Step 1: Understand the problem
We have a wooden trolley with a mass of 1.2 kg sitting at rest. A small ball of mass 0.52 g (which is 0.00052 kg) moves towards the trolley, embeds itself in it, and then the combined system (trolley + ball) moves with a speed of 0.065 m/s.
Step 2: Convert all units into standard SI units
- Mass of ball = 0.52 g = 0.00052 kg
- Mass of trolley = 1.2 kg
- Initial speed of trolley = 0 m/s (at rest)
- Final speed of system = 0.065 m/s
Step 3: Use the principle of conservation of momentum
Before collision, only the ball is moving, trolley is at rest.
After collision, ball and trolley move together with speed 0.065 m/s.
So, initial momentum of ball = final momentum of trolley + ball
Let the initial speed of ball be v.
Initial total momentum = momentum of ball + momentum of trolley = m_b * v + m_t * 0 = m_b * v
Final total momentum = (mass of trolley + mass of ball) * final velocity = (m_t + m_b) * 0.065
By conservation of momentum:
m_b * v = (m_t + m_b) * 0.065
Step 4: Calculate the initial speed of the ball
Substitute the masses:
0.00052 * v = (1.2 + 0.00052) * 0.065
0.00052 * v = 1.20052 * 0.065 = 0.07803
v = 0.07803 / 0.00052 ≈ 150.06 m/s
Step 5: Calculate the impulse exerted on the trolley
Impulse is the change in momentum.
Initial momentum of trolley = 0 (at rest)
Final momentum of trolley = mass * velocity = 1.2 kg * 0.065 m/s = 0.078 kg·m/s
So, impulse on the trolley = final momentum - initial momentum = 0.078 - 0 = 0.078 kg·m/s
Summary:
- The impulse exerted on the trolley is 0.078 kg·m/s.
- The initial speed of the ball as it hits the trolley is approximately 150 m/s.