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.

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).

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.

Answer

A compact car and a large truck collide head on and stick together. Which undergoes the larger momentum change?

1. car2. truck3. The momentum change is the same for both vehicles.4. Can’t tell without knowing the final velocity of combined mass.

A compact car and a large truck collide head on and stick together. Which vehicle undergoes the larger acceleration during the collision?

1. car2. truck3. Both experience the same acceleration.4. Can’t tell without knowing the final velocity of combined mass.

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 – 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.

ri rcm

i

iicm rmM

r 1

dmrM

rcm 1

Discrete particles

Continuous object

The derivation of these equations involves Torque, which we will learn about in the next chapter.

i

iicm rmM

r 1

321

332211

mmm

rmrmrm

ii

iii

m

rm

The position of the center of mass rcm can be separated into x, y and z components.

i

iicm xmM

x1

i

iicm ymM

y1

i

iicm zmM

z1

321

332211

mmm

xmxmxm

321

332211

mmm

ymymym

321

332211

mmm

zmzmzm

If the position changes in time, we can look at the velocity of the center of mass.

i

ii

cmcm dt

rdm

Mdt

rdv

1

iiivmM

1 dmv

Mvcm

1or

332211 vmvmvmvM cm

Notice that:The momentum of the center of mass is equal to the sum of the momentums of each part of the mass.This is not conservation of momentum!!