A block of mass m = 25 kg has a speed V and is behind a block of mass M = 64 kg that has a speed of 0.50 m/s. The surface is frictionless. The blocks collide and couple.After the collision, the blocks have a common speed of 0.90 m/s. How much kinetic energy is lost in the collision?Express your answer in Joules.
Question
A block of mass m = 25 kg has a speed V and is behind a block of mass M = 64 kg that has a speed of 0.50 m/s. The surface is frictionless. The blocks collide and couple.After the collision, the blocks have a common speed of 0.90 m/s. How much kinetic energy is lost in the collision?Express your answer in Joules.
Solution
To find the amount of kinetic energy lost in the collision, we can use the principle of conservation of momentum.
- First, let's calculate the initial momentum of the system before the collision. The momentum of an object is given by the product of its mass and velocity.
The momentum of the block with mass m is given by p1 = m * V. The momentum of the block with mass M is given by p2 = M * 0.50 m/s.
- Next, let's calculate the final momentum of the system after the collision. Since the blocks couple and have a common speed, their final momentum will be the same.
The final momentum of the system is given by p_final = (m + M) * 0.90 m/s.
- According to the principle of conservation of momentum, the initial momentum of the system should be equal to the final momentum of the system.
Therefore, we can set up the equation: p1 + p2 = p_final.
m * V + M * 0.50 m/s = (m + M) * 0.90 m/s.
- Now, let's solve the equation for V, the initial speed of the block with mass m.
m * V + M * 0.50 m/s = m * 0.90 m/s + M * 0.90 m/s.
m * V + M * 0.50 m/s = (m + M) * 0.90 m/s.
m * V + 0.50 M = 0.90 m + 0.90 M.
m * V - 0.90 m = 0.90 M - 0.50 M.
V = (0.90 M - 0.50 M) / m.
V = 0.40 M / m.
- Now that we have the initial speed V, we can calculate the initial kinetic energy of the block with mass m using the formula: KE = 0.5 * m * V^2.
KE_initial = 0.5 * m * (0.40 M / m)^2.
- Similarly, we can calculate the final kinetic energy of the system using the formula: KE = 0.5 * (m + M) * (0.90 m/s)^2.
KE_final = 0.5 * (m + M) * (0.90 m/s)^2.
- Finally, we can find the amount of kinetic energy lost in the collision by subtracting the final kinetic energy from the initial kinetic energy.
Kinetic energy lost = KE_initial - KE_final.
Substituting the values and solving the equation will give us the answer in Joules.
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