two suitcases are on a 7.89 m high ramp to passengers waiting in a baggage terminal. The top suitcase is released from rest, and it slides down the ramp and hits the second suitcase. If the suitcase at the top has a mass of 16.6 kg and the other suitcase has a mass of 33.2 kg, what is their combined speed if an inelastic collision is achieved? Assume the ramp to be frictionless.
m1v1i+m2v2i=(m1+m2)vf
Hope this helps :)
To determine the combined speed of the suitcases after an inelastic collision, we need to use the principle of conservation of momentum. Let's break down the problem into steps:
1. Calculate the potential energy of the top suitcase at the top of the ramp:
The potential energy (PE) can be calculated using the formula PE = mgh, where m is the mass (16.6 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ramp (7.89 m).
PE = 16.6 kg * 9.8 m/s^2 * 7.89 m = 1,218.042 joules
2. Calculate the initial velocity of the top suitcase at the bottom of the ramp using the principle of conservation of energy:
The potential energy at the top is equal to the kinetic energy (KE) at the bottom of the ramp. Therefore, we can use the equation KE = 0.5 * m * v^2, where v is the velocity.
1,218.042 joules = 0.5 * 16.6 kg * v^2
Solving for v: v^2 = (2 * 1,218.042 joules) / 16.6 kg
v^2 = 146.988 m^2/s^2
v = √146.988 m/s ≈ 12.127 m/s
3. Since the top suitcase is released from rest, its initial velocity is 0 m/s, and its final velocity after the collision is the same as the combined velocity of both suitcases.
4. Apply the principle of conservation of momentum to find the final velocity:
The total momentum before the collision is given by p = m1 * v1 + m2 * v2, where m1 and m2 are the masses of the suitcases, and v1 and v2 are their respective velocities.
Initially, the first suitcase has a mass of 16.6 kg and a velocity of 0 m/s.
Initially, the second suitcase has a mass of 33.2 kg and a velocity of 0 m/s.
After the collision, the two suitcases move together with a combined final velocity, which can be represented as v_final.
Therefore, the equation becomes: 0 + 0 = (16.6 kg * 0 m/s) + (33.2 kg * v_final)
Solving for v_final: 0 = 0 + (33.2 kg * v_final)
v_final = 0 m/s
Hence, after the inelastic collision, the combined speed of the suitcases is 0 m/s. This means they come to a stop after colliding.