Please Check to See if I'm Doing Work-Energy Problem Correctly

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[SOLVED] Please Check to See if I'm Doing Work-Energy Problem Correctly

Homework Statement



A child riding a bicycle has a total mass of 40 kg. The child approaches the top of a hill that is 10 m high and 100 m long at 5 m/s. If the force of friction between the bicycle and the hill is 20 N, what is the child's velocity at the bottom of the hill?

Homework Equations



K = 1/2 * mv^2, U = mgh, W = delta E, W = Fx * cos(theta)

The Attempt at a Solution



Can someone check to see if I'm doing this correctly. I think what they're trying to say is that you're already at the top.

I would first do K-initial + U-initial = 4420 J. Then Then set that to Fx and solve for F which is 44.2 N. Subtract 20 N from that and you get 24.2 N and multiply it back by x which gives you 242 J. Set that to K-final and solve for v and you get 11 m/s.

Did I do everything correctly?
 
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Answers and Replies

  • #2
Shooting Star
Homework Helper
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Use the energy equation properly. What you have written seems complicated to me. Where is cos theta comin from?

KE at bottom = KE at top + PE at top + Work done against friction.
 
  • #3
Kurdt
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Science Advisor
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I get 11m/s as well and I used the kinematic equations. So I guess you've done everything correctly.
 

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