Lafayette College
Department of Physics
March 4,2009
Physics 131 LevelIIHomework Set Section 1
Youmay discuss these problems with one or twoother students (or with your instructor), but
your final solutions should be written out by you alone. Under no circumstances should you see
another student’swritten solutions. If you have discussed these problems with anyone you must
acknowledge the collaboration at the beginning of the corresponding problem. Homework is due
in my office by 3:30 PM on the due date and solutions will then be made available on the course
web site. No homework will be accepted after this time.
Youare expected to carefully explain how, starting from basic principles, you have arrivedat
your answers. Please do not use paper with edges frayed from being ripped out of a spiral bound
notebook. If the papers are illegible or disorganized, we reservethe right to return these papers
without being graded. Unless instructed otherwise, all answers should be correct to 3 or 4 sig.
figs.
Assignment 6: Due Friday,March 6, 2009
Problem 1: A switch engine is pulling 3 box cars up a long incline of 1. 5°onarainyday.
Each box car weighs 60 metric tons (including its load), and there is rolling friction between the
wheels and the road. Note that rolling friction is modelled by equations that look just likesliding
friction, except the coefficent of rolling friction is much smaller that that of sliding friction. The
switch engine weights 20 metric tons and is moving with constant speed. The static coefficient of
friction between the wheels of the engine and the rails is 0.75 and the kinetic coefficient of fric-
tion is 0.55 for these same surfaces. The rolling friction acts only on the loaded box cars and the
sliding friction acts only on the switch engine.
What is the maximum coefficient of rolling friction between the box car wheels and the
rails that will allowthe switch engine to pull this load up the hill. Is this value reasonable
giventhe information above.
What is the tension in the coupling that connects the first box car to the second box car?
Problem 2: A block with a mass Mis resting on an incline plane making an angle
θ
=12°
with the horizontal, the coefficient of static friction between these surfaces is 0. 35and the coeffi-
cient of kinetic friction between these surfaces is 0. 30. Sitting on the top of this lower block is
an upper block with a mass m=M/4.The coefficient of static friction between the blocks is
0. 25and the coefficient of kinetic friction between them is 0. 20. A student is pushing on the
lower block with a horizontal force FAdirected so that the lower block movesupthe incline.
What is the maximum force the student can apply to the lower block so that the two
blocks will not slip relative toeach other?
