A pitcher throws a fastball during a ballgame. The velocity of the ball is 44 m/s. The mass of the ball is 150 grams. The catcher catches the ball in his glove at 0.2 seconds.
a) Compute the impulse the glove exerts catching the ball.
I'm lost on part a.
b) Compute the force exerted to catch the ball.
F = (0.15 kg) (44 m/s) / 0.2 seconds = 33 N (is this correct?)
impulse=massball*velocitiyball=.150*44
b is correct.
Thank you!
a) To compute the impulse the glove exerts while catching the ball, we can use the formula for impulse:
Impulse = change in momentum
The momentum of an object is defined as the product of its mass and velocity. So, we need to calculate the change in momentum of the ball while it is caught.
Change in momentum = final momentum - initial momentum
Given:
Initial velocity of the ball (u) = 44 m/s
Mass of the ball (m) = 150 grams = 0.15 kg
At rest, the final velocity of the ball (v) is 0 m/s because it comes to a stop when caught. Therefore, the final momentum is:
Final momentum = mass x final velocity = 0.15 kg x 0 m/s = 0 kg·m/s
The initial momentum is:
Initial momentum = mass x initial velocity = 0.15 kg x 44 m/s = 6.6 kg·m/s
Substituting these values into the formula for change in momentum:
Change in momentum = 0 kg·m/s - 6.6 kg·m/s = -6.6 kg·m/s
Note: The negative sign indicates that the momentum of the ball is decreasing.
Therefore, the impulse the glove exerts while catching the ball is 6.6 kg·m/s.
b) To compute the force exerted to catch the ball, we can use the formula:
Force = Impulse / time
Given:
Impulse = 6.6 kg·m/s
Time (Δt) = 0.2 s
Substituting these values into the formula:
Force = 6.6 kg·m/s / 0.2 s = 33 N
So, yes, your calculation of 33 N for the force exerted to catch the ball is correct.
Remember to keep track of units and convert them if necessary for accurate calculations.