Question

A 1 170.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 800.0 kg truck moving in the same direction at 20.000 m/s. The velocity of the car right after the collision is 18.000 m/s to the east. (a) What is the velocity of the truck right after the collision? (Give your answer to five significant figures.)   m/s east (b) What is the change in mechanical energy of the car-truck system in the collision?  J (c) Account for this change in mechanical energy.

Answer 1

Concepts and reason

The concepts used to solve this problem are the conservation of momentum, law of conservation of energy, and the change in kinetic energy.

Initially, use the concept of conservation of momentum to calculate the speed of the truck after collision.

Use the initial and final kinetic energy to find the change in mechanical energy of the system.

Finally, use the law of conservation of energy to account the change in mechanical energy.

Fundamentals

The law of conservation of energy states that “energy the energy can neither be created nor destroyed”.

The expression for the momentum is as follows:

Here, the momentum is , the mass is , and the velocity is .

The expression for the conservation of momentum for two masses is as follows:

Here, the mass of the first body is , the initial velocity of the first mass is , the mass of the second body is , the initial velocity of the second mass is , the final velocity of the first mass is , and the final velocity of the second mass is .

The expression for the kinetic energy is as follows:

Here, the kinetic energy is .

(a)

The expression for the conservation of momentum for the system is as follows:

Here, the mass of car is , the mass of truck is , the initial speed of car is , the initial speed of truck is , the final speed of car is , and final speed of truck is .

Rearrange the expression for .

Substitute for , for , for , for , and for .

(b)

The expression for the initial kinetic energy is as follows:

Here, the initial kinetic energy is .

Substitute for , for , for , and for .

The expression for the final kinetic energy of the cars is as follows:

Here, the final kinetic energy is .

Substitute for , for , for , and for .

The expression for the change in mechanical energy is as follows:

Here, the change in mechanical energy is .

Substitute for and for .

(c)

According to conservation of energy, the energy can neither be created nor destroyed.

The loss in mechanical energy is converted to energy like heat, sound, and so on.

Ans: Part a

The speed of the truck after collision is .

Part b

The change in mechanical energy is .

Part c

The loss in mechanical energy is converted to energy like heat, sound, and so on.