Momentum, conservation, collision

[Jimmy Tango]

Homework Statement

Olaf is standing on a sheet of ice that covers the football stadium parking lot in Buffalo, New York; there is negligible friction between his feet and the ice. A friend throws Olaf a ball of mass 0.400 that is traveling horizontally at 10.6 . Olaf's mass is 72.8 .

If Olaf catches the ball, with what speed do Olaf and the ball move afterward?

Vfinal = 5.79 cm/s

If the ball hits Olaf and bounces off his chest horizontally at 7.20 in the opposite direction, what is his speed after the collision?

Taking the direction in which the ball was initially traveling to be positive, what is , the ball's final momentum?

Homework Equations

Pi=Pf

P=mv

I = Force times change in time

change in momentum = Impulse

The Attempt at a Solution

 

[superdave]

Conservation of momentum, you said it right there. Olaf is standing still and has no momentum. The ball hits him and bounces off with some momentum. The rest of the momentum can't disappear, so it had to go into Olaf.

 

[tomcue]

In this scenario, we can use the principle of conservation of momentum to solve for the final velocity of Olaf and the ball after the collision. This principle states that the total momentum of a closed system remains constant, meaning that the initial momentum of the ball must be equal to the final momentum of Olaf and the ball combined.

Using the equation P=mv, we can calculate the initial momentum of the ball before the collision as (0.400 kg)(10.6 m/s) = 4.24 kg*m/s. Since momentum is a vector quantity, we must also take into account the direction of motion. In this case, we can take the direction of the ball's initial motion to be positive, so the initial momentum is +4.24 kg*m/s.

After the collision, the ball bounces off Olaf's chest and moves in the opposite direction with a speed of 7.20 m/s. Using the same equation, we can calculate the final momentum of the ball as (0.400 kg)(-7.20 m/s) = -2.88 kg*m/s.

Since momentum is conserved, the final momentum of Olaf and the ball combined must be equal to the initial momentum of the ball. Therefore, the final momentum of Olaf and the ball combined is (4.24 kg*m/s) + (-2.88 kg*m/s) = 1.36 kg*m/s.

To solve for the final velocity, we can rearrange the equation P=mv to solve for v, giving us v=P/m. Plugging in the final momentum of 1.36 kg*m/s and the combined mass of Olaf and the ball (72.8 kg), we get v = (1.36 kg*m/s)/(72.8 kg) = 0.0187 m/s. Converting to centimeters per second, we get a final velocity of 1.87 cm/s for Olaf and the ball after the collision.

If the ball were to hit Olaf and bounce off in the opposite direction, then the final momentum of the ball would be equal to the initial momentum, but with a negative sign since it is now moving in the opposite direction. Therefore, the final momentum would be (-4.24 kg*m/s).

To calculate the final speed of Olaf after the collision, we can use the equation P=mv again, but this time solving for v.