pressure of the gas
V is volume of the gas
C is constant
Differentiate this equation using product rule:
[tex]V\frac{dp}{dt} +P\frac{dv}{dt} = \frac{d(C)}{dt}[/tex]
Given;
[tex]\frac{dP}{dt}[/tex] (increasing pressure rate of the gas) = 40 kPa/min
V (volume of the gas) = 600 cm³
P (pressure of the gas) = 150 kPa
Substitute in these values in the differential equation above and calculate the rate at which the volume is decreasing ( [tex]\frac{dv}{dt}[/tex]);
(600 x 40) + (150 x [tex]\frac{dv}{dt}[/tex]) = 0
[tex]\frac{dv}{dt} = -\frac{(600*40)}{150} = -160 \ cm^3/min[/tex]
Therefore, the volume is decreasing at 160 cm³/min
Final answer:
Boyle's law states that the volume of a gas is inversely proportional to its pressure when temperature and the amount of gas are constant. Mathematically, this can be expressed as PV = C. To find the rate at which the volume is decreasing at a given instant, we differentiate the equation PV = C with respect to time and substitute the given values.
Explanation:
Boyle's law states that the volume of a gas is inversely proportional to its pressure when temperature and the amount of gas are constant. Mathematically, this can be expressed as PV = C, where P is the pressure, V is the volume, and C is a constant. In this scenario, the pressure is increasing at a rate of 40 kPa/min. To find the rate at which the volume is decreasing at this instant, we differentiate the equation PV = C with respect to time. Applying the chain rule, we get:
d(PV)/dt = d(C)/dt
P(dV/dt) + V(dP/dt) = 0
dV/dt = - (V/P)(dP/dt)
We substitute the given values where the volume V = 600 cm3 and pressure P = 150 kPa:
dV/dt = - (600 cm3 / 150 kPa) (40 kPa/min)
dV/dt = -160 cm3/min
Therefore, the volume is decreasing at a rate of 160 cm3/min at this instant.
What measurement stays the same at any point in a parallel circuit?
A. current
B. voltage
C. resistivity
D. power
Answer:Voltage
Explanation:
Voltage stays the same at any point in a parallel circuit
In aircraft design, the pressure coefficient Cp is usually measured during wind tunnel testing of an aircraft component to predict structural loads, as well as lift and drag forces. Let Cp=(p−p[infinity])/ (0.5*rhoU[infinity]^2)where U[infinity] is the airspeed of the test at pressure p[infinity] and using a fluid of density rho. The pressure difference p ‐ p[infinity] is measured directly where p is the pressure located at a point on the surface of the test component. Estimate the uncertainty in Cp under the following conditions: Δp = p − p[infinity] = 1,000 N/m2, uΔp = 15 N/m2; rho = 1.20 kg/m3, urho = 0.01 kg/m3; U[infinity] = 50.0 m/s, u_U[infinity] = 0.21 m/s. Assume 95% confidence in stated values.
Answer:
Check the explanation
Explanation:
From given data, it can be noted that 95% of given confidently data, means 5% of data is uncertain. According to the question, we have to calculate uncertainty in Cp .
Kindly check the attached image below for the step by step explanation to the question above.
What can you infer about the prefix "thermo-" from the
word "thermoregulation?"
A
It refers to the brain
reser to the brain
It refers to temperature
It refers to feedback
It refers to nerves and hormones
Answer:
it refers to temperature I did test with the same question and got it correct.
Explanation:
The three small spheres are welded to the light rigid frame which is rotating in a horizontal plane about a vertical axis through O with an angular velocity w= 20 rad/s. If a couple MO= 30 N.m is applied to the frame for 5 seconds, compute the new angular velocity.
The new angular velocity is computed using the kinematic expression w² = wo² + 2a0, where 'wo' is the original angular velocity 'a' is the angular acceleration and 'w' is the new angular velocity. The calculation is guided by principles of physics primarily involving angular momentum and acceleration.
Explanation:The calculation for the new angular velocity can be gleaned from the kinematic expression w² = wo² + 2a0. The formula described represents the angular motion of the frame. The angular velocity originally is 20 rad/s and a couple MO of 30 N.m is applied to the frame for 5 seconds. The development of this concept involves principals of angular momentum as well as angular acceleration.
The angular acceleration can be calculated using the relation a = nett
Bearing in mind the initial angular velocity, the applied couple MO, and the duration of its application, the new angular velocity can be computed using the given formula. Note that the laws of physics, specifically the law of conservation of angular momentum, play an essential part in this calculation.
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g A simple pendulum (consisting of a point mass suspended by a massless string) on the surface of the earth has a period of 1.00 s. On a distant planet, a pendulum of identical length but twice the mass is found to have the same period. What is true about the acceleration due to gravity on the distant planet? [Assume both pendulums operate free of any friction or air resistance force]
Answer:
Explanation:
The formula for time period of a pendulum is given as follows :
T = 2π[tex]\sqrt{\frac{l}{g} }[/tex]
l is length of pendulum and g is acceleration due to gravity .
So time period of pendulum is not dependent on the mass of the pendulum . If time period is same and length is also the same then acceleration due to gravity will also be the same . Hence the acceleration due to gravity at distant planet will be same as that on the earth.
A plane circular loop of conducting wire of radius with possesses turn is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of 30° with respect to the normal direction to the loop. The magnetic field-strength Bis increased at a constant rate from to in a time interval of 10s. (a) What is the emf generated around the loop? (b) If the electrical resistance of the loop is , what current flows around the loop as the magnetic field is increased?
Complete question;
A plane circular loop of conducting wire of radius r-10 cm which possesses 15 turns is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of 30° with respect to the normal direction to the loop. The magnetic field-strength is increased at a constant rate from IT to 5T in a time interval of 10 s.
a) What is the emf generated around the loop?
b) If the electrical resistance of the loop is 15Ω, what current flows around the loop as the magnetic field is increased?
Answer:
A) E.M.F generated around loop = 0.163 V
B)Current in loop; I = 0.011 A
Explanation:
A) We are given;
Initial magnetic field strength;B1 = 1T
Final magnetic field strength;B2 = 5T
Number of turns;N = 15 turns
Radius; r = 10cm = 0.1m
Angle;θ = 30°
Time interval; Δt = 10 s
Now, the formula for magnetic flux is: Φ = NABcosθ
Where;
N is number of turns
A is area = πr²
B is magnetic field strength
θ is angle
So, initial magnetic flux is;
Φ1 = NA(B1)cosθ
Plugging in the relevant values to obtain;
Φ1 = 15*(π*0.1²)(1)cos30
Φ1 = 0.4081 Wb
Similarly, final magnetic flux is;
Φ2 = NA(B2)cosθ
Plugging in the relevant values to obtain;
Φ2 = 15*(π*0.1²)(5)cos30
Φ2 = 2.0405 Wb
The time rate of change of the flux is;
dΦ_B/dt = (Φ2 - Φ1)/Δt
So, dΦ_B/dt = (2.0405 - 0.4081)/10
dΦ_B/dt = 0.163 Wb/s
Thus, the emf generated around the loop is; E = dΦ_B/dt = 0.163 V
B) from Ohm's law, the current which flows around the loop in response to the emf is given as;
I = E/R
We are given R =15Ω
Thus; I = 0.1632/15
I = 0.011 A
7. Which one of the following statements best describes the concept of the electric field? a) The electric field is a vector quantity that is the reaction force of electrons. b) The electric field at each point is the potential energy of a test charge divided by the amount of the test charge. c) The electric field is a distribution of vectors at points due to the presence of one or more charged objects. d) The electric field is a scalar quantity related to the total amount of charge on one or more charged objects. e) The electric field is a scalar field, which has a magnitude at each given point, similar to the temperature or pressure field.
Answer:(c)
Explanation:
The electric field is a distribution is a distribution of vectors at point due to the presence of one or more charged objects.
If two or more charged particles are present in a system then the net electric field at a point is the vector addition of all the charges.
For example if a negative and a positive charge is present then electric field of negative charge is towards the negative charge while it is away for positive charge.
option d and e are wrong as Electric field is a vector quantity
The expression known as Froude's number is given as Upper F equals StartFraction v squared Over gl EndFraction . This number was used in shipbuilding and also in research on dinosaurs. In this example, l is given as well as Froude's number. Find the velocity, v (in meters per second) of a rhinoceros. It is known that gequals9.8 meters per second squared. Rhinoceros: lequals 1.2; Froude number equals 2.6
Answer:[tex]v=5.529\ m/s[/tex]
Explanation:
Given
number is given as [tex]=\frac{v^2}{gl}[/tex]
and [tex]number=2.6[/tex]
[tex]l=1.2\ m[/tex]
g=acceleration due to gravity[tex](9.8\ m/s^2)[/tex]
calculating for [tex]v[/tex]
[tex]v^2=gl(2.6)[/tex]
[tex]v=\sqrt{2.6\times 9.8\times 1.2}[/tex]
[tex]v=\sqrt{30.576}[/tex]
[tex]v=5.529\ m/s[/tex]
The hydronium ion concentration in an aqueous solution is [H+] = 5.3 x10-4 M. What is the hydroxide ion concentration? Is this solution acidic or basic?
A.) [OH-] = 1.9 x10-11 M, acidic
B.) [OH-] = 4.7 x10-6 M, basic
C.) [OH-] = 1.1 x10-9 M, acidic
D.) [OH-] = 3.2 x10-8 M, acidic
Answer:a
Explanation:
Given
[tex][H^+]=5.3\times 10^{-4}\ M[/tex]
and [tex]pH+pOH=14[/tex]
Also [tex]pH=-\log [H^+][/tex]
therefore [tex]pH=-\log (5.3\times 10^{-3})[/tex]
[tex]pH=-(-4-\log (5.3))[/tex]
[tex]pH=3.275[/tex]
Thus [tex]pOH=14-3.275[/tex]
[tex]pOH=10.275[/tex]
and [tex]pOH=-\log [OH^{-}][/tex]
[tex][OH]^{-1}=10^{-10.25}[/tex]
[tex][OH]^{-1}=1.88\times 10^{-11}\ M[/tex]
As the pH is less than 7 therefore solution is acidic
An aluminum calorimeter with a mass of 100 g contains 250 g of water. The calorimeter and water are in thermal equilibrium at 10.0°C. Two metallic blocks are placed into the water. One is a 75.0-g piece of copper at 60.0°C. The other has a mass of 70.0 g and is originally at a temperature of 100°C. The entire system stabilizes at a final temperature of 20.0°C.
Determine the specific heat of the unknown sample.
Answer:
The specific heat of the unknown sample is 1822.14 J/kg.k
Explanation:
Given;
mass of aluminum calorimeter, [tex]M_c[/tex] = 100 g
mass of water, [tex]M_w[/tex] = 250 g
stabilizing temperature of water-calorimeter, ΔT = 10.0°C
mass of copper, [tex]M_c_u[/tex] = 75 g
initial temperature of copper, [tex]T_{cu}[/tex] = 60.0°C
mass of unknown sample, [tex]M_u[/tex] = 70.0 g
initial temperature of unknown sample, [tex]T_u[/tex] = 100°C.
The final temperature of the entire system, t = 20.0°C
Apply the principle of conservation of energy;
energy used to heat water and calorimeter is equal to energy released by copper and unknown sample.
[tex]Q = M_{cu}C_{cu} \delta T_{cu} + M__{u}C{_u} \delta T_u[/tex]
where;
Q is energy used to heat water and calorimeter
[tex]C_c_u[/tex] is the specific heat capacity of copper
[tex]C_u[/tex] is the specific heat capacity of unknown sample
Make [tex]C_u[/tex] subject of the formula;
[tex]C_u = \frac{Q-M_c_u C_c_u \delta T_c_u}{M_u \delta T_u} \\\\C_u = \frac{(C_wM_w +C_cM_c)\delta T-M_c_u C_c_u \delta T_c_u}{M_u \delta T _u} \\\\C_u = \frac{(4186*0.25 +900*0.1)10-0.075* 387 *40}{0.07* 80} \\\\C_u = \frac{11365 -1161}{5.6} \\\\C_u = 1822.14 \ J/kg.k[/tex]
Therefore, the specific heat of the unknown sample is 1822.14 J/kg.k
The specific heat of the unknown sample is;
c_u = 1823 J/Kg.k
We are given;
Mass of Aluminum calorimeter; m_c = 100 g = 0.1 kg
Mass of water; m_w = 250 g = 0.25 kg
Initial temperature of Calorimeter and water; T_c = T_w = 10°C = 283 K
Mass of Copper; m_cu = 75 g = 0.075 kg
Initial temperature of Copper; T_cu = 60°C = 333 K
Mass of unknown sample; m_u = 70 g = 0.07 kg
Initial temperature of unknown substance = 100°C = 373 K
Final temperature of system; T_f = 20°C = 293 K
Formula for quantity of heat is;
Q = mcΔt
where;
m is mass
c is specific heat capacity
Δt is change in temperature;
For the calorimeter and water , we have;
Q_cw = (m_w*c_w + m_c*c_c)Δt
Specific heat capacity of water is; c_w = 4186 J/Kg.K
Specific heat capacity of aluminium is 900 J/Kg.K
Thus;
Q_cw = ((0.25 * 4186) + (0.1 * 900))(293 - 283)
Q_cw = 11365 J
For the unknown sample and the piece of copper;
Q_cu,u = (m_cu*c_cu*Δt) + (m_u*c_u*Δt)
specific heat capacity of copper; c_cu = 385 J/Kg.K
Thus;
Q_cu,u = (0.075*385*(333 - 293)) + (0.07*c_u*(373 - 293))
Q_cu,u = 1155 + 5.6c_u
From conservation of energy principle;
Q_cw = Q_cu,u
Thus;
11365 = 1155 + 4.2c_u
c_u = (11365 - 1155)/5.6
c_u = 1823 J/Kg.k
Read more at; https://brainly.com/question/16588023
What is the unit for force?
Answer:
N / NEWTONS
Explanation:
Named after Isaac Newton, the man who discovered gravity
Answer:
newtons and the symbol is N
Explanation:
In a laundromat, during the spin-dry cycle of a washer, the rotating tub goes from rest to its maximum angular speed of 2.2 rev/s in 8.8 s. You lift the lid of the washer and notice that the tub accelerates and comes to a stop in 20.0 s. Assuming that the tub rotates with constant angular acceleration while it is starting and stopping, determine the total number of revolutions undergone by the tub during this entire time interval.
Answer:
[tex]n_{T} = 31.68\,rev[/tex]
Explanation:
The angular acceleration is:
[tex]\ddot n_{1} = \frac{2.2\,\frac{rev}{s} -0\,\frac{rev}{s} }{8.8\,s}[/tex]
[tex]\ddot n_{1} = 0.25\,\frac{rev}{s^{2}}[/tex]
And the angular deceleration is:
[tex]\ddot n_{2} = \frac{0\,\frac{rev}{s}-2.2\,\frac{rev}{s} }{20\,s}[/tex]
[tex]\ddot n_{2} = -0.11\,\frac{rev}{s^{2}}[/tex]
The total number of revolutions is:
[tex]n_{T} = n_{1} + n_{2}[/tex]
[tex]n_{T} = \frac{\left(2.2\,\frac{rev}{s} \right)^{2}-\left(0\,\frac{rev}{s} \right)^{2}}{2\cdot \left(0.25\,\frac{rev}{s^{2}} \right)} + \frac{\left(0\,\frac{rev}{s} \right)^{2}-\left(2.2\,\frac{rev}{s} \right)^{2}}{2\cdot \left(-0.11\,\frac{rev}{s^{2}} \right)}[/tex]
[tex]n_{T} = 31.68\,rev[/tex]
A spring hangs from the ceiling with an unstretched length of x0=0.45 m . A m1=7.9 kg block is hung from the spring, causing the spring to stretch to a length x1=0.74 m.Find the length x2of the spring when a m2=3.3 kg block is hung from the spring. For both cases, all vibrations of the spring are allowed to settle down before any measurements are made.
To find the new length of the spring when a different mass is hung from it, calculate the spring constant using the initial mass, and then use Hooke's Law to solve for the extension caused by the new mass. Add this extension to the original unstretched length of the spring to find the stretched length.
Explanation:The student's question involves finding the new length of a spring x2 when a block with mass m2 of 3.3 kg is hung from it. Given an initial unstretched length (x0) and a stretched length (x1) with block m1, we can solve for the spring constant k using Hooke's Law, which states F = k * x, where F is the force, k is the spring constant, and x is the extension from the natural length of the spring.
First, we calculate the extension caused by m1: extension_m1 = x1 - x0 = 0.74 m - 0.45 m = 0.29 m. The force exerted by m1 is F1 = m1 * g, where g is the acceleration due to gravity (9.81 m/s2). Calculating the force, we get F1 = 7.9 kg * 9.81 m/s2. Then, the spring constant k can be found using k = F1 / extension_m1.
With the value of k, we can find the extension caused by m2: extension_m2 = F2 / k, where F2 = m2 * g. Finally, the length x2 of the spring with m2 hung from it is x2 = x0 + extension_m2.
You are packing for a trip to another star. During the journey, you will be traveling at 0.99c. You are trying to decide whether you should buy smaller sizes of your clothing because you will be thinner on your trip due to length contraction. You also plan to save money by reserving a smaller cabin to sleep in because you will be shorter when you lie down. Should you (a) buy smaller sizes of clothing, (b) reserve a smaller cabin, (c) do neither of these things, or (d) do both of these things?
Answer:
Do neither of these things ( c )
Explanation:
For length contraction : Is calculated considering the observer moving at a speed that is relative the object at rest applying this formula
L = (l) [tex]\sqrt{1 -\frac{v^{2} }{c^{2} } }[/tex]
where l = Measured distance from object at rest, L = contracted measured in relation to the observer , v = speed of clock , c = speed of light
you will do neither of these things because before you can make such decisions who have to view the object in this case yourself from a different frame from where you are currently are, if not your length and width will not change hence you can't make such conclusions/decisions .
the force that is exerted when a shopping cart is pushed. the forces that causes a metal ball to move toward a magnet
Answer:
The force that is exerted when a shopping cart is pushed is a type of push force, supplied by the muscles of the cart pusher's body.
The forces that causes a metal ball to move toward a magnet is a type of pull force that is as a result of the magnetic field forces.
Explanation:
Forces are divided into push forces that tends to accelerate a body away from the source of the force, and pull forces that accelerates the body towards the force source.
Examples of push forces includes pushing a cart, pushing a table, repulsion of two similar poles of a magnet etc. Examples of pull forces includes a attractive force between two dissimilar poles of a magnet, pulling a load by a rope, a dog pulling on a leash etc.
Answer:
The force that is exerted when a shopping cart is pushed:
-Contact
The force that causes a metal ball to move toward a magnet:
-Noncontact
This force will cause the path of the particle to curve. Therefore, at a later time, the direction of the force wil At a given moment the particle is moving in the +x direction (and the magnetic field is always in the +z direction). If q is positive, what is the direction of the force on the particle due to the magnetic field?
Answer:
force is -y direction
Explanation:
The magnetic force is given by the equation
F = q v x B
where bold letters indicate vectors.
The direction of this force can be found by the right-hand rule, where the thumb points in the direction of speed, the other fingers extend in the direction of the magnetic field and the palm is in the direction of force for a positive charge
let's apply this to our case
the speed is in the direction + x the thumb
the magnetic field in the + z direction fingers extended
the palm is in the direction - y
force is -y direction
Final answer:
The force due to the magnetic field on a positively charged particle moving in the +x direction and perpendicular to the magnetic field will be in the +-y direction.
Explanation:
At a given moment the particle is moving in the +x direction (and the magnetic field is always in the +z direction). If q is positive, the direction of the force on the particle due to the magnetic field will be in the +-y direction.
A bungee jumper jumps from a tall bridge that is 60m above a flat, dry creek bed. She is carrying an audio generator that emits sound at frequency 1200 Hz. The unstretched length of the bungee cord is 26m, and the spring constant is selected so that she stops just before hitting the creek bed. At what point in her fall is the beat frequency, determined by listening to the audio generator and the reflection from the creek bed, a maximum
Answer:
Explanation:
The original frequency of sound f₀
The apparent frequency of sound fa
For apparent frequency the formula is
fa = [tex]f_0\times\frac{V+v}{V-v }[/tex] , v is velocity of jumper which increases as he goes down .
Beat frequency
= fa - f₀
= [tex]f_0\times(\frac{V+v}{V-v }-1)[/tex]
= [tex]f_0\times(\frac{2v}{V-v })[/tex]
since v is very small in comparison to V , velocity of sound , in the denominator , v can be neglected.
beat frequency = [tex]f_0\times(\frac{2v}{V })[/tex]
v , the velocity of jumper will go on increasing as long as net force on the jumper is positive or
mg > kx where x is extension in the cord and k is its force constant . Below this point kx or restoring force becomes more than weight of the jumper and then net force on the jumper directs upwards. At this point beat frequency becomes maximum.