1. Yes, it moves to the right. 2. Yes, it moves to the left. Suppose you are on a cart, initially at rest on a track with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown in the figure, is the cart put in motion? 1. Yes, it moves to the right. 2. Yes, it moves to the left. 3. No, it remains in place. Answer: 2*. Because all the balls bounce back to the right, then in order to conserve momentum, the cart must move forward. *(Note: this assumes that there is no interaction between the man and the cart. If that interaction is included the answer would be 3!)

The device in the photograph above is called a "fan cart" because of the electrical fan mounted on it. The fan blows air toward the right in the photograph, so with the sail removed and the fan ON the cart will move to the left (click here for video). On the other hand, with the fan OFF and the sail mounted on the cart, you can blow into the sail from the left with your breath or a larger stationary fan and make the cart move to the right (click here for video). Notice that the propeller is not rotating and the wind from the fan at the left causes the sail to bend to the right. When the fan is turned ON with the sail mounted on the cart, if you hold the cart you can again notice the sail bending due to the air from the cart fan blowing into the sail (click here for video). Answer Suppose that the sail is mounted in place as shown in the photograph, the fan turned ON, and the cart released to move if it wants to. What will the cart do? (1) It will move to the left. (2) It will move to the right. (3) It will remain motionless.

3. The momentum change is the same for both vehicles. A compact car and a large truck collide head on and stick together. Which undergoes the larger momentum change? 1. car 2. truck 3. The momentum change is the same for both vehicles. 4. Can’t tell without knowing the final velocity of combined mass. Answer: 3. Conservation of momentum tells us that the changes in momentum must add up to zero. So the change in the car’s momentum must be equal to the change in the truck’s momentum, and the two changes must be in the opposite directions.

3. Both experience the same acceleration. A compact car and a large truck collide head on and stick together. Which vehicle undergoes the larger acceleration during the collision? 1. car 2. truck 3. Both experience the same acceleration. 4. Can’t tell without knowing the final velocity of combined mass. Answer: 1. Say the car has inertial mass m and the truck has inertial mass M >> m. Because the changes in momentum are equal (neglecting the fact that they are in opposite directions), we have mΔv = MΔV, where Δv is the change in the car’s speed and ΔV the change in the truck’s speed. Because m << M, Δv >> ΔV. The acceleration is proportional to the change in speed, and both changes in speed take place over the same time interval (the duration of the collision). Therefore the car undergoes a much larger acceleration than the truck.

CH 8: Systems of Particles and Extended objects

Center of Mass (Center of Gravity) Center of mass – Average location of the mass of an object if all the mass is concentrated at a single point. The center of mass does not have to be inside the object! Center of gravity – Average location of the weight of an object if all the weight is concentrated at a single point. ri rcm ri – Position of small part of the total mass. rcm – Position of the center of mass. Dmi or dmi – Small part of total mass. M – Total mass. DWi or dWi – Small part of the total weight. W – Total weight. Talk about importance of center of mass in balance. Example: Person bends over and sticks their butt out. Why? Discrete particles The derivation of these equations involves Torque, which we will learn about in the next chapter. Continuous object

The position of the center of mass rcm can be separated into x, y and z components. If the position changes in time, we can look at the velocity of the center of mass. or The momentum of the center of mass is equal to the sum of the momentums of each part of the mass. Notice that: This is not conservation of momentum!!