Mechanics Assignment I
(1) Imagine a tank traveling with constant speed v1 along direction AB, and a missile
is chasing the tank with constant speed v2. The direction of motion of the missile
is always pointing towards the tank. At time t the tank is at position F and the
missile is at position D, where FDAB and FD = L (see figure). What is the
acceleration of the missile at this instant?
F
B
A
L
D
(2) A uniform rod AB with length l and weight W is placed as shown in the figure,
with end A touching a rough wall and end B hanging by a strong, inextensible
string. The other end of the string is fixed at point C on the wall. The coefficient
of friction between the rod and the wall is . The rod is hung horizontally and the
angle between the string and the rod is . Derive the condition that  and  should
satisfy such that the rod stays at equilibrium.
C
A

B
(3) An empty cylindrical container has height L, mass m and inner radius r. The
center of gravity of the container is located at height h from its bottom. How much
water (in terms of height) should one pour into the container to make it most
stable? The density of water is .
(4) A car accelerating at uniform rate ao has a small ball hung under the roof by a
string of length L. What is the angle  between the string and the vertical direction
when the ball is in steady state? What will be the frequency of oscillation if the
ball is set in small oscillation?
(5) A boat of mass M and length l has a shape symmetric with respect to a reflection
between front and end. When it is resting on still water, a man with mass m is
standing at the front of the boat. If the man walks with constant speed v from the
front to the end of the boat, how much distance will the boat move backward?
(6) A boat with mass M (>> 1 kg) is moving forward with a constant speed v = 2 ms-1.
A man on the boat throws a ball with mass m = 1kg forward at speed v’ = 4 ms-1
relative to the boat. What is the work done by the man? How about if the man
throws the ball backward? Discuss where the work goes (to the ball and/or to the
boat) in the reference frame of (a) moving at 2 m/s in the same direction as the
boat; and (b) ground.
(7) A mass m1 is moving at constant speed vo towards a rest mass m2 on a frictionless
surface. A (massless) spring with spring constant k is attached to m2. What is the
maximum displacement of the spring during the process of collision of the two
masses? (see figure)
m1
m2
(8) A ball with mass m is attached to the wall by a massless spring with spring
constant k. The coefficient of kinetic friction between the ball and the surface is 
(see figure). The ball stays at point O when the spring is at its natural length.
Suppose the ball is released at position A located at distance d at the left of O at
time zero. What is the allowed range of values of  where the ball stops at the
right of O after passing through O only once?
A
O
d