Linear Momentum/Energy Loss

[lo31415926535]

Homework Statement

A 1110 kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9900 kg truck moving in the same direction at 20.0 m/s (Fig. P9.21). The velocity of the car right after the collision is 18.0 m/s to the east.

image: http://www.webassign.net/sb5/p9-21.gif

(a) What is the velocity of the truck right after the collision?

(b) How much mechanical energy is lost in the collision? (Use input values with an adequate number of significant figures to calculate this answer.)

(c) Account for this loss in energy. (Select all that apply.)
Kinetic
Sound
Internal energy
Elastic Potential
Heat
Gravitational Potential

Homework Equations

m1v1i + m2v2i = m1v1f + m2v2f
K=.5mv^2

The Attempt at a Solution

So I figured out parts a and b, but I cannot get part c.
Honestly, I do not remember anything like this question from class.
So far I these were my guesses:
(1) just kinetic
(2) kinetic, internal, elastic
(3) kinetic, elastic

But the truth is I don't really know what this means, and I want to stop guessing and actually understand it…
I think kinetic would be one of them because both vehicles slow down.
I don't know what else though

Thanks for your help

 

[tiny-tim]

welcome to pf!

hi lo31415926535! welcome to pf!

(b) How much mechanical energy is lost in the collision? (Use input values with an adequate number of significant figures to calculate this answer.)

(c) Account for this loss in energy. (Select all that apply.)
Kinetic
Sound
Internal energy
Elastic Potential
Heat
Gravitational Potential

i think they mean account for mechanical-energy-before minus mechanical-energy-after

if all the energy was included (and not merely the mechanical energy), then the difference would be zero

so, essentially, they're asking you to list the energy that isn't mechanical energy

 

[HallsofIvy]

You should be able to drop "Gravitational Potential Energy" from that list- the vehicles don't go up at all! And the same for "Elastic Potential Energy". In fact just seeing "potential" in those should tell you they cannot be responsible for loss of mechanical energy in a collision.

 

[lo31415926535]

thank you both! i got it :)

 

[Nickie]

!



As a scientist, it is important to understand the concept of linear momentum and energy loss in collisions. In this situation, we have a car of mass 1110 kg and a truck of mass 9900 kg colliding with each other. The initial velocity of the car is 25.0 m/s and the initial velocity of the truck is 20.0 m/s, both moving in the same direction. After the collision, the car's velocity is 18.0 m/s to the east. Using the conservation of momentum equation, we can solve for the final velocity of the truck to be 20.7 m/s to the east.

Now, let's focus on the energy loss in this collision. From our calculations, we can see that the kinetic energy of the system (car + truck) before the collision is greater than the kinetic energy after the collision. This difference in energy is known as the energy lost in the collision. To calculate this, we can use the equation for kinetic energy, K=.5mv^2, and plug in the values for the initial and final velocities of the system. This gives us an energy loss of 105,150 J.

Now, to answer part c, we need to understand what types of energy can be lost in a collision. Kinetic energy is one form of energy that can be lost, as we can see in this situation. Sound energy can also be lost, as the collision would produce sound waves. Internal energy is another form of energy that can be lost, as the collision may cause the vehicles to deform or result in friction, which would generate heat and therefore, energy loss. Elastic potential energy can also be lost, as the collision may cause deformation of the vehicles' materials. Heat energy can also be lost, as mentioned before, due to friction during the collision. Finally, gravitational potential energy can also be lost, as the vehicles' positions and heights may change after the collision.

In this specific situation, the energy loss is mainly due to the decrease in kinetic energy of the system, as well as some internal energy and elastic potential energy losses. Therefore, the correct answer for part c would be: Kinetic, Internal energy, and Elastic Potential. It is important to note that the specific types of energy lost in a collision can vary depending on the situation and should be analyzed carefully in each case.