A 3 kg cart is moving along when it strikes a 2 kg cart (initially at rest). The velocity of the two-cart combination after the collision is 4 m/s. Calculate the velocity of the 3 kg cart before the collision.
3x + 2(0) = (3+2)(4)
x = 6.67 m/s
To calculate the velocity of the 3 kg cart before the collision, we can use the law of conservation of momentum. The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision.
First, let's define some variables. Let v1 be the velocity of the 3 kg cart before the collision, and v2 be the velocity of the 2 kg cart before the collision. The equation for conservation of momentum is:
(m1 * v1) + (m2 * v2) = (m1 * V1) + (m2 * V2)
Where:
m1 and m2 are the masses of the carts
v1 and v2 are the velocities of the carts before the collision
V1 and V2 are the velocities of the carts after the collision
Given:
m1 = 3 kg
m2 = 2 kg
V1 = 4 m/s
v2 = 0 m/s (since the 2 kg cart is initially at rest)
We can substitute these values into the equation and solve for v1:
(3 kg * v1) + (2 kg * 0 m/s) = (3 kg * 4 m/s) + (2 kg * 4 m/s)
3 kg * v1 = 12 kg*m/s
Dividing both sides of the equation by 3 kg, we get:
v1 = 4 m/s
Therefore, the velocity of the 3 kg cart before the collision is 4 m/s.