Physics 2210 (Schroeder) Name
spring 2006
Problem Set 6
(due Wednesday, February 15)
1. Paddy the bricklayer (whose mass is 75 kg) has 100 kg of leftover bricks that he needs to bring
down from the top of a 14-story building. To avoid hauling them down by hand, he hangs a
rope from a pulley and hoists a barrel to the top, tying off the rope at ground level. After
loading the bricks into the barrel, he goes back down to untie the rope, clinging tightly to it.
Much to his surprise (as he has not studied physics), he begins to accelerate upwards. (a)
What is his acceleration? (Please neglect the mass of the barrel, rope, and pulley, as well as
any friction in the pulley.) (b) How fast is Paddy going when he collides into the descending
barrel, 7 floors (25 meters) above the ground?
2. You need to drive your car (mass 1000 kg) and tow a trailer (mass 500 kg) up an icy 10%
incline, at constant speed. The coefficient of friction between your tires and the road surface
is 0.18. Can you make it? (A 10% incline is one that rises 10 meters for every 100 meters of
horizontal distance.)
3. A frictionless puck of mass mmoving in a circle of radius Ron a horizontal tabletop, attached
to a string which runs through a hole in the center of the circle. Hanging motionless from the
other end of the string (below the table) is a weight of mass M. Assuming that m,M, and
Rare all known, find a formula for the speed of the puck.
4. (a) How far is the center of mass of the earth-moon system from the center of the earth?
(Look up the data you need in the back of your textbook.) (b) Express the answer to part
(a) as a fraction of the earth’s radius.
5. The distance between the centers of the carbon and oxygen atoms in a carbon monoxide
molecule is 1.131 ×10−10 m. Where is the center of mass of this molecule, relative to either
atom? (You can look up the atomic masses in your textbook or on any periodic table.)
6. While out taking a stroll by moonlight, you stumble upon a man with a long nose who claims
he has just fallen from the moon. Putting aside the matter of how he could have survived
the fall, you ask him how he got to the moon in the first place. He then describes a most
ingenious method: Stand on a large iron plate with a large magnet in your hands. Throw the
magnet upwards; the iron plate will then be pulled up to it. Catch the magnet, and repeat
the procedure, working your way up as high as you please! Having studied physics, you are
skeptical. Explain why, using the concept of the center of mass.
7. Carmelita, mass 58 kg, and Ricardo, who is heavier, are enjoying Lake Merced at dusk in a
30 kg canoe. When the canoe is at rest in still water, they exchange seats, which are 3.0 m
apart and symmetrically located with respect to the canoe’s center. Carmelita notices that the
canoe moved 40 cm relative to a submerged log during the exchange, and calculates Ricardo’s
mass, which he has not told her. What is it?
8. A car with mass 1000 kg is moving at 55 mph in a direction 25◦south of east. Taking the x
axis to point east and the yaxis to point north, find the xand ycomponents of its momentum
vector. Express your answers in SI units.
9. Suppose your mass is 80 kg. How fast would you have to run, in order to have the same
momentum as a 1600-kg car moving at 1.2 km/hr?
