In the late 1960s, John and Leonid raced from the Earth to the Moon at relativistic speeds. According to the judges on the Moon, John finished the race first with a time of 8.670 s, while Leonid finished 1.330 s later. The distance from the Earth to the Moon according to the judges is 1.300 ls. (a) What are vJ and vL, the average speeds of John and Leonid, according to the judges on the Moon. Give your answer as a fraction of c. (b) According to Leonid, by how much did John beat him at the race? (c) Is there any reference frame in which Leonid might actually have won the race? Explain.
In: Physics
The terminal voltage across a single phase of a stepper motor used as a generator is applied across a load resistor of 33 ohms. This terminal voltage has an amplitude of 18.7V and a frequency of 242 Hz. From a previous measurement, we know that this stepper motor phase has an internal resistance of 11.2 ohms. What is the time-averaged power delivered to the load? What is the electrical efficiency of this circuit? Write down an expression for the instantaneous (i.e. as a function of time) current flowing through the load.
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A line of charge is placed on the x-axis between x = -5 m and x = 5 m . The linear charge density is -10 microcoulomb per cm . Consider a field point on the y-axis, located at y - 2.0 m.
a. (2 points) How much charge dq is contained in a segment of the wire of length dx?
b. (5 points) Charge element dq is located at the point (x, 0). What is the distance r from the charge element to the field point? (Hint: Your answer should be a function of x.)
c. (5 points) What is the unit vector r hat associated with the electric field for this charge element dq? (Hint: Your answer should be a function of x and the unit vectors i hat and j hat)
d. (5 points) If there is symmetry to the problem, what is the only component of r hat needed (is not zero after integration)? If there is no symmetry that can be exploited, say “no symmetry”.
e. (20 points) What is the electric field vector at the field point? (Use the Cartesian unit vectors in your answer for E; do not simply say “up”, “left”, etc.)
f. (10 points) Suppose you placed a +10 microcoulomb charge at the field point. Would it be attracted toward the x-axis, pushed away from the x-axis, or neither? What is the magnitude of the force acting upon it?
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(a) An unstable particle with a mass equal to 3.34 ✕ 10−27 kg is initially at rest. The particle decays into two fragments that fly off with velocities of 0.977c and −0.851c, respectively. Find the masses of the fragments. (Hint: Conserve both mass–energy and momentum.)
| m(0.977c) = | kg |
| m(-0.851c) = | kg |
(b) An unstable particle at rest breaks up into two fragments of
unequal mass. The mass of the lighter fragment is equal to
4.00 ✕ 10−28 kg and that of the heavier fragment is 1.63
✕ 10−27 kg. If the lighter fragment has a speed of
0.893c after the breakup, what is the speed of the heavier
fragment?
c
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Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities σ1,σ2,σ3and σ4 on their surfaces, as shown in the following figure(Figure 1). These surface charge densities have the values σ1 = -5.50 μC/m2 , σ2=5.00μC/m2, σ3= 1.60 μC/m2 , and σ4=4.00μC/m2. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets.
What is the magnitude of the electric field at point A, 5.00 cm from the left face of the left-hand sheet?
Express your answer to three significant figures and include the appropriate units.
What is the direction of the electric field at point A, 5.00 cm from the left face of the left-hand sheet?
What is the direction of the electric field at point , 5.00 from the left face of the left-hand sheet?
| to the left. |
| to the right. |
| upwards. |
| downwards. |
What is the magnitude of the electric field at point B, 1.25 cm from the inner surface of the right-hand sheet?
Express your answer to three significant figures and include the appropriate units.
What is the direction of the electric field atpoint B, 1.25 cm from the inner surface of the right-hand sheet?
What is the direction of the electric field atpoint B , 1.25 from the inner surface of the right-hand sheet?
| to the left. |
| to the right. |
| upwards. |
| downwards. |
What is the magnitude of the electric field at point C, in the middle of the right-hand sheet?
Express your answer to three significant figures and include the appropriate units.
What is the direction of the electric field at point C, in the middle of the right-hand sheet?
| to the left. |
| to the right. |
| upwards. |
| downwards. |
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A Gaussian surface in the shape of a right circular cylinder with end caps has a radius of 15.0 cm and a length of 89.7 cm. Through one end there is an inward magnetic flux of 20.2 ?Wb. At the other end there is a uniform magnetic field of 2.00 mT, normal to the surface and directed outward. What is the magnitude of the net magnetic flux through the curved surface?
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A mass weighing 12lb stretches a spring 10in. The mass is attached to a viscous damper with damping constant 3lb⋅s/ft. The mass is pushed upward, contracting the spring a distance of 2in, and then set into motion with a downward velocity of 4in/s. Determine the position u of the mass at any time t. Use 32ft/s2 as the acceleration due to gravity. Pay close attention to the units. u(t)=
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1. The constant force (3 î - 8 ĵ - 11 ƙ ) N is applied over a displacement (6j - 7ƙ) m. What is the work done by this force during this process? Answer in joules.
2. Whenever net work is done on an object, what will always be true?
| the height of the object will change |
| the energy of the object will change |
| the gravitational potential energy of the object will change |
| the speed of the object will change |
| heat is produced |
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The figure shows a 11.8 V battery and four uncharged capacitors of capacitances C1 = 1.16 μF,C2 = 2.31 μF,C3 = 3.26 μF, and C4 = 4.19 μF. If only switch S1 is closed, what is the charge on (a) capacitor 1, (b) capacitor 2, (c) capacitor 3, and (d) capacitor 4? If both switches are closed, what is the charge on (e) capacitor 1, (f) capacitor 2, (g) capacitor 3, and (h) capacitor 4?
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what factors do you think may cause the experimental value to be different from the accepted value
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A 49.6 g marble moving at 3.99 m/s strikes a 13.6 g marble at rest.
A) What is the speed of the initially moving marble immediately
after the collision?
2.2728 m/s
B)What is the speed of the initially not moving marble immediately after the collision?
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The control panel on a spaceship contains a light that blinks every 1.81 s as observed by an astronaut in the ship. If the spaceship is moving past Earth with a speed of 0.793c, determine the proper time interval between blinks and the time interval between blinks as observed by a person on Earth.
(a)
the proper time interval (in s) between blinks
s
(b) the time interval (in s) between blinks as observed by a person on Earth
s
(c) An electron has a momentum with magnitude six times the
magnitude of its classical momentum. Find the speed of the
electron.
c
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How would gravitational mass and inertial mass change in an elevator (if at all)? Why is this true?
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