Two carts with masses of 4.3 kg and 3.9 kg move toward each other on a frictionless track with speeds of 5.6 m/s and 5.0 m/s, respec- tively. The carts stick together after colliding head-on.
Find their final speed.
To find the final speed of the carts after colliding, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Momentum is defined as the product of mass and velocity:
Momentum = mass * velocity
The momentum of an object in one direction is positive, while the momentum in the opposite direction is negative.
Given:
Mass of cart 1 (m1) = 4.3 kg
Mass of cart 2 (m2) = 3.9 kg
Initial velocity of cart 1 (v1) = 5.6 m/s (moving to the right)
Initial velocity of cart 2 (v2) = 5.0 m/s (moving to the left)
Before the collision, the momentum of cart 1 can be calculated as follows:
Momentum1 = m1 * v1
Before the collision, the momentum of cart 2 can be calculated as follows:
Momentum2 = m2 * v2
Since the carts stick together after the collision, their masses combined would be m1 + m2, and their final velocity would be the same.
After the collision, the momentum of the combined carts can be calculated as follows:
Combined Momentum = (m1 + m2) * final velocity
Since momentum is conserved, the total momentum before the collision is equal to the total momentum after the collision:
Momentum1 + Momentum2 = Combined Momentum
Substituting the values:
m1 * v1 + m2 * v2 = (m1 + m2) * final velocity
Solving for the final velocity:
final velocity = (m1 * v1 + m2 * v2) / (m1 + m2)
Plugging in the given values:
final velocity = (4.3 kg * 5.6 m/s + 3.9 kg * 5.0 m/s) / (4.3 kg + 3.9 kg)
Calculating this expression will give you the final velocity.
conservation of momentum
M1*V1+M2*V2=(M1+M2)V
solve for V