- #1

peesha

- 6

- 0

A heads up - while this problem clearly deals with momentum and elastic collisions, we haven't actually covered these concepts in class yet. I'm getting the idea, but am still a bit hazy here and there.

## Homework Statement

A ball bounces off a wall. The ball is traveling at an angle 10 degrees below the horizontal when it hits the wall. The friction force by the wall is equal to the weight of the ball.

For the sake of clarity, let's say that the ball was thrown from left to right.

We are asked to:

1)Draw a free body diagram of the ball during contact with the wall

2)Sketch all 6 x-motion and y-motion graphs - that is, x/y vs t, velocity vs t, and acceleration vs t. The graphs must specifically identify three time periods: before, during, and after contact.

**2. The attempt at a solution**

The free body diagram seems pretty simple. The vertical forces are the force due to gravity (down) and friction force (up). These forces, as stated in the problem, are opposite and equal. There is one horizontal force: the normal force of the wall on the ball. The force is

*perpendicular to the wall*(The normal force would be perpendicular regardless of the angle of impact, correct?) There is a net force in the leftward direction and no net vertical force while the ball is in contact with the wall.

As for the motion diagrams: I have no problem with the x-motion. The x vs t graph will increase steadily, be horizontal while the ball is in contact with the wall, then decrease steadily at the same rate. The v vs t graph will be horizontal and positive before contact, horizontal and negative after, and have a negative (but not linear) slope during contact. The a vs t graph will be zero except for a negative 'blip' during contact.

The y-motion graphs I'm having a bit more trouble with. If the wall was frictionless, the y-motion graphs would look no different than if the ball did not hit a wall, correct? The y vs t graph would resemble a parabolic curve, v vs. t: a line with a negative slope intersecting zero at a point corresponding with the apex of the parabola, and the acceleration would be negative (-9.8).

My big question is what happens when the ball is in contact with the wall if the net vertical force is zero during contact (due to friction)? It seems like there will be a very short 'break' in the parabola of the y vs. t graph, where ∆y is zero. What about the v vs. t graph? In this case, it seems like there would be two points in the graph that intersected zero. A vs t would also have to reach zero for a moment.

Any guidance on the y-motion would be much appreciated.

Thanks so much for any help.