Practice Problems for mid-term 1
1. A neutron in a reactor makes an elastic head-on collision with a carbon atom that is initially at rest.
(a) What fraction of the neutron’s kinetic energy is transferred to the carbon nucleus?
(b) If the neutron’s initial kinetic energy is 1.6 × 10–13 J, find its final kinetic energy and the kinetic energy of
the carbon nucleus after the collision.
(Mass of the carbon nucleus = 12x Mass of the neutron)
2. Two identical containers of sugar are connected by a massless cord that passes over a massless, frictionless
pulley with a diameter of 50 mm. The two containers are at the same level. Each originally has a mass of 500g.
a) What is the horizontal position of their center of mass?
b) Now 20 g of sugar is transferred from one container to the other, but the containers are prevented from
moving. What is the new horizontal position of their center of mass, relative to the central axis through
the lighter container?
c) The two containers are now released. In what direction does the center of mass move?
d) What is its acceleration?
3. A 4.0 kg physics book and a 6.0kg calculus book, connected by a spring, are stationary on a horizontal
frictionless surface. The spring constant is 8000 N/m. The books are pushed together, compressing the spring,
and then they are released from rest. When the spring has returned to its unstretched length, the speed of the
calculus book is 4.0m/s. How much energy is stored in the spring at the instant the books are released?
4. A spring with spring constant k=400 N/m is placed in a vertical orientation with its lower end supported by a
horizontal surface. The upper end is depressed 25.0cm, and a block with a weight of 40.0 N is placed
(unattached) on the depressed spring. The system is then released from rest. Assume the gravitational potential
energy Ug of the block is zero at the release point (y=0) and calculate the gravitational potential energy, the
elastic potential energy , and the kinetic energy of the block for y equal to:
a) 0
b) 5.00 cm
c) 30.0 cm
d) how far above its point of release does the block rise?
5. A man is sitting in a ‘bosun’s chair’ (similar to the chair hanging from the pulley shown in class). The chair
dangles from a massless rope, which runs over a massless, frictionless pulley and back down to the man’s hand.
The combined mass of man and chair is 95.0kg. With what force must the man pull on the rope if he is to rise
a) with a constant velocity
b) with an upward acceleration of 1.30m/s2
Suppose, instead, that the rope extends all the way to the group, where it is pulled by a co-worker. With what
force must the co-worker pull for the man to rise
c) with a constant velocity
d) with an upward acceleration of 1.30m/s2
6. A person (m1) walks on top of a board (m2) on top of frozen lake. If person walks at speed v1 relative to the
board, what is the speed of board relative to lake?
7. Judy (mass 40.0 kg), standing on slippery ice, catches her leaping dog, Atti (mass 15 kg), moving
horizontally at 3.0 m/s. what is the speed of Judy and her dog after the catch?
8. Comic-strip hero Superman meets an asteroid in outer space and hurls it at 800 m/s, as fast as a bullet. The
asteroid is a thousand times more massive than Superman. In the strip, Superman is seen at rest after the throw.
Taking physics into account, what would be his recoil velocity?
9. There are two situations:
In the first, two cars, one going 30 mph and the other going 15mph, collide in traffic accident. They both come
to a complete stop upon colliding.
In the second, a car (exactly like the first car that was going 30mph) hits a brick wall at 30 mph (again, coming
to a complete stop upon colliding).
(a.) Which is greater: the force exerted by the 15mph car or the force exerted by the brick wall? Why?
(b.) What can you say about the mass of the two cars, given what you know about the problem?
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Conceptual Problems:
1. Is it possible for an energy potential around an equilibrium position to depend on x^3, to lowest order?
2. Why must particles that collide elastically in the CM frame maintain the same respective velocities
through the collision?
3. If a stick with non-uniform mass distribution is at rest on a frictionless table, how might you determine
the center of mass (using, say, a hammer)?
4. True or false: When you are riding on the T and you stumble into someone as the train stops, it is due to
the acceleration of the train.