Physics Inelastic Collision: Initial Velocities & Kinetic Energy

[onecoolcat]

Can anyone help me with a physics Inelastic Collision question:

A truck mass weighing 3000kg collides into a car that is at rest weighing mass 1000kg. they stick together after the collision and the kinetic energy loss was 100kj=J. The final velocity after the collision is 15 m/s. I need to find out what the initial velocity of the two vehicles were prior to the collision and change in kinetic energy. My teacher show how to find the velocity AFTER the collision but nothing about how to find the velocity PRIOR to the collision. Can anyone help?

 

[Doc Al]

My teacher show how to find the velocity AFTER the collision but nothing about how to find the velocity PRIOR to the collision.

You use a similar method/equation. The only difference is that you'll be solving for a different unknown.

What's conserved during the collision? Set up a conservation equation.

 

[nlightner]

In an inelastic collision, the kinetic energy of the system is not conserved because some of it is lost to other forms of energy, such as heat or sound. In this case, we know that the kinetic energy loss was 100kJ, which means that the initial kinetic energy of the system was 100kJ higher than the final kinetic energy after the collision.

To find the initial velocities of the two vehicles, we can use the conservation of momentum principle, which states that the total momentum of a system before and after a collision is equal. This can be expressed as:

m1v1 + m2v2 = (m1 + m2)v'

Where m1 and m2 are the masses of the two vehicles, v1 and v2 are their initial velocities, and v' is their final velocity after the collision.

We can rearrange this equation to solve for the initial velocities:

v1 = (m1 + m2)v' - m2v2 / m1

v2 = (m1 + m2)v' - m1v1 / m2

Plugging in the values given in the problem, we get:

v1 = (3000kg + 1000kg) x 15m/s - 1000kg x 0m/s / 3000kg = 11.25m/s

v2 = (3000kg + 1000kg) x 15m/s - 3000kg x 11.25m/s / 1000kg = 3.75m/s

Therefore, the initial velocity of the truck was 11.25m/s and the initial velocity of the car was 3.75m/s.

As for the change in kinetic energy, we can calculate it by subtracting the final kinetic energy from the initial kinetic energy:

Change in kinetic energy = Initial kinetic energy - Final kinetic energy

= (1/2)(3000kg)(11.25m/s)^2 + (1/2)(1000kg)(3.75m/s)^2 - (1/2)(4000kg)(15m/s)^2

= 168,750J - 140,000J = 28,750J

Therefore, the change in kinetic energy is 28,750J, which is the difference between the initial and final kinetic energies.

I hope this helps with your question. Remember to always use the conservation