Before a collision, a 24 kg object is moving at +13 m/s. Find the impulse that acted on the object if, after the collision, it moved at the following velocities.
(a) +8.0 m/s
(b) -8.0 m/s
impulse=mass(Vf-Vi)
To find the impulse that acted on the object, we can use the equation for impulse, which is given by:
Impulse = Change in momentum
The momentum of an object is defined as the product of its mass and velocity:
Momentum = Mass × Velocity
So, the initial momentum of the object before the collision is:
Initial momentum = Mass × Initial velocity
Given that the mass of the object is 24 kg and the initial velocity is +13 m/s, we can calculate the initial momentum:
Initial momentum = 24 kg × 13 m/s = 312 kg·m/s
Now, let's calculate the impulse for each scenario:
(a) After the collision, the object moves at +8.0 m/s.
We use the same equation for momentum to find the final momentum:
Final momentum = Mass × Final velocity
Final momentum = 24 kg × 8.0 m/s = 192 kg·m/s
Impulse = Final momentum - Initial momentum
Impulse = 192 kg·m/s - 312 kg·m/s
Impulse = -120 kg·m/s
Therefore, the impulse that acted on the object when it moves at +8.0 m/s is -120 kg·m/s.
(b) After the collision, the object moves at -8.0 m/s.
Using the same equation for momentum:
Final momentum = Mass × Final velocity
Final momentum = 24 kg × -8.0 m/s = -192 kg·m/s
Impulse = Final momentum - Initial momentum
Impulse = -192 kg·m/s - 312 kg·m/s
Impulse = -504 kg·m/s
Therefore, the impulse that acted on the object when it moves at -8.0 m/s is -504 kg·m/s.
To determine the impulse that acted on the object, 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 to calculate impulse is as follows:
Impulse = Change in Momentum
Now, let's calculate the impulse for each scenario:
(a) +8.0 m/s:
To calculate the change in momentum, we need to subtract the initial momentum from the final momentum:
Initial momentum = mass × initial velocity
Final momentum = mass × final velocity
Initial momentum = 24 kg × 13 m/s = 312 kg·m/s
Final momentum = 24 kg × 8 m/s = 192 kg·m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = 192 kg·m/s - 312 kg·m/s
Change in momentum = -120 kg·m/s
Therefore, the impulse that acted on the object when it moved at +8.0 m/s is -120 kg·m/s.
(b) -8.0 m/s:
Similarly, we'll calculate the change in momentum:
Initial momentum = mass × initial velocity
Final momentum = mass × final velocity
Initial momentum = 24 kg × 13 m/s = 312 kg·m/s
Final momentum = 24 kg × -8 m/s = -192 kg·m/s
Change in momentum = Final momentum - Initial momentum
Change in momentum = -192 kg·m/s - 312 kg·m/s
Change in momentum = -504 kg·m/s
Therefore, the impulse that acted on the object when it moved at -8.0 m/s is -504 kg·m/s.