Calculating Energy Absorbed in a Collision: Quad vs. Tree

[jbm1939]

Homework Statement

A 400 lb quad hits a tree moving at 20 mph, if the time of impact is .02 seconds what would the average force be on the tree? Also how much energy would be absorbed in the collision?

Homework Equations

I was able to solve the first part of the question, the force on the tree. I will put my work on that part below, what I am confused about is how to start the part about finding how much energy was absorbed. Any help would be greatly appreciated.

The Attempt at a Solution

20mph = 29.333 fps
F = M(v/t)
so
FΔT=MΔT
F(.02) = (400lbs/32.2ft/s) * (29.3 ft/s)
F = 18,198.8 lbs

 

[24forChromium]

Assuming the object stops completely after collision:

For the force:
force*impact time = impulse;
impulse = change in momentum
momentum = speed * mass

therefore: force = (change in speed)*mass/time

For the energy:
kinetic energy = 0.5 * mass * (velocity)^2
Calculate the change in kinetic energy before and after and you are set.

 

[jbm1939]

so for KE=.5mv^2
=.5(400/32.2)(29.3)^2
= 5332.24
so would this be the amount absorbed by the tree in the impact? their would be no KE after the collision because v=0, so the tree has to absorb all that energy? am i correct with this deduction?

 

[24forChromium]

so for KE=.5mv^2
=.5(400/32.2)(29.3)^2
= 5332.24
so would this be the amount absorbed by the tree in the impact? their would be no KE after the collision because v=0, so the tree has to absorb all that energy? am i correct with this deduction?

As far as I can tell, that is correct. I didn't actually do the calculations because I am not really familiar with imperial units, also, I am not sure what unit of energy that is going to produce, but I trust that your calculations is accurate.

 

[jbm1939]

thank you 24forChromium! its getting to the end of the semester here and my brain is overwhelmed at the moment. this forum is awesome for an extra set of eyes to help you see what you've overlooked.

 

[insightful]

so would this be the amount absorbed by the tree in the impact?

Remember, the original question is: "How much energy would be absorbed in the collision?" Both the tree and the quad absorb part of this energy.

Also, I assume your instructor isn't a stickler about significant figures...

 

[jbm1939]

No he did not say anything about significant figures, I generally just round to the nearest whole number. The question just say how much energy would be absorbed in the collision, so that would be the total amount of kinetic energy correct? What is derived from 1/2mv²?

 

[insightful]

The question just say how much energy would be absorbed in the collision, so that would be the total amount of kinetic energy correct? What is derived from 1/2mv2?

Correct.

About significant figures, the problem implies no more than 3 are suitable, giving an answer of 5330 ft-lbf.
Adding significant figures implies accuracy that simply isn't there.

 

[jbm1939]

Thanks insightful, I'll fix that on my problem.