What is the Kinetic and Internal Energy of a Car-Truck Collision?

[gmagnus]

Homework Statement

A 1200 kg car moving at 88 km/h collides with a 7600 kg truck moving in the same direction at 65 km/h. The two stick together, continuing in their original direction at 68 km/h. Determine the kinetic energy of the center of mass of the (car + truck) system. Determine the internal energy of the (car + truck) system before the collision. Determine the internal energy of the (car + truck) system after the collision.

Homework Equations

m₁v₁ + m₂v₂ = (m₁ + m₂)v_f

Kinetic energy of a system is K = K_cm + K_int

K = 1/2mv²

The Attempt at a Solution

88 km/h converted to 24.4444 m/s
65 km/h converted to 18.0556 m/s

 

[rock.freak667]

You'd need to find the velocity of the (car+truck) system after collision to get the kinetic energy.

 

[thomate1]

68 km/h converted to 18.8889 m/s

Using the equations provided, we can determine the kinetic energy of the center of mass of the system before the collision:

Kcm = 1/2(m1+m2)vcm^2 = 1/2(1200+7600)(18.0556)^2 = 1.2 x 10^6 J

To determine the internal energy before the collision, we need to calculate the kinetic energy of each individual object:

K1 = 1/2m1v1^2 = 1/2(1200)(24.4444)^2 = 4.444 x 10^5 J
K2 = 1/2m2v2^2 = 1/2(7600)(18.0556)^2 = 6.888 x 10^5 J

Therefore, the total internal energy before the collision is 1.233 x 10^6 J.

After the collision, the two objects stick together and continue in their original direction at 68 km/h. Thus, the velocity of the system remains the same and the kinetic energy of the center of mass remains 1.2 x 10^6 J.

However, the internal energy of the system changes as the two objects have now combined into one. The internal energy after the collision can be calculated using the equation Kint = K - Kcm:

Kint = 1.233 x 10^6 J - 1.2 x 10^6 J = 3.3 x 10^4 J

Overall, we can see that the internal energy of the system decreases after the collision, indicating that some of the initial kinetic energy was converted into other forms of energy, such as heat and sound. This is expected in an inelastic collision, where some energy is lost due to deformation and friction between the objects.