Nitha Mulungu
Sep 10
1000kg truck travelling at straight track at speed of 12m/s collide with identical stationary truck.If truck lock together after collision, calculate the common speed and the loss of kinetic energy?
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ChatGPT
Sep 10
To solve this problem, we can use the principle of conservation of momentum and conservation of energy.
1. Conservation of momentum:
Before the collision:
Initial momentum = mass x velocity = 1000kg x 12m/s = 12000 kg m/s
After the collision:
Final momentum = (1000kg + 1000kg) x V (common speed)
Final momentum = 2000kg x V
According to the principle of conservation of momentum:
Initial momentum = Final momentum
12000 = 2000V
V = 12000 / 2000
V = 6 m/s
Therefore, the common speed after the collision is 6 m/s.
2. Loss of kinetic energy:
Initial kinetic energy = 0.5 x mass x velocity^2
Initial kinetic energy = 0.5 x 1000kg x (12m/s)^2
Initial kinetic energy = 0.5 x 1000kg x 144m^2/s^2
Initial kinetic energy = 72000 J
Final kinetic energy = 0.5 x (1000kg + 1000kg) x (6m/s)^2
Final kinetic energy = 0.5 x 2000kg x 36m^2/s^2
Final kinetic energy = 36000 J
Loss of kinetic energy = Initial kinetic energy - Final kinetic energy
Loss of kinetic energy = 72000 J - 36000 J
Loss of kinetic energy = 36000 J
Therefore, the loss of kinetic energy during the collision is 36000 Joules.
1. Conservation of momentum:
Before the collision:
Initial momentum = mass x velocity = 1000kg x 12m/s = 12000 kg m/s
After the collision:
Final momentum = (1000kg + 1000kg) x V (common speed)
Final momentum = 2000kg x V
According to the principle of conservation of momentum:
Initial momentum = Final momentum
12000 = 2000V
V = 12000 / 2000
V = 6 m/s
Therefore, the common speed after the collision is 6 m/s.
2. Loss of kinetic energy:
Initial kinetic energy = 0.5 x mass x velocity^2
Initial kinetic energy = 0.5 x 1000kg x (12m/s)^2
Initial kinetic energy = 0.5 x 1000kg x 144m^2/s^2
Initial kinetic energy = 72000 J
Final kinetic energy = 0.5 x (1000kg + 1000kg) x (6m/s)^2
Final kinetic energy = 0.5 x 2000kg x 36m^2/s^2
Final kinetic energy = 36000 J
Loss of kinetic energy = Initial kinetic energy - Final kinetic energy
Loss of kinetic energy = 72000 J - 36000 J
Loss of kinetic energy = 36000 J
Therefore, the loss of kinetic energy during the collision is 36000 Joules.
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Google Gemini AI
Sep 10
1. Calculate the total kinetic energy before the collision:
Kinetic energy = 1/2 - mass - velocity^2
Kinetic energy before = 1/2 - 1000 kg - 12 m/s^2 = 72,000 J
2. Calculate the velocity after the collision (assuming perfectly inelastic collision):
Momentum is conserved, so the total momentum before the collision is equal to the total momentum after the collision:
Momentum before = mass - velocity before
Momentum after = (mass of both trucks) - velocity after
Momentum before = 1000 kg - 12 m/s
Momentum after = 2000 kg - velocity after
Equating the two equations, we get:
Velocity after = Momentum before / 2000 kg = 12 m/s / 2 = 6 m/s
3. Calculate the loss of kinetic energy:
Loss of kinetic energy = Initial kinetic energy - Final kinetic energy
Final kinetic energy = 1/2 - 2000 kg - 6 m/s^2 = 36,000 J
Loss of kinetic energy = 72,000 J - 36,000 J = 36,000 J
Therefore, the common speed after the collision is 6 m/s, and the loss of kinetic energy is 36,000 J.
Kinetic energy = 1/2 - mass - velocity^2
Kinetic energy before = 1/2 - 1000 kg - 12 m/s^2 = 72,000 J
2. Calculate the velocity after the collision (assuming perfectly inelastic collision):
Momentum is conserved, so the total momentum before the collision is equal to the total momentum after the collision:
Momentum before = mass - velocity before
Momentum after = (mass of both trucks) - velocity after
Momentum before = 1000 kg - 12 m/s
Momentum after = 2000 kg - velocity after
Equating the two equations, we get:
Velocity after = Momentum before / 2000 kg = 12 m/s / 2 = 6 m/s
3. Calculate the loss of kinetic energy:
Loss of kinetic energy = Initial kinetic energy - Final kinetic energy
Final kinetic energy = 1/2 - 2000 kg - 6 m/s^2 = 36,000 J
Loss of kinetic energy = 72,000 J - 36,000 J = 36,000 J
Therefore, the common speed after the collision is 6 m/s, and the loss of kinetic energy is 36,000 J.
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