Kinetic Energy & Work Problem -- Tractor Pull Competition

[Lori]

Homework Statement

Homework Equations

W = ΔKE
W = KE_f-KE_i

The Attempt at a Solution

W = .5mv_f² -.5mv_i²
I know that final KE for A is 4 times the KE of B because for A ... KE_f = 1/2 m (2v)^2
4KE = 1/2 m v ^2 for A

I don't know what initial KE for both of them are... so how do i know if that had equal losses of energy to friction??

 

[Doc Al]

so how do i know if that had equal losses of energy to friction??

How would you determine the energy loss due to friction? Hint: How would you calculate the work done by friction?

 

[Lori]

Hmmmm. I see where this might go. Let me see:

W_friction = F_friction*d
F_friction = μ_k*N
N = mg --> Normal force is same for both cases

F_frction = same for both cases

thus...! W_friction = F_f*d (same for both blocks right cause same distance too)

Energy loss is W_friction = energy of friction loss

I think that is it, so it proves that they loss equal amounts of friction.Also, couldn't i have found the answer by elimination? I know that b) is definitely false because there is friction and it's loss to displacement. I also know a) , d), e) is falso because I found that KE for A is 4 times B which doesn't fit for these choices... so what's left is c) --which i thought would be false, but it was proved otherwise.

 

[Doc Al]

I think that is it, so it proves that they loss equal amounts of friction.

Good job!

Also, couldn't i have found the answer by elimination?

Only if you were sure about d & e being false, which requires knowing something about the energy lost to friction.