If a stationary cart is struck head-on by a cart with twice mass of the stationary one and a velocity of 5 m/s, what will be the new velocity of the stationary cart if the collision is inelastic?
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(2m)u = (m+2m)v
v= (2/3)u
= (2/3)(5meters/s)
= 3.33 meters/s
Correct, well-done!
:)
To find the new velocity of the stationary cart after the collision, we can use the principle of conservation of momentum.
According to the principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of a cart is given by the product of its mass and velocity: momentum = mass * velocity.
Let's assume the mass of the stationary cart is m1 and its initial velocity is 0 m/s.
The mass of the striking cart is twice the mass of the stationary cart, so the mass of the striking cart is 2m1. The initial velocity of the striking cart is given as 5 m/s.
Therefore, the initial momentum of the stationary cart is 0, and the initial momentum of the striking cart is (2m1 * 5).
Since the collision is inelastic, the two carts stick together after the collision. Let the final velocity of the combined carts be Vf.
The total momentum after the collision is the sum of the momentum of the combined carts: (2m1 + m1) * Vf.
According to the conservation of momentum principle, the initial momentum equals the final momentum:
(2m1 * 5) = (3m1) * Vf
We can now solve this equation for Vf:
10m1 = 3m1 * Vf
Dividing both sides of the equation by 3m1:
Vf = 10/3 m/s
Therefore, the new velocity of the stationary cart after the collision, if the collision is inelastic, is 10/3 m/s.