Understanding the Problem
We have a wooden trolley of mass 1.2 kg initially at rest on a rough bench. A ball with mass 0.52 g (which is 0.00052 kg) travels and embeds itself into the trolley. After embedding, the trolley moves at 0.065 m/s.
What is Impulse?
Impulse is the product of the force applied on an object and the time duration for which the force is applied. It is also equal to the change in momentum of the object.
Step-by-step Solution
- Convert the mass of the ball to kilograms:
0.52 g = 0.52 / 1000 = 0.00052 kg
- Calculate the final velocity of the combined trolley and ball:
Given as 0.065 m/s.
- Calculate the initial momentum of the system:
- The trolley is initially at rest, so its momentum is 0.
- The ball is moving, but its initial velocity is unknown (we are not asked to find it for impulse).
- Calculate the change in momentum (impulse) on the trolley:
The trolley's initial velocity is 0 m/s and final velocity is 0.065 m/s.
Impulse on trolley = change in momentum = mass × (final velocity - initial velocity)Impulse = 1.2 kg × (0.065 m/s - 0) = 1.2 × 0.065 = 0.078 kg·m/s
Final Answer:
The impulse exerted on the trolley is 0.078 kg·m/s.
Summary:
Impulse can be calculated as the change in momentum of the trolley. Since the trolley was at rest and then moves after the collision, the impulse it experienced equals the trolley's mass times its change in velocity.