To solve this problem, we can apply the principle of conservation of momentum, which states that in a collision, the total momentum before the collision is equal to the total momentum after the collision. We can also use the principle of conservation of kinetic energy, which states that in an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Let's break down the problem step by step to find the answers:
1. What is the resulting velocity of the pucks?
Since the collision is perfectly inelastic, the two pucks stick together after the collision. To find the resulting velocity, we can calculate the momentum before and after the collision.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v). So, the total momentum before the collision is:
P_initial = (mass1 * velocity1) + (mass2 * velocity2)
= (2.0 kg * 5.5 m/s) + (2.0 kg * 3.0 m/s)
= 11.0 kg⋅m/s + 6.0 kg⋅m/s
= 17.0 kg⋅m/s
After the collision, the two pucks stick together, so they have the same resulting velocity (v_result). We can calculate the resulting velocity using the principle of conservation of momentum:
P_initial = P_resulting
17.0 kg⋅m/s = (4.0 kg) * (v_result)
v_result = 17.0 kg⋅m/s / 4.0 kg
v_result = 4.25 m/s
Therefore, the resulting velocity of the pucks is 4.25 m/s.
2. What is the initial kinetic energy Eki of the system?
The initial kinetic energy (Ek_initial) of the system can be calculated by adding the kinetic energies of each puck before the collision.
The kinetic energy (Ek) of an object can be calculated using the formula: Ek = (1/2) * mass * velocity^2.
Ek_initial = (1/2) * mass1 * velocity1^2 + (1/2) * mass2 * velocity2^2
= (1/2) * 2.0 kg * (5.5 m/s)^2 + (1/2) * 2.0 kg * (3.0 m/s)^2
= 1.0 kg * 30.25 m^2/s^2 + 1.0 kg * 9.0 m^2/s^2
= 30.25 J + 9.0 J
= 39.25 J
Therefore, the initial kinetic energy of the system is 39.25 Joules.
3. What is the change in kinetic energy, ΔEk, of the system as a result of the collision?
To find the change in kinetic energy (ΔEk) of the system, we can subtract the initial kinetic energy (Ek_initial) from the final kinetic energy (Ek_final).
In this case, the two pucks stick together after the collision, so their final kinetic energy is zero since they are not moving. Thus:
ΔEk = Ek_final - Ek_initial
= 0 J - 39.25 J
= -39.25 J
The change in kinetic energy of the system as a result of the collision is -39.25 Joules.
4. If the mass (m) is doubled, but the initial velocities are unchanged, does the resulting velocity increase, decrease, or remain unchanged?
To answer this question, we need to consider the principle of conservation of momentum. In a collision, the total momentum before the collision is equal to the total momentum after the collision.
If the mass is doubled, the total momentum before the collision will also double to maintain momentum conservation. However, since the initial velocities are unchanged, the resulting velocity will decrease.
Therefore, if the mass is doubled but the initial velocities are unchanged, the resulting velocity will decrease.