**a list of equations will be given on the final**

**Multiple choice section**

1. Joe Schmetterling is running at 4m/s and accelerating at a constant rate of 2m/s$^2$. How far did he run after 3 s?

2. Joe Schmetterling is heading Northeast at 4 mph while Josephine heads West at 6 mph. What is the magnitude of the cross product of their velocities?

3. A 5 kg block sits on a rough plane inclined at 30 degrees and is sloping down to the right. What must the coefficient of static friction be if the block does not slide when the inclined plane is accelerated to the right at 3 m/s$^2$?

4. Joe Schmettering sinks through a viscous fluid with a constant velocity. Which statement is true?

(a) no forces act on Joe (b) only gravity acts on Joe (c) at least two forces at on Joe (d) Joe is drowning in turpitude (e) Joe is drowning in turpentine

5. A block of mass 2.5 kg sits on a rough 30 degree inclined plane of mass 8 kg that sits on a horizontal frictionless surface. When the block is released, the plane moves to the right with a speed of 4 m/s, what is the horizontal component of the velocity of the block?

6. A boat travelling at 10 m/s must expend 50 hp to maintain a constant speed, what is the magnitude of the force of friction exerted by the water on the boat?

7. A 750 kg car rolls from the top of a 200 m hill to the top of a 100 m hill. If its initial speed was 10 m/s and if it lost 1000J of energy to friction, what is its final speed?

8. A nonuniform sphere with moment of inertia $I= MR^2/4$ rolls down a slope without slipping. If $v$ is the speed of the center of mass of the sphere, what is its total kinetic energy?

(a) $Mv^2/2$ (b) $Mv^2$ (c) $3 M v^2/4$ (d) 5 Mv^2/8$ (e) $7 M v^2/8$

9. When a constant net torque acts on a rigid body it produces a (a) constant angular velocity (b) constant angular momentum (c) changing angular acceleration (d) changing angular velocity.

10. A ball of mass 1 kg and a radius of 10 cm rolls without slipping over a large upside down sphere of radius 2 m. What is the speed of the center of mass of the ball after it has rolled through an angle of $\phi$ degrees?

**Written Answer Questions**

1. A ball of mass 0.8 kg is attached to a massless cord which passes through a hole in a table and is attached to a hanging 1.2 kg mass. The ball rolls without slipping in a circle of radius 50 cm with a center of mass speed of 2 m/s. If the lower mass drops 10 cm, what is the resulting speed of the ball. Assume that it continues to roll and that no frictional losses occur while the lower mass is in motion.

2. A sphere of radius R and mass M is pierced by a cylinder of radius r, mass m, and length L. A massless cord is wrapped around one end of the cylinder, making a yoyo. The cord is attached to the ceiling and the yoyo is dropped. How fast is it going after falling 2m?

3. A knife held against a rotating motor-driven grinding wheel exerts a torque of 0.80 Nm. If the wheel rotates with a constant angular speed of 20 rad/s, what is the work done by the motor on the wheel in 1 minute?

4. Two blocks of mass M and 3M are attached together by a cord which passes over a pulley of radius, $r$ and moment of inertia $I$. The pulley is at the apex of an inclined plane which has the shape of an isoceles triangle with the long edge as the base. The blocks rest on either side of the pulley at an angle, phi. Derive an expression for the acceleration of the system.