# Week 12 (Oct. 28 - Nov. 1)

**Reading:**PSE Chap 9, Linear momentum and collisions

**Topics:**impulse, momentum, collisions, conservation of momentum, center of mass

**Lab:**

**Homework Problems:**These problems are due on Tuesday of Week 13. They involve conservation of momentum and center of gravity.

**Perfectly inelastic collision:**A 10 kg block sliding across a table is moving to the right with a speed of 5 m/s. It strikes an initially stationary block having mass 5 kg. The blocks collide, and stick together. Assume that there is no friction between the table and the sliding blocks.- What is the final speed of the blocks?
- What is the speed of the center of mass immediately after the collision?
- What is the speed of the center of mass just before the collision?
**Perfectly elastic collision:**Now consider the same collision. This time, the collision is completely elastic (that is: kinetic energy is conserved; no energy is converted into heat or sound or any other form).

- What is the final speed of the blocks?
- What is the speed of the center of mass immediately after the collision?
- What is the speed of the center of mass just before the collision?

**Optional additional Review/Practice Problems:**For those of you who want additional practice. Note: I took these problems from a textbook; the answers are based on using g = 9.81 m/s^2 for the acceleration of gravity near earth (not 10 m/s^2, as we typically approximate).

- A 200 gram block is pressed against a spring of force constant 1.40 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60 degrees to the horizontal. Use energy considerations to determine how far up the incline the block moves before it stops (a) if there is no friction between block and ramp (
*4.12 mete*rs) and (b) if the coefficient of kinetic friction is 0.400 (*3.35 meters*). - A bead slides without friction around a loop-the-loop. If the bead is released from a heigh t of 3.50 R, where R is the radius of the loop, what is the speed of the bead (a) at the bottom? and (b) half-way up the loop? What is the normal force exerted by the loop (c) at the bottom and (d) half way up the loop?
- A 5.0 kg block is placed on top of a 10 kg block. A horizontal force of 45 N is used to pull the 10 kg block to the right. A rope is tied between the 5 kg block and a wall on the left. The coefficient of kinetic friction between the surfaces is 0.20. (a) draw a free body diagram for each block and identify the action-reaction forces between the blocks. (b) determine the tension in the string and the acceleration of the 10 kg block (Tension = 9.80 Newtons; a = 0.580 m/s^2).
- During WWI, the Prussians had a gun called Big Bertha. The shell had an initial speed of 1.70 km/s at an inclination of 55 degrees above the horizontal. Ignoring drag due to air, (a) how far away did the shell hit? (277 km) (b) How long was it in the air? (4.74 minutes) (c) what was its speed on impact?
- A particle moves along the x axis according to the equation x = 2 + 3t - t^2. At t=3 seconds, find (a) the position (2.00 meters), (b) the velocity (-3.00 m/s) and (c) the acceleration of the particle (-2.00 m/s^2).

**Quiz: We will have a quiz on monday of Week 13.**