A 3-kg toy car with a speed of 6 m/s collides head-on with a 2-kg car traveling in the opposite direction with a speed of 4 m/s. If the cars are locked together after the collision with a speed of 2 m/s, how much kinetic energy is lost? (in units of Joules)
Given: M1 = 3kg, V1 = 6m/s.
M2 = 2kg, V2 = -4m/s.
V3 = 2m/s = velocity of M1 and M2 after crash.
KEb = 0.5M1*V1^2+0.5M2*V2^2
KEb = 0.5*3*6^2 + 0.5*2*(-4)^2 = 54+16 = 70 J. = Tot. KE before crash.
KEa = 0.5*3*2^2 + 0.5*2*2^2 = 6+4 = 10 J. = Tot. KE after crash.
KEb-KEa = 70-10 = 60 J. = KE lost.
Well, it seems like those cars had a pretty interesting collision! Let's calculate how much kinetic energy was lost.
The initial kinetic energy of the 3-kg car is given by KE1 = (1/2) * mass1 * speed1^2.
Substituting the values, we have KE1 = (1/2) * 3 kg * (6 m/s)^2 = 54 J.
Similarly, the initial kinetic energy of the 2-kg car is given by KE2 = (1/2) * mass2 * speed2^2.
Substituting the values, we have KE2 = (1/2) * 2 kg * (4 m/s)^2 = 16 J.
Now, after the collision, the cars are locked together and have a speed of 2 m/s.
The final kinetic energy of the combined cars is given by KE_final = (1/2) * (mass1 + mass2) * speed_final^2.
Substituting the values, we have KE_final = (1/2) * (3 kg + 2 kg) * (2 m/s)^2 = 10 J.
So, the kinetic energy lost during the collision is KE_lost = KE1 + KE2 - KE_final = 54 J + 16 J - 10 J = 60 J.
Looks like a lot of kinetic energy was lost in that collision! Maybe they should consider bumper cars next time.
To find the kinetic energy lost, we need to calculate the initial kinetic energy of the system (before the collision) and the final kinetic energy of the system (after the collision), and then subtract the final kinetic energy from the initial kinetic energy.
1. Calculate the initial kinetic energy of the system:
- The initial kinetic energy of the 3-kg car can be calculated using the formula: KE = (1/2) * m * v^2, where m is the mass and v is the velocity.
- The mass of the 3-kg car is 3 kg, and its velocity is 6 m/s.
- Substituting the values into the formula, we get KE1 = (1/2) * 3 kg * (6 m/s)^2.
2. Calculate the initial kinetic energy of the 2-kg car:
- The initial kinetic energy of the 2-kg car can be calculated using the same formula: KE = (1/2) * m * v^2.
- The mass of the 2-kg car is 2 kg, and its velocity is 4 m/s.
- Substituting the values into the formula, we get KE2 = (1/2) * 2 kg * (4 m/s)^2.
3. Calculate the initial total kinetic energy of the system:
- The initial total kinetic energy of the system is the sum of the initial kinetic energies of the two cars: KE_initial = KE1 + KE2.
4. Calculate the final kinetic energy of the system:
- The final kinetic energy of the system can be calculated using the same formula: KE = (1/2) * m * v^2.
- After the collision, the two cars are locked together and have a mass of 3 kg + 2 kg = 5 kg.
- Their velocity is given as 2 m/s.
- Substituting the values into the formula, we get KE_final = (1/2) * 5 kg * (2 m/s)^2.
5. Calculate the kinetic energy lost:
- The kinetic energy lost is the difference between the initial kinetic energy and the final kinetic energy: KE_lost = KE_initial - KE_final.
Let's perform the calculations:
KE1 = (1/2) * 3 kg * (6 m/s)^2 = 54 J
KE2 = (1/2) * 2 kg * (4 m/s)^2 = 16 J
KE_initial = KE1 + KE2 = 54 J + 16 J = 70 J
KE_final = (1/2) * 5 kg * (2 m/s)^2 = 10 J
KE_lost = KE_initial - KE_final = 70 J - 10 J = 60 J
Therefore, the kinetic energy lost is 60 Joules.
To find the amount of kinetic energy lost during the collision, we need to calculate the initial kinetic energy before the collision and the final kinetic energy after the collision.
The formula for kinetic energy is given by:
Kinetic Energy = 1/2 * mass * velocity^2
First, let's calculate the initial kinetic energy of the 3-kg toy car:
Mass1 = 3 kg
Velocity1 = 6 m/s
Initial Kinetic Energy1 = 1/2 * 3 kg * (6 m/s)^2
Similarly, let's calculate the initial kinetic energy of the 2-kg car:
Mass2 = 2 kg
Velocity2 = 4 m/s
Initial Kinetic Energy2 = 1/2 * 2 kg * (4 m/s)^2
The total initial kinetic energy before the collision is the sum of the individual kinetic energies:
Total Initial Kinetic Energy = Initial Kinetic Energy1 + Initial Kinetic Energy2
Next, we need to calculate the final kinetic energy after the collision:
Mass_f = Mass1 + Mass2
Velocity_f = 2 m/s
Final Kinetic Energy = 1/2 * Mass_f * (Velocity_f)^2
Finally, the kinetic energy lost during the collision is the difference between the initial kinetic energy and the final kinetic energy:
Kinetic Energy Lost = Total Initial Kinetic Energy - Final Kinetic Energy
Now we can plug in the values and calculate the kinetic energy lost.