A bowling ball of mass 9 kg hits a wall going 11 m/s and rebounds at a speed of 8 m/s. What was the impulse applied to the bowling ball?
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To calculate the impulse applied to the bowling ball, we can use the formula:
Impulse = change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass * velocity
Let's start by calculating the initial momentum of the bowling ball:
Initial momentum = mass * initial velocity
= 9 kg * 11 m/s
= 99 kg·m/s
Next, let's calculate the final momentum of the bowling ball:
Final momentum = mass * final velocity
= 9 kg * 8 m/s
= 72 kg·m/s
Now, we can find the change in momentum by subtracting the initial momentum from the final momentum:
Change in momentum = Final momentum - Initial momentum
= 72 kg·m/s - 99 kg·m/s
= -27 kg·m/s
Impulse is equal to the change in momentum, so the impulse applied to the bowling ball is -27 kg·m/s.
To find the impulse applied to the bowling ball, you can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it.
The momentum of an object is given by the product of its mass and velocity. The symbol for momentum is "p", and it can be calculated using the formula:
p = m * v
where:
p is the momentum,
m is the mass, and
v is the velocity.
In this case, before hitting the wall, the momentum of the bowling ball is given by:
initial momentum = mass * initial velocity = 9 kg * 11 m/s = 99 kg·m/s
After rebounding off the wall, the momentum of the bowling ball is given by:
final momentum = mass * final velocity = 9 kg * 8 m/s = 72 kg·m/s
The change in momentum is simply the difference between the initial and final momentum:
change in momentum = final momentum - initial momentum = 72 kg·m/s - 99 kg·m/s
change in momentum = -27 kg·m/s
Since impulse is defined as the change in momentum, the impulse applied to the bowling ball is 27 kg·m/s in the opposite direction.
impulse = change in momentum
= 9*11 + 9*8
kg m/s