Download Physics 121 - Spring 2001

PHY 113, Summer 2007
Langenbrunner
HW 7 – due Thursday, 6/14/07
1. a) If the legendary apple of Newton could be released from rest at a height of 2 m from
the surface of a neutron star with a mass 1.5 times that of our sun and a radius of 20 km,
what would be its speed when it reached the surface of the star? (You may not assume the
force is constant over this range like we do while at the surface of the Earth.)
b) If the apple could rest on the surface of the star, what would be the approximate
difference between the gravitation acceleration at the top and at the bottom of the apple?
(Choose a reasonable size for an apple; the answer indicates that an apple would never
survive near a neutron star.)
2. Escape Speed
a) If you fire a projectile upward, usually it will slow, stop momentarily, and return to
Earth. There is, however, a certain minimum initial speed that will cause it to move
upward forever, theoretically coming to a rest only at infinity (this is of course assuming
no other forces other than the gravitational force from the Earth act on it…). This initial
speed is called the escape speed. Considering conservation of mechanical energy (ignore
energy lost to air friction), find this speed in terms of the mass and radius of the Earth.
b) Now, suppose you want this object to have a speed of 100 m/s when it reaches infinity,
instead of coming to rest at infinity. What should the initial speed be in this case?
3. In 1920, a prominent newspaper editorialized as follows about the pioneering rocket
experiments of Robert H. Goddard, dismissing the notion that a rocket could operate in a
vacuum: “That Professor Goddard, with his 'chair' in Clark College and the
countenancing of the Smithsonian Institution, does not know the relation of action to
reaction, and of the need to have something better than a vacuum against which to react –
to say that would be absurd. Of course, he only seems to lack the knowledge ladled out
daily in high schools.” What is wrong with this argument?
4. A 60 kg man is ice-skating due north with a velocity of 6.0 m/s when he collides with a
38 kg child. The man and child stay together and have a velocity of 3.0 m/s at an angle
of 35º north of east immediately after the collision. What are the magnitude and direction
of the velocity of the child just before the collision?
5. In a game of billiards, the cue ball is given an initial speed V and strikes the pack of 15
stationary balls. All 16 balls then engage in numerous ball-ball and ball-cushion
collisions. Some time later, all 16 balls have the same speed v (as improbable as that is).
Assuming that all collisions are elastic and ignoring the rotational aspect of the balls'
motion, calculate v in terms of V.
6. In the figure below a 3.2 kg box of running shoes slides on a horizontal frictionless
table and collides with a 2.0 kg box of ballet slippers initially at rest on the edge of the
table. The speed of the 3.2 kg box is 3.0 m/s just before the collision. If the two boxes
stick together because of packing tape on their sides, what is their kinetic energy just
before they strike the floor 0.40 m below the table's surface?
7. The linear momentum of a 1500 kg car increased in magnitude by 9.0 x 103 kg m/s in
12 s.
a) What is the magnitude of the constant force that accelerated the car?
b) By how much did the speed of the car increase?