A 0.255-kg volleyball approaches a player horizontally with a speed of 14.2 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s.
(a) What impulse is delivered to the ball by the player?
(b) If the player's fist is in contact with the ball for 0.0600 s, find the magnitude of the average force exerted on the player's fist
Well, well, well, looks like we have a volleyball player here. Let's calculate some things, shall we?
(a) To find the impulse, we can use the formula:
Impulse = Change in momentum
The initial momentum of the ball is:
Initial momentum = mass × initial velocity
Substituting in the given values, we have:
Initial momentum = 0.255 kg × 14.2 m/s
Now, the final momentum of the ball is:
Final momentum = mass × final velocity
Substituting in the given values again, we have:
Final momentum = 0.255 kg × (-22.0 m/s) [opposite direction]
Now you just need to subtract the final momentum from the initial momentum to find the impulse delivered to the ball by the player.
(b) To find the magnitude of the average force exerted on the player's fist, we can use the formula:
Average force = Impulse / Time
Substituting in the given values, we have:
Average force = [the impulse you calculated in part (a)] / 0.0600 s
Calculating all this should give you the answers you're looking for. Remember, though, that I'm just a clown bot, so don't expect any volleyball jokes from me.
To find the impulse delivered to the ball by the player, we can use the impulse-momentum principle, which states that the impulse on an object is equal to the change in its momentum. The impulse can be calculated using the formula:
Impulse = change in momentum
The momentum of an object is given by the equation:
Momentum = mass × velocity
(a) First, let's calculate the initial and final momenta of the ball. The initial momentum is given by the equation:
Initial momentum = mass × initial velocity
Initial momentum = 0.255 kg × 14.2 m/s
Initial momentum = 3.621 kg·m/s
The final momentum is given by the equation:
Final momentum = mass × final velocity
Final momentum = 0.255 kg × (-22.0 m/s) [since the ball moves in the opposite direction]
Final momentum = -5.61 kg·m/s
Now, we can calculate the change in momentum:
Change in momentum = Final momentum - Initial momentum
Change in momentum = -5.61 kg·m/s - 3.621 kg·m/s
Change in momentum = -9.231 kg·m/s
Therefore, the impulse delivered to the ball by the player is -9.231 kg·m/s.
(b) To find the average force exerted on the player's fist, we can use the formula:
Force = impulse / time
The impulse was already calculated in part (a) as -9.231 kg·m/s. The time of contact is given as 0.0600 s.
Force = -9.231 kg·m/s / 0.0600 s
Force = -153.85 N
The magnitude of the average force exerted on the player's fist is 153.85 N.
To find the impulse delivered to the ball by the player, we can use the principle of conservation of momentum.
The formula for impulse is:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity, so we can calculate the initial and final momenta of the ball.
(a) Calculating the impulse:
Initial momentum (p_initial) = mass of the ball * initial velocity
p_initial = 0.255 kg * 14.2 m/s
Final momentum (p_final) = mass of the ball * final velocity
p_final = 0.255 kg * (-22.0 m/s)
Change in momentum (Δp) = p_final - p_initial
Substituting the values into the equation, we can find the impulse:
Impulse = Δp = (-0.255 kg * 22.0 m/s) - (0.255 kg * 14.2 m/s)
(b) To find the average force exerted on the player's fist, we can use the formula:
Average force = impulse / time
Given that the time of contact between the ball and the player's fist is 0.0600 s, we can plug in the values:
Average force = Impulse / 0.0600 s
By performing the necessary calculations, we can determine the magnitude of the average force exerted on the player's fist.