a 60 kg person falls off a 15 kg sled moving at 2 m/s. The person doesn't move after falling. Assuming no friction with the ice, and not other net forces acting on the sled, what is the change in velocity of the sled after the person falls off.
To find the change in velocity of the sled after the person falls off, we need to understand the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on it. Momentum is the product of mass and velocity.
Initially, the total momentum of the system (person + sled) is given by:
Initial momentum = (mass of person + mass of sled) × (velocity of sled)
Given:
Mass of person (m₁) = 60 kg
Mass of sled (m₂) = 15 kg
Velocity of sled (v) = 2 m/s
The initial momentum is:
Initial momentum = (60 kg + 15 kg) × (2 m/s)
Now, when the person falls off, the final momentum of the system will be only the momentum of the sled since the person is not moving. The change in velocity of the sled is equal to its final velocity (after the person falls off) minus its initial velocity.
Final momentum = mass of sled × final velocity
Since momentum is conserved, the initial momentum of the system is equal to the final momentum of the system. Therefore:
Initial momentum = Final momentum
(m₁ + m₂) × v = m₂ × final velocity
Now we can solve for the final velocity:
final velocity = (m₁ + m₂) × v / m₂
Plugging in the given values, we get:
final velocity = (60 kg + 15 kg) × (2 m/s) / 15 kg
Calculating the final velocity:
final velocity = 75 kg × (2 m/s) / 15 kg
final velocity = 150 m/s / 15 kg
final velocity = 10 m/s
Therefore, the change in velocity of the sled after the person falls off is 10 m/s.