A railroad car with a mass of 1.93 ✕ 104 kg moving at 3.12 m/s joins with two railroad cars already joined together, each with the same mass as the single car and initially moving in the same direction at 1.04 m/s.
What is the decrease in kinetic energy during the collision?
J
to conserve momentum,
(1.93*10^4)(3.12) + (2)(1.93*10^4)(1.04) = 3(1.93*10^4)(v)
3.12+2.08 = 5.79v
v = 0.898 m/s
Old KE = 1/2 m*3.12^2 + 1/2 * 2m * 1.04^2 = 5.949m
new KE = 1/2 * 3m * 0.898^2 = 1.209m
loss of KE = 4.739m = 9.147*10^4 J
To find the decrease in kinetic energy during the collision, we need to first calculate the initial total kinetic energy before the collision and the final total kinetic energy after the collision. The difference between these two values will give us the decrease in kinetic energy.
1. Calculate the initial kinetic energy before the collision:
The formula for kinetic energy is given by:
K.E. = 1/2 * m * v^2
For the single car:
Mass (m1) = 1.93 ✕ 10^4 kg
Velocity (v1) = 3.12 m/s
K.E.1 = 1/2 * m1 * v1^2
For the two cars already joined together:
Mass (m2) = 2 * m1 = 2 * 1.93 ✕ 10^4 kg
Velocity (v2) = 1.04 m/s
K.E.2 = 1/2 * m2 * v2^2
2. Calculate the final kinetic energy after the collision:
Since the cars are joined together after the collision, their velocities will become the same. Let's denote the final velocity as v_f.
For the three cars joined together:
Mass (m3) = 3 * m1 = 3 * 1.93 ✕ 10^4 kg
Velocity (v_f) = ?
K.E.3 = 1/2 * m3 * v_f^2
3. Calculate the decrease in kinetic energy:
The decrease in kinetic energy (ΔK.E.) is given by the difference between the initial and final kinetic energies:
ΔK.E. = (K.E.1 + K.E.2) - K.E.3
Substitute the values into the equation and calculate the decrease in kinetic energy.