A cart of mass M1 = 6.00 kg and initial speed = 4.00 m/s collides head on with a second cart of mass M2 = 4.00 kg at rest. Assuming that the collision is elastic, find the speed of M2 after the collision.
write the conservatoin of momentum equation, you get two unknowns, which are the final speeds of each cart.
solve this equation for one of the speeds in terms of the other.
Then, write the conservation of energy equation. PUT the value of the expression you just found above in for one of the speeds, you then have an equation with one unknown.
Have fun, a lot of algebra.
To find the speed of M2 after the collision, we can use the principle of conservation of momentum. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity. Therefore, the momentum of cart M1 before the collision can be calculated as follows:
Momentum(M1) = Mass(M1) * Velocity(M1)
= M1 * V1
Given:
Mass (M1) = 6.00 kg
Initial Velocity (V1) = 4.00 m/s
Using the same logic, the momentum of cart M2 before the collision can be calculated as:
Momentum(M2) = Mass(M2) * Velocity(M2)
= M2 * V2
Given:
Mass (M2) = 4.00 kg
Velocity (V2) = 0 m/s (since M2 is at rest)
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
Momentum(M1) + Momentum(M2) = Momentum(M1) + Momentum(M2)
Since M2 is at rest initially, its momentum before the collision is zero. Hence, we can rewrite the equation as:
M1 * V1 = M1 * V1' + M2 * V2'
where V1' and V2' are the velocities of M1 and M2 after the collision, respectively.
Since the collision is elastic, kinetic energy is conserved as well. Therefore, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Mathematically, this can be expressed as:
(1/2) * Mass(M1) * Velocity(M1)^2 + (1/2) * Mass(M2) * Velocity(M2)^2 = (1/2) * Mass(M1) * Velocity(M1')^2 + (1/2) * Mass(M2) * Velocity(M2')^2
Using the given values, we can substitute:
(1/2) * 6.00 kg * (4.00 m/s)^2 + (1/2) * 4.00 kg * 0^2 = (1/2) * 6.00 kg * V1'^2 + (1/2) * 4.00 kg * V2'^2
Now we have two equations:
1) M1 * V1 = M1 * V1' + M2 * V2'
2) (1/2) * M1 * V1^2 = (1/2) * M1 * V1'^2 + (1/2) * M2 * V2'^2
We can solve these two equations simultaneously to find V2' (the speed of M2 after the collision).