Anyone who is really good at Physics, please get in here!?

Question

When I hit a ball with a bat, doesn't the baseball bat slow down and the ball speed up?

-My choices are: the bat slows down with the ball speeding up, the ball slowing down with the bat speeding up, both speeding up, both slowing down, or none of these. I thought that since the bat hits the ball, the ball slows down and so does the bat, but I'm not sure.

Oh, and does anyone know the answer to this problem:

Two people are tugging on a light rope. The rope doesn't slip in either one of their hands. Are the forces equal? Who will win?

- I think that the forces are equal but that the person who weighs more and has better footing will come out as the winner. Any thoughts?

My friend said that they both don't slow down, so I don't get it.

Answer 1

The bat definitely will slow down since it imparted a lot of energy to the ball. The ball speed is reversed, so you cannot say it slows down (slowing has meaning only when movement remains in the same direction). The ball might leave the bat at a speed with smaller magnitude than when it was thrown or larger magnitude or even equal. It all depends on the speed of the bat and the angle of incidence with the ball.

For the tug-of-war, if either contestant are not moving the forces are equal. The winner is the one with better footing, not necessarily the heaviest, although if they have the same type of shoes and thus the same coefficient of static friction, the heaviest can sustain a higher force before starting to slide.

Answer 2

1: Momentum (p) is conserved and equals mass X velocity.

They can't both speed up as this would increase the total velocity of both items, same with both slowing down.

The momentum of the ball is significantly changed because it changes direction. Newtons laws of motion say that an object travelling in a direction cannot change direction until acted on by an external force.
The only force available to change the trajectory of the ball is the impulse force from the bat. the bat must give up some energy to change the direction of the ball.

I think the bat will slow, the ball will speed up. If you take the extreme case of hitting a ball at rest this is clerly the case.
This discussion excludes friction losses and angles of impact etc.

for the tug of war, where there are no friction losses, the heaviest person will win. consider hanging two weights tied together over a pole. The heaviest weight will fall and pull the other weight up.
F = m x a. Assuming only gravity, the heavier body is glued to its position with a greater force.

..phew... I don't know - really interesting questions!

Answer 3

For the bat and the ball one I believe that both of them will slow down, although the ball does both slow down and speed up.

The ball is moving towards you and when you strike the ball with the bat it will slow down in a split second. The ball doesnt immediately change direction without slowing down instantaneously. Then the ball will speed up due to the force of the bat.

Answer 4

The forces exerted on the rope ARE equal. Who will win the tug o war depends on the forces acting on each person. Consider person A, acting on them are the tension in the rope, friction, gravity and the normal force exerted on them by the ground. That person will accelerate at a rate determined by Newton's second law: Tension - Friction = m a

Consider the forces on person B, the tension on the rope, the friction on person B, that person will also accelerate at a rate determined by Newton's second law and the forces acting on them.

The person whose friction force is greater than the tension will win. (To have a large friction force, you can be heavy and have a larger normal force, or have a larger coefficient of friction.)

Your thoughts are right.