Problem 1:

A box of mass m slides across a horizontal table with coefficient of friction m.  The box is connected by a rope which passes over a frictionless pulley to a body of mass M hanging along side the table.  Find the acceleration of the system and the tension in the rope.

Problem 2:

In the figure below the coefficient of friction is the same at the top and the bottom of the 700-g block. 
(a)  Draw a free body diagrams for both the 200-g and the 700-g blocks, considering all forces.
(b)  If the acceleration is a = 70 cm/s² when F = 1.3 N, how large is the coefficient of friction

Problem 3:

(a)  An elevator in which a woman is standing moves upward at 4 m/s.  If the woman drops a coin from a height 1.4 m above the elevator floor, how long does it take the coin to strike the floor?  What is the speed of the coin relative to the floor just before impact?  (b)  Now assume that the elevator is moving downward with zero initial velocity and acceleration of 1 m/s² at t = 0, the women releases the coin at t = 1 sec.  How long does it take the coin to strike the floor?  What is the speed of the coin relative to the floor just before impact?

Problem 4:

Two trucks are parked back to back in opposite directions on a straight, horizontal road.  The trucks quickly accelerate simultaneously to 3.0 m/s in opposite directions and maintain these velocities.  When the backs of the trucks are 20 meters apart, a boy in the back of one truck throws a stone at an angle of 40 degrees above the horizontal at the other truck.  How fast must he throw, relative to the truck, if the stone is to just land in the back of the other truck?

 Problem 5:

A rock is launched from the ground level at a speed v directed at an angle q with the horizontal.  It is noticed that after some (unknown) time t after the launch, the distance between the rock and the launch point begins to decrease.
(a)  Find the smallest launch angle q consistent with this observation.
(b)  Find t, neglecting the air resistance.

Problem 6:

Consider a pendulum consisting of a rigid thin rod with length L and negligible mass supporting a ball of mass M.  The pendulum is immersed in a viscous medium which causes a frictional force F whose magnitude is proportional to the speed v of the ball, F = -mv.  It swings in a vertical plane under the influence of gravity.
(a)  Derive the equation of motion of the pendulum, allowing for arbitrary angles q of deflection from the vertical axis.
(b)  Determine the fixed points for which d²q/dt² = 0 when dq/dt = 0.  Determine for each fixed point the critical value of the drag coefficient m above which there is no oscillation about the point for small displacements.

Problem 7:

A child slides down a frictionless slide as shown in figure.
(a) What is the minimum value of R for the child to not immediately loose contact with the section of Radius R?
(b) If R is larger than that minimum value at what height h will the child loose contact with the section of radius R?

(c)  If R is smaller than that minimum value, how far from the end of the section with radius R will the child land?