SP221/2141&4341
Chapter 8 Homework
Due Monday October 31, 2016
Question 1: Two people, each of mass m, stand on a railcar of mass M . They each jump off one
end of the railcar with a velocity of magnitude u relative to the railcar and the railcar rolls in the
opposite direction without friction. (a) Suppose that both people jump at the same time. What is
the final speed of the railcar? (b) Suppose that the two people jump one at a time, with the second
person waiting for the first person to hit the ground before jumping. What is the final speed of the
railcar? [10 points]
Question 2: Rudy has a mass of 80 kg and is sitting at one end of a large canoe that is 4.5 m long
and has a mass of 40 kg. The canoe is initially at rest with respect to the water, and we can assume
that there is no friction between the water and canoe. Rudy stands up and slowly walks 4.5 m (with
respect to the canoe) until he is at the far other end of the can. How far does the canoe move (with
respect to the water) when Rudy switches sides? [5 points]
Question 3: (Tipler & Mosca Problem 8-40) A wedge of mass M is placed on a frictionless, horizontal
surface, and a block of mass m is placed on the wedge, which also has a frictionless surface (Figure
8-46). The block’s center of mass moves down a distance h as the block slides from its initial position
to the horizontal floor. (a) What are the speeds of the block and of the wedge as they separate from
each other and go their own ways? (b) Check your calculation plausibility by considering the limiting
case when M m. [10 points]
Question 4: (a) An object of mass m=2.5 kg is initially at rest at time t=0. It is then subject to
a time-varying force given by Fx (t) = 5t−2/3 , where Fx has units of newtons when t has units of
seconds. What is the object’s momentum at time t=3.0 s? What is the object’s kinetic energy at
time t=3.0 s? (b) An object of mass m=2.5 kg is initially at rest and located at position x=0. It
is then subject to a spatially-varying force given by Fx (x) = 5x−2/3 , where Fx has units of newtons
when x has units of meters. What is the object’s momentum when it is located at x=3.0 m? What
is the object’s kinetic energy when it is located at x=3.0 m? [5 points]