SP221/2141&4341
Chapter 6 Homework
Due Monday October 17, 2016
Question 1: Suppose that the net force acting on a particle of mass m=0.75 kg is given by
F (x) = 25e−0.25x , where F is given in Newtons when x is given in meters. The particle starts
from rest at an initial position of xi =0. What is the speed of the particle when it reaches x=5.0 m?
[10 points]
Question 2: A puck of mass m is attached by a string and lies on a horizontal frictionless surface
with a small hole in it. The string runs through the hole and is attached to a spring with spring
constant k; the other end of the spring is fixed to the floor. The length of the string is chosen so that
if the puck is right on top of the hole (i.e. r=0), the spring will be at its unstretched (equilibrium)
length. The puck starts at rest with the spring unstretched. We then do work on the puck until it
is rotating at a constant speed in a circle of radius r. (a) What is the pucks kinetic energy? Give
your answer in terms of the given quantities (m, k, and r) - not the speed v. (b) How much work
does the spring do on the puck? (Strictly speaking the string is between the spring and puck so this
is the work done by the spring on the puck and string system.) (c) How much work must you do to
get the puck rotating at a constant speed in a circle of radius r? Again, give your answer only in
terms of the given quantities (m, k, and r). [10 points]
r
SP221/2141&4341
Chapter 6 Homework
Due Monday October 17, 2016
Question 3: A loaded elevator car has a mass of 3.00×103 kg. The elevator car starts at rest on the
ground. The elevator is pulled upwards by a motor with a constant power output of 1.00×105 W.
After the motor has been running for 0.350 s, the elevator car has risen to a height of 0.771 m above
the ground. What is the tension in the cable lifting the elevator car at that moment? [10 points]
Question 4: (Tipler & Mosca Problem 7-34) An Atwood’s machine (Figure 7-39) consists of masses
m1 and m2 and a pulley of negligible mass and friction. Starting from rest, the speed of the two
masses is 4.0 m/s at the end of 3.0 s. At that time, the kinetic energy of the system is 80 J and each
mass has moved a distance of 6.0 m. Determine the values of m1 and m2 . [10 points]