Cart A (mass 10kg) and cart B (mass= 10kg) are connected by a compressed spring. When the spring is released, cart A has a velocity of 5m/s east. Find:
a. momentum of cart A
b. momentum of cart B
c. velocity of cart B
There should be a figure to go with this question. If there are no other forces acting other than the spring, and the center of mass of the two carts remains fixed, then
a) Momentum of cart A = 10 kg*5 m/s (east) = 50 kg m/s east-50 kg m/s
The minus sign means west.
(c) Cart B momentum divided by 10 kg
To find the momentum of an object, you need to multiply its mass by its velocity.
a. Momentum of cart A:
Cart A has a mass of 10 kg and a velocity of 5 m/s east.
The formula for momentum is p = m * v.
So, the momentum of cart A is 10 kg * 5 m/s = 50 kg·m/s east.
b. Momentum of cart B:
Since the carts are connected, the total momentum of the system should be conserved. If cart A has a momentum of 50 kg·m/s east, then cart B should have an equal but opposite momentum in order to conserve momentum.
So, the momentum of cart B is -50 kg·m/s west.
c. Velocity of cart B:
Momentum is defined as the product of mass and velocity. To find the velocity of cart B, rearrange the momentum formula, p = m * v, to solve for velocity.
The formula becomes v = p / m.
So, the velocity of cart B is -50 kg·m/s west divided by its mass of 10 kg, which gives us -5 m/s west.
Therefore, the answers are:
a. The momentum of cart A is 50 kg·m/s east.
b. The momentum of cart B is -50 kg·m/s west.
c. The velocity of cart B is -5 m/s west.