Consider a frictionless track as shown in the figure below. A block of mass m1 = 5.75 kg is released from A. It makes a head on elastic collision at B with a block of mass m2 = 8.00 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision. Point A is 5.oom above the ground.
To calculate the maximum height to which block m1 rises after the collision, we can use the principle of conservation of mechanical energy.
First, we need to find the kinetic energy before and after the collision.
1. Kinetic energy before the collision:
The block at A, m1, is released from rest, so its initial kinetic energy is zero.
Kinetic energy before collision = 0
2. Kinetic energy after the collision:
Since the collision is elastic, the total kinetic energy of the system is conserved.
Total initial kinetic energy = Total final kinetic energy
Now, let's find the final kinetic energy after the collision.
The block m1 will rise after the collision to a certain height, H. At that height, its velocity will momentarily become zero (v = 0).
The final kinetic energy of m1 = 0 (since v = 0)
The initial kinetic energy of m2 = 0 (since m2 is initially at rest)
Therefore, the total final kinetic energy = 0
Next, we can find the potential energy (PE) at the maximum height achieved by m1.
2. Potential energy at the maximum height (PE):
The potential energy at the maximum height is given by the formula PE = m1 * g * H, where g is the acceleration due to gravity.
We need to find H, so rearrange the formula:
H = PE / (m1 * g)
Now, let's find the potential energy at the maximum height.
Since the total initial kinetic energy = total final kinetic energy, the change in kinetic energy is zero. This means that the potential energy is equal to the decrease in kinetic energy.
The decrease in kinetic energy (∆KE) = KE before the collision - KE after the collision
Therefore:
∆KE = 0 - 0 = 0
The potential energy at the maximum height (PE) = ∆KE = 0
Thus, the maximum height (H) to which m1 rises after the collision is 0 meters.
Note: In this problem, since it is mentioned that the track is frictionless, and there is no other external force acting on the system, the mechanical energy remains conserved.