A 0.224-kg volleyball approaches a player horizontally with a speed of 18.0 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?
kg·m/s
(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.
N
a. Impulse = 0.224 * 22 =
b. V = Vo + a*t = -22, 18 + a*0.06 = -22, 0.06a = -40, a = 667 m/s^2.
F = M*a = 0.224* (-667) =
To solve this problem, we need to use the principle of conservation of momentum and the definition of impulse.
(a) Impulse is defined as the change in momentum of an object. It can be calculated using the equation:
Impulse = Change in momentum
Momentum is defined as the product of mass and velocity. In this case, the initial and final momenta of the ball can be calculated using the given information.
Initial momentum = mass × initial velocity
Final momentum = mass × final velocity
The change in momentum is given by the difference between the final and initial momenta.
So,
Impulse = Final momentum - Initial momentum
(b) Average force can be calculated using the following equation:
Average force = Change in momentum / Time
We already know the change in momentum from part (a), and the time is given in the problem.
Now, let's calculate the answers:
(a) Impulse = Final momentum - Initial momentum
To find the final and initial momenta, we multiply the mass of the ball by the respective velocities given in the problem.
Initial momentum = 0.224 kg × 18.0 m/s
Final momentum = 0.224 kg × (-22.0 m/s) [opposite direction, so negative]
Impulse = (-0.224 kg × 22.0 m/s) - (0.224 kg × 18.0 m/s)
Calculate the values to find the result.
(b) Average force = Change in momentum / Time
We already know the change in momentum from part (a), and the time is given as 0.0600 s.
Average force = Change in momentum / 0.0600 s
Use the value of the change in momentum calculated in part (a) and divide it by 0.0600 s to find the result.
Perform the calculations to get the final answers.