Physics 3221
Spring Term 2007
Test 2, March 7, 2007
• This is an open notes/text book/Homework test lasting 50 minutes.
• There are 5 problems, divided into subsections. The points for each part are
marked.
• Begin each problem on a fresh sheet of paper. Use only one side of a
sheet of paper.
• Put your name, the problem number, and the page number in the upper
right hand corner of each sheet.
• To receive partial credit you must explain what you are doing. Carefully
labeled figures are important. Randomly scrawled equations aren't helpful.
• Draw a box around important results.
There are 3 pages including this page. Do not forget to look at all parts of the
problems.
Problem 1
Two masses m and 2m are connected by a massless string. They slide on a fixed table
when a force F is exerted on one of the masses, as shown in the figure. The coefficient of
friction between each mass and the table is µ. Find the tension in the string. (3 points)
F
m
2m
table
Problem 2
A particle with mass m falls under gravity in a medium under the influence of a retarding
force with magnitude given by kv3, where v is the velocity of the particle. Find the
terminal velocity. (Hint: you can get the answer without solving the differential equation)
(3 points)
Problem 3
A spacecraft moves through space with constant velocity v. It encounters a stream of dust
particles which embed themselves onto the spacecraft at a rate α = dm/dt. Assuming the
dust is stationary before it hits the spacecraft. Find the external force F necessary to keep
the spacecraft moving at constant velocity v. (In practice, F will come from the
spacecraft’s engine) (3 points)
Problem 4
A particle with mass m moves in one dimension along the x axis in the region where x>0.
It is acted on by two forces F1 and F2. F1 is a constant force directed away from the origin
with magnitude B. F2 is an inverse square law force with magnitude A/x2 directed towards
the origin.
(a) Find the potential energy U(x). (2 points)
(b) Find the equilibrium position xo. (2 points)
(c) Is the equilibrium stable or unstable? (assume A > 0 and B > 0) (1 point)
Problem 5
A mass m is initially at rest at point A on a track. As indicated by the diagram (not to
scale), the right half of the track takes the shape of a quarter of a circle with radius 25R,
while the left half takes the shape of three quarters of a circle radius R. The mass m
slides down the track and collides with a second mass 2m at the bottom of the track. After
the collision, the two masses are stuck together. The composite mass continues to move
up the left half of the track. Ignore friction and air resistance throughout this problem.
(a) Find the velocity V1 of m immediately before it collides with 2m, in terms of g and R
(1 point)
(b) Find the velocity V2 immediately after the collision, in terms of g and R. (2 points)
(c) Find the magnitude and direction of the normal force exerted by the track on the
composite mass when it reaches point B, in terms of g and R. (3 points)
m
25R
gravity
Point B
R
2m
Point A