AJM:12/14/01 Score
/100
Physics 13101 Second Midterm Exam Winter 2000
Name
PLEASE READ THIS FIRST: Work the problems on separate sheets of paper and staple this sheet to the front. Read each
problem carefully. Show your work and/or give explanations for all answers. Make sure that all numerical answers are given
with a reasonable number of sig figs and that you have included appropriate units. Check your answers for physical
reasonableness whenever possible. I do give partial credit, but only if I can follow your work, so try to be clear about what
you are doing.
1. A child launches an 80 gram toy car along a frictionless track using a spring
with force constant 3 x 103 N/m that she had first compressed by 2.0 cm.
After being launched, the car travels around a circular loop-the-loop of radius
25 cm as shown at right.
a) [15 pts] What is the speed of the car when it is at the top of the loop-the-
loop as shown? (No friction, so energy is conserved!)
b) [10 pts] What force does the track exert on the car at the top of the loop?
(Just apply Newton’s Second Law to the car.)
c) [extra credit, 5 pts] What minimum initial compression of the spring would be required for the car to make it all
the way around the loop without losing contact with the track?
2. As shown at right, a fly starts out (at t = 0) at a position ri = 4.0 m, north relative to a
spider (who defines the “origin”), and flying with an initial velocity vi = 3 m/s, east. It
has a constant acceleration
a = 2.0 m/s2, 30° south of west.
a) [5 pts] At t = 0, is the fly’s speed increasing or decreasing?
b) [20 pts] Since a is constant, the fly’s position at any later time is given by the
vector sum rf = ri + vit + (1/2)at2. Find the fly’s position at t = 4.0 s by
performing this vector sum.
c) [extra credit, 5 pts] What is the angle between a and v at t = 4.0 s?
3. A ball moves in a horizontal circle around a vertical pole to which it is attached by two
strings as shown at right. The ball moves at just the right speed to make the tension the
same in both strings.
a) [20 pts] What is the ball’s speed? (Just apply Newton’s Second Law to the ball and
see what the resulting equations tell you!)
b) [5 pts] Would the tension in the longer string increase, decrease, or remain the same
if the ball moved faster?
4. Two identical bar magnets of length L held as shown at right exert an attractive force on
each other with a magnitude given approximately by F = β/x3 where x is the center-to-center
distance.
a) [5 pts] What are the dimensions of β (in terms of M, L, and T as always)?
b) [20 pts] If the two magnets start out in contact (i.e., x i = L), how much work must you
do to separate them by twice their length, (i.e., x f = 3L). Express your answer in terms
of β and L.
c) [extra credit, 5 pts] How much more work would you have to do to separate them “to infinity.”
r
i
a
v
i
spider
fly
East
30°
1.50 m
x
L