A 2.0 kg puck is moving east at 5.5 m/s. It catches up to and collides with a second identical puck moving due east at 3.0 m/s. The collision is perfectly inelastic.
What is the resulting velocity of the pucks?
What is the initial kinetic energy Eki of the system?
What is the change in kinetic energy, ΔEk, of the system as a result of the collision?
If the mass m is doubled, but the initial velocities are unchanged, does the resulting velocity increase, decrease, or remain unchanged?
2.0*5.5 + 2.0*3.0 = 4.0v
v = 4.25 m/s east
KEi = 1/2 * 2.0 * 5.5^2 + 1/2 * 2.0 * 3.0^2 = 39.25 J
KEf = 1/2 * 4.0 * 4.25^2 = 36.125 J
doubling the mass does not affect the velocity. Note that
2m1*v1 + 2m2*v2 = (2m1+2m2)v
2(m1*v1 + m2*v2) = 2(m1+m2)v
the 2 just cancels out
since KE = 1/2 mv^2, doubling the mass doubles the KE
Well, let's tackle these questions one joke at a time!
What is the resulting velocity of the pucks?
After the collision, the two pucks stick together and move as one. So the resulting velocity can be calculated using the law of momentum conservation. But let's not be too serious about it - I'll just say that the resulting velocity is "totally stuck together"!
What is the initial kinetic energy Eki of the system?
To calculate the initial kinetic energy, we can use the formula Eki = 1/2 * mass * velocity^2 for each puck, and then add them up. But let's just say the initial kinetic energy is like a can of energy drink - it's "energizing"!
What is the change in kinetic energy, ΔEk, of the system as a result of the collision?
Since the collision is perfectly inelastic, the kinetic energy decreases. But let's put a funny spin on it - the change in kinetic energy is like a sad balloon losing air, it goes "whoosh"!
If the mass m is doubled, but the initial velocities are unchanged, does the resulting velocity increase, decrease, or remain unchanged?
Well, if the initial velocities are unchanged, then the resulting velocity will remain the same. But let's make it more fun - it's like trying to carry twice the amount of groceries, but your walking speed remains the same - it's a "balance act"!
Remember, these answers are just for laughs. If you need proper calculations and explanations, please consult your physics textbook or a qualified instructor.
To find the resulting velocity of the pucks after the collision, we can use the principle of conservation of momentum.
Step 1: Calculate the initial momentum of the system.
Momentum (p1) = mass (m1) * velocity (v1)
p1 = (2.0 kg)(5.5 m/s) + (2.0 kg)(3.0 m/s)
p1 = 11 kg.m/s + 6 kg.m/s
p1 = 17 kg.m/s
Step 2: After the collision, the two pucks will stick together and move with a common final velocity.
To find this final velocity, we can use the principle of conservation of momentum again.
Momentum (p2) = Total mass (m1 + m2) * Final velocity (Vf)
p2 = (2.0 kg + 2.0 kg) * Vf
p2 = 4 kg * Vf
Step 3: Apply conservation of momentum:
p1 = p2
17 kg.m/s = 4 kg * Vf
Vf = 17 kg.m/s / 4 kg
Vf = 4.25 m/s
Therefore, the resulting velocity of the pucks after the collision is 4.25 m/s.
To find the initial kinetic energy Eki of the system, we can use the formula:
Eki = 0.5 * mass (m1 + m2) * (velocity1^2 + velocity2^2)
Eki = 0.5 * (2.0 kg + 2.0 kg) * [(5.5 m/s)^2 + (3.0 m/s)^2]
Eki = 0.5 * 4.0 kg * [30.25 m^2/s^2 + 9 m^2/s^2]
Eki = 0.5 * 4.0 kg * 39.25 m^2/s^2
Eki = 78.5 J
Therefore, initial kinetic energy Eki of the system is 78.5 J.
To find the change in kinetic energy ΔEk of the system as a result of the collision, we can subtract the final kinetic energy from the initial kinetic energy.
Since the collision is perfectly inelastic, the kinetic energy is completely converted to other forms of energy like heat or deformation.
ΔEk = Eki - Ekf
ΔEk = 78.5 J - 0 J (as the pucks stick together and have zero velocity after the collision)
ΔEk = 78.5 J
Therefore, the change in kinetic energy ΔEk of the system as a result of the collision is 78.5 J.
If the mass m is doubled but the initial velocities are unchanged, the resulting velocity will change. To find the new resulting velocity, we can use the principle of conservation of momentum as before.
Initial momentum (p1) = (2 * mass (m1) * velocity1) + (2 * mass (m2) * velocity2)
p1 = (2 * 2.0 kg * 5.5 m/s) + (2 * 2.0 kg * 3.0 m/s)
p1 = 22 kg.m/s + 12 kg.m/s
p1 = 34 kg.m/s
After the collision, the two pucks will stick together and move with a common final velocity (Vf) which needs to be calculated.
Momentum (p2) = Total mass (2 * m1 + 2 * m2) * Final velocity (Vf)
p2 = (2 * 2.0 kg + 2 * 2.0 kg) * Vf
p2 = 8 kg * Vf
Now, apply the conservation of momentum:
p1 = p2
34 kg.m/s = 8 kg * Vf
Vf = 34 kg.m/s / 8 kg
Vf = 4.25 m/s
Therefore, the resulting velocity remains unchanged and is still 4.25 m/s even when the mass is doubled and the initial velocities are unchanged.
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.