Physics 207-02 – Introductory Physics I

Solution Set 10

Nazareth College

Department of Chemistry & Biochemistry

Robert F Szalapski, PhD – Adjunct Lecturer

www.CallMeDrRob.com

Fall 2011

## § Chapter 7, Problem 3

A baseball pitched is hit on a horizontal line drive back toward the pitcher at . If the contact time between the bat and ball is , calculate the average force between the ball and bat during the contact.

Use

For our coordinate system choose the positive axis pointing from the batter towards the pitcher. Watch the signs!

## § Chapter 7, Problem 4

A child in a boat throws a package out horizontally with a speed of . Calculate the velocity of the boat immediately after assuming it was initially at rest. The mass of the child is , and that of the boat is . Ignore water resistance.

Use conservation of linear momentum. We cant treat the child and the boat as one object of mass since they will be moving together at the same speed. Since initially everything is at rest, the initial linear momentum is zero. Hence

The negative sign indicates that the motion of the boat is in the opposite direction as the velocity of the package.

## § Chapter 7, Problem 5

Calculate the force exerted on a rocket given that the propelling gases are expelled at a rate of with a speed of at the moment of takeoff.

We assume that the rocket is initially at rest, and so the initial linear momentum is zero. Whatever momentum is imparted to the propelling gases, the equal bot opposite momentum will be imparted to the rocket. For problems of this type I like to consider the momentum in an arbitrary time period . During this time the mass of propelling gas that is expelled is

which will have a momentum

and the force is

## § Chapter 7, Problem 7

A railroad car travels alone on a level frictionless track with a constant speed of . A load, initially at rest, is dropped on the car. What will be the car’s new speed?

Use conservation of momentum realizing that both masses will be moving together after the load is dropped onto the car.

## § Chapter 7, Problem 8

A boxcar traveling at strikes a second boxcar at rest. The two stick together and move off with a speed of . What is the mass of the second car?

Using conservation of momentum.

## § Chapter 7, Problem 16

A hammer strikes a nail at a velocity of and comes to rest in a time of .

### § (a)

What is the impulse given to the nail?

### § (b)

What is the average force acting on the nail?

## § Chapter 7, Problem 17

A tennis ball of mass and speed strikes a wall at a angle and rebounds with the same speed at . What is the impulse, magnitude and direction, given to the ball?

Remember that momentum is a vector quantity.

Recall also

The problem is straightforward if we work with components as indicated in the figure. Assume the usual coordinate system, and note that the component of the velocity does not change while the component flips direction.

So the magnitude of the impulse is directed outward from the wall.

## § Collisions in one Dimension

For the next few problems we may use the equations discussed in class and also presented in Problem 30. The scenario with one object initially at rest and the other in motion as depicted in the figure. We assume a perfectly elastic collision.

The figure shows reversing direction, but depending upon the masses it could be moving to the right after the collision. In particular,

## § Chapter 7, Problem 22

A ball of mass moving East ( direction) with a speed of collides head-on with an at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

Since both velocities have a positive sign, both masses are moving East ( direction).

## § Chapter 7, Problem 23

An ice puck moving East ( direction) with a speed of collides head-on with an puck initially at rest. If the collision is perfectly elastic, what will be the speed and direction of each puck after the collision?

## § Chapter 7, Problem 26

An softball moving with a speed of collides head-on and elastically with another ball initially at rest. Afterward the incoming softball bounces backward with a speed of

, the negative sign to indicate backwards.

### § (a)

Calculate the velocity of the target ball.

We have

and

We have two equations in two unknowns. Notice that the first equation (for ) has only one unknown, , so I will solve for that first.

We may substitute this into the second equation.

and

### § (b)

Calculate the mass of the target ball.

From part (a):

## § Chapter 7, Problem 46

Find the center of mass of the three mass system. Specify relative to the left-hand mass.

to the right of the left-hand mass.

## § Chapter 7, Problem 47

The distance between a carbon atom () and an oxygen atom () in the CO molecule is . How far from the carbon atom is the center of mass of the molecule?

As in the figure we choose to place the origin coincident with the carbon atom.

## § Chapter 7, Problem 58

A woman and an man stand apart on frictionless ice.

### § (a)

How far from the woman is their center of mass (CM)?

Notice that I have chosen the coordinate system so the woman is initially standing at the origin.

While we were given the distance between the two to three significant figures, the man’s mass is only given to one and the woman’s mass to two significant figures. Because the woman is at the origin, the CM is from her.

### § (b)

If each holds one end of a rope, and the man pulls on the rope so that he moves , how far from the woman will the man be now?

There will be tension in the rope only if he pulls on it and she pulls back. The tension can only draw them towards each other. (You cannot push away with a flexible rope.) If he has moved , then his new coordinate is at as indicated in the figure. We do not know her position, so let’s call it . We can now calculate their CM again with their new positions, but it must be the same as the CM in part (a) since their are no external forces to change their CM.

To obtain their separation use the distance formula for one dimension.

### § (c)

How far will the man have moved when he collides with the woman?

Now they are both at the same unknown position which we shall label as . Again computer their center of mass and equate it with the original value since no external forces have acted upon the system.

In other words, they will be standing at their mutual center of mass. With a little experience a student of physics knows intuitively that this is the only possibility. To calculate the distance the man has traveled we again use the distance formula.