Question

If two gliders of equal mass m and equal and opposite initial velocity v collide and stick together, using equation (78), derive a formula for the total initial kinetic energy, the total final kinetic energy, and the amount of energy converted to heat, in terms of m and v?

Answer 1

In a collision where two gliders of equal mass and opposite velocity collide and stick together, the total initial kinetic energy is mv². After the collision, the final kinetic energy is 0, and the energy converted to heat is mv².

Step-by-step explanation:

If two gliders of equal mass m and equal and opposite initial velocity v collide and stick together, the total initial kinetic energy (KEi) can be calculated using the formula KEi = ½mv2 + ½mv2 for each glider, which simplifies to KEi = mv2 when combined. Since the masses are equal and velocities are opposite, they cancel each other out in terms of momentum. After the collision, because they stick together and their velocities become zero, the total final kinetic energy (KEf) is 0, which means all initial kinetic energy has been converted to other forms of energy, such as heat.

The amount of energy converted to heat can be derived by finding the difference between the initial and final kinetic energies: Heat energy = KEi - KEf = mv2 - 0 = mv2.