A volleyball is spiked so that its incoming velocity of +3.6 m/s is changed to an outgoing velocity of -16 m/s. The mass of the volleyball is 0.27 kg. What impulse does the player apply to the ball?
Answer will be in kg*m/s
Impulse=mv(final)-mv(initial)
impulse(kgm/s)=.27(-16)-.27(3.6)
outgoing is the initial velocity and incoming is final velocity though
To find the impulse applied to the ball, we can use the impulse-momentum principle, which states that the impulse on an object is equal to the change in its momentum.
The formula for impulse is given by:
Impulse = Change in momentum
We can calculate the change in momentum using the formulas:
Change in momentum = final momentum - initial momentum
The initial momentum can be calculated by multiplying the mass of the volleyball by its initial velocity:
Initial momentum = mass * initial velocity
The final momentum can be calculated by multiplying the mass of the volleyball by its final velocity:
Final momentum = mass * final velocity
Substituting these values into the formula for impulse:
Impulse = Final momentum - Initial momentum
Let's plug in the given values:
Mass of the volleyball (m) = 0.27 kg
Initial velocity (u) = +3.6 m/s
Final velocity (v) = -16 m/s
Initial momentum = mass * initial velocity = 0.27 kg * 3.6 m/s = 0.972 kg*m/s
Final momentum = mass * final velocity = 0.27 kg * (-16 m/s) = -4.32 kg*m/s
Impulse = Final momentum - Initial momentum
Impulse = -4.32 kg*m/s - 0.972 kg*m/s
Impulse = -5.292 kg*m/s (rounded to three decimal places)
Therefore, the player applies an impulse of -5.292 kg*m/s to the ball.
To find the impulse applied to the volleyball, you can use the impulse-momentum equation:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass * velocity
Change in momentum, therefore, can be calculated as the final momentum minus the initial momentum:
Change in momentum = final momentum - initial momentum
In this case, the final momentum is the product of the mass and the final velocity, while the initial momentum is the product of the mass and the initial velocity:
final momentum = mass * final velocity
initial momentum = mass * initial velocity
Substituting these values into the equation for change in momentum, we get:
Change in momentum = (mass * final velocity) - (mass * initial velocity)
Now, let's calculate the impulse applied to the ball using the given values:
Mass of the volleyball = 0.27 kg
Initial velocity = +3.6 m/s
Final velocity = -16 m/s
Change in momentum = (0.27 kg * -16 m/s) - (0.27 kg * 3.6 m/s)
Now, calculate it:
Change in momentum = (-4.32 kg*m/s) - (0.972 kg*m/s)
Change in momentum = -5.292 kg*m/s
Therefore, the player applied an impulse of -5.292 kg*m/s to the ball.
Note that the impulse is negative since the final velocity is in the opposite direction of the initial velocity.