Step 1: Understand the Problem
We have a wooden trolley (mass = 1.2 kg) initially at rest. A ball (mass = 0.52 g) travels horizontally and embeds itself in the trolley.
After the ball hits, the trolley moves with a speed of 0.065 m/s.
Step 2: Convert Units
First, convert the ball's mass from grams to kilograms because SI units must be consistent.
Mass of ball = 0.52 g = 0.52 / 1000 = 0.00052 kg
Step 3: Calculate the Impulse Exerted on the Trolley
Impulse (J) is the change in momentum of an object.
Since the trolley was initially at rest, its initial momentum was 0.
Final momentum of trolley = mass × velocity = 1.2 kg × 0.065 m/s = 0.078 kg·m/s
Impulse exerted on the trolley = change in momentum = final momentum - initial momentum = 0.078 kg·m/s - 0 = 0.078 Ns (Newton-seconds)
Step 4: Calculate the Speed of the Ball as it Hits the Trolley
Since the ball embeds itself in the trolley and both move together, use conservation of momentum:
Initial momentum of ball = Final momentum of trolley + ball
Let v = speed of ball before collision.
(mass of ball) × v = (mass of trolley + mass of ball) × 0.065
So, v = [(1.2 + 0.00052) × 0.065] / 0.00052
Calculate the numerator:
1.20052 × 0.065 ≈ 0.07803
Now divide by 0.00052:
v ≈ 0.07803 / 0.00052 ≈ 150.06 m/s
Final Answers:
- Impulse exerted on the trolley: 0.078 Ns
- Speed of the ball as it hits the trolley: approximately 150 m/s