Answer :
Final answer:
The change in velocity of the 7.3-kg bowling ball after a force of 186 N is applied for 0.40 seconds is 10.2 m/s.
Explanation:
To find the change in velocity of the bowling ball, we can use Newton's second law of motion and the impulse-momentum theorem. The force applied to the bowling ball and the duration for which it is applied (the impulse) will result in a change in momentum, which leads to a change in velocity.
The impulse-momentum theorem states that the impulse on an object is equal to the change in momentum of the object: impulse = change in momentum = force × time.
In this case, the applied force is 186 N and the time interval is 0.40 s. Using the formula:
- Impulse = Force × Time
- Change in momentum = Impulse
- Momentum = mass × velocity
So we get:
Impulse = 186 N × 0.40 s = 74.4 N·s
The change in momentum equals the impulse, thus:
Δ(momentum) = 74.4 kg·m/s
Since the mass of the bowling ball is 7.3 kg, the change in velocity (Δv) can be found by dividing the change in momentum by the mass:
Δv = Δ(momentum) / mass
Δv = 74.4 kg·m/s / 7.3 kg
Δv = 10.2 m/s
Hence, the change in velocity of the bowling ball is 10.2 m/s.
