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Chapter 3: Q11P (page 123)
Masses and attract each other with a gravitational force of magnitude F. Mass m is replaced with a mass , and it is moved four times farther away. Now, what is the magnitude of the force?
The magnitude of the force is
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Suppose that all the people of the Earth go to the North Pole and, on a signal, all jump straight up. Estimate the recoil speed of the Earth. The mass of the Earth is , and there are about 6 billion people ().
At t = 532.0s after midnight, a spacecraft of mass 1400 kg is located at position (3x105, 7x105,-4x105 ) m, and at that time an asteroid whose mass is 7 x 10 15 kg is located at position (9 x 10 ^ 5, - 3 x 10 ^ 5, - 12 x 10 ^ 5) m. There are no other objects nearby. (a) Calculate the (vector) force acting on the spacecraft. (b) At t=532.0: the spacecraft's momentum was
and at the later time t = 538.0s its momentum was
.Calculate the (vector) change of momentum
A roughly spherical asteroid has a mass ofand a radius of 270 km. (a) What is the value of the constant g at a location on the surface of the asteroid? (b) What would be the magnitude of the gravitational force exerted by the asteroid on a 70 kg astronaut standing on the asteroid鈥檚 surface? (c) How does this compare to the gravitational force on the same astronaut when standing on the surface of the Earth?
A 60 kg person stands on the Earth鈥檚 surface. (a) What is the approximate magnitude of the gravitational force on the person by the Earth? (b) What is the magnitude of the gravitational force on the Earth by the person?
Two balls of mass 
are connected by a low-mass spring (Figure 3.63). This device is thrown through the air with low speed, so air resistance is negligible. The motion is complicated: the balls whirl around each other, and at the same time the system vibrates, with continually changing stretch of the spring. At a particular instant, the
ball has a velocity 
and the
ball has a velocity
. a) At this instant, what is the total momentum of the device? b) What is the net gravitational (vector) force exerted by the earth on the device? c) At a time 
later, what is the total momentum of the device?
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