A 1,500kg truck moving at 15 m/s strikes a 750 kg automobile stopped at a traffic light the vehicle. The vehicles hook bumpers and skid together at 10 m/s. What is the decrease in kinetic energy?
original KE=1/2 1500*25^2
new KE=1/2 (1500+750)10^2
10
To find the decrease in kinetic energy, we need to calculate the initial kinetic energy and the final kinetic energy, and then subtract the final kinetic energy from the initial kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity^2
First, let's calculate the initial kinetic energy of the truck:
Mass of the truck = 1500 kg
Velocity of the truck = 15 m/s
Initial kinetic energy of the truck = 1/2 * 1500 kg * (15 m/s)^2
Next, let's calculate the initial kinetic energy of the automobile:
Mass of the automobile = 750 kg
Velocity of the automobile = 0 m/s (since it is stopped)
Initial kinetic energy of the automobile = 1/2 * 750 kg * (0 m/s)^2
Now, let's calculate the final kinetic energy of the combined vehicles:
Combined mass = 1500 kg + 750 kg = 2250 kg
Combined velocity = 10 m/s
Final kinetic energy of the combined vehicles = 1/2 * 2250 kg * (10 m/s)^2
Now, let's calculate the decrease in kinetic energy:
Decrease in kinetic energy = Initial kinetic energy - Final kinetic energy
Substitute the values we calculated into the formula:
Decrease in kinetic energy = (1/2 * 1500 kg * (15 m/s)^2) - (1/2 * 750 kg * (0 m/s)^2) - (1/2 * 2250 kg * (10 m/s)^2)
Simplifying the equation:
Decrease in kinetic energy = 112,500 J
Therefore, the decrease in kinetic energy is 112,500 Joules.
To determine the decrease in kinetic energy, we need to find the initial and final kinetic energies of the system. The decrease in kinetic energy can then be calculated as the difference between the initial and final kinetic energies.
1. First, let's calculate the initial kinetic energy (KE) of the system.
The formula for kinetic energy is: KE = 0.5 * mass * velocity^2
For the truck:
Mass (m1) = 1,500 kg
Velocity (v1) = 15 m/s
KE1 = 0.5 * 1500 kg * (15 m/s)^2
= 0.5 * 1500 kg * 225 m^2/s^2
= 168,750 J
For the automobile:
Mass (m2) = 750 kg
Velocity (v2) = 0 m/s (as it is stopped)
KE2 = 0.5 * 750 kg * (0 m/s)^2
= 0 J (since the automobile is not moving initially)
2. Next, let's calculate the final kinetic energy of the system after the collision.
Since the truck and automobile bumpers hook and skid together, they move as one unit with a shared velocity. Therefore, the final velocity (vf) is given as 10 m/s.
To calculate the final kinetic energy:
Total mass (m_total) = m1 + m2 = 1500 kg + 750 kg = 2250 kg
KE_final = 0.5 * 2250 kg * (10 m/s)^2
= 0.5 * 2250 kg * 100 m^2/s^2
= 112,500 J
3. Finally, we can calculate the decrease in kinetic energy:
Decrease in KE = KE_initial - KE_final
= 168,750 J - 112,500 J
= 56,250 J
Therefore, the decrease in kinetic energy is 56,250 Joules.