A(n) 0.364 kg soccer ball approaches a player
horizontally with a speed of 19.7 m/s. The
player illegally strikes the ball with her hand
and causes it to move in the opposite direction
with a speed of 22.4 m/s.
What is the magnitude of the impulse delivered
to the ball by the player?
Answer in units of kg · m/s
Impulse=changemomentum
=.364*(Vf-Vi)=.364(22.4+19.7)
6.08
To find the magnitude of the impulse delivered to the ball by the player, we can use the impulse-momentum principle which states that the impulse delivered to an object is equal to the change in momentum of the object.
The magnitude of impulse is given by the formula:
Impulse = |Δp| = |m * Δv|
Where:
Δp is the change in momentum of the ball
m is the mass of the ball
Δv is the change in velocity of the ball
The initial momentum of the ball is given by:
p_initial = m * v_initial
The final momentum of the ball is given by:
p_final = m * v_final
The change in momentum is given by:
Δp = p_final - p_initial = m * v_final - m * v_initial
Substituting the given values:
m = 0.364 kg (mass of the ball)
v_initial = 19.7 m/s (initial velocity)
v_final = -22.4 m/s (final velocity in opposite direction)
Δp = 0.364 kg * (-22.4 m/s) - 0.364 kg * 19.7 m/s
Calculating the change in momentum:
Δp = -8.1536 kg·m/s - 7.1628 kg·m/s
= -15.3164 kg·m/s
Since we are interested in the magnitude of the impulse, we take the absolute value:
Impulse = |Δp| = |-15.3164 kg·m/s|
≈ 15.32 kg·m/s
Therefore, the magnitude of the impulse delivered to the ball by the player is approximately 15.32 kg·m/s.
To determine the magnitude of the impulse delivered to the ball, we can use the equation:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass (m) and its velocity (v).
The initial momentum of the ball before the player strikes it can be calculated as:
Initial momentum = mass × initial velocity
Final momentum of the ball after the player strikes it can be calculated as:
Final momentum = mass × final velocity
The change in momentum is therefore:
Change in momentum = Final momentum - Initial momentum
Now, let's calculate each of these quantities:
Given:
Mass of the ball (m) = 0.364 kg
Initial velocity (v1) = 19.7 m/s
Final velocity (v2) = -22.4 m/s (opposite direction)
Initial momentum = mass × initial velocity
Initial momentum = 0.364 kg × 19.7 m/s
Final momentum = mass × final velocity
Final momentum = 0.364 kg × (-22.4 m/s)
Change in momentum = Final momentum - Initial momentum
Now, let's substitute the values and calculate the magnitude of the impulse:
Change in momentum = (0.364 kg × -22.4 m/s) - (0.364 kg × 19.7 m/s)
The negative sign for final momentum is because the velocity is in the opposite direction.
When you perform the calculations, you get:
Change in momentum ≈ -16.23744 kg·m/s
The magnitude of impulse is the absolute value of the change in momentum:
Magnitude of impulse ≈ | -16.23744 kg·m/s |
Magnitude of impulse ≈ 16.23744 kg·m/s
Therefore, the magnitude of the impulse delivered to the ball by the player is approximately 16.23744 kg·m/s.