Finding speed using energy equations

  • #1

Homework Statement


Two masses are connected by a light string running over a frictionless pulley as shown below. The system is initially at rest and the incline is frictionless. If m1 = 10.0 kg, m2 = 8.00 kg and the incline makes a 30o angle from the horizontal, use energy methods to find the speed of the 8.00 kg mass just as the 10.0 kg mass reaches the ground 4.00 m below. (Hint: Think about how far the second mass will rise vertically as the first mass drops 4.00 m downward.)

mAlo1.png


Homework Equations


KEf + Uf = KEi + Ui
(.5)mvf² + mgyf = (.5)mvi² + mgyi

The Attempt at a Solution


I'm really not sure what to do here. Here is one of my attempts.

(.5)(18)(vf)² +(18)(9.8)(0) = (.5)(18)(0)² + (18)(9.8)(4)

Solving for vf I get vf = 8.854, which is not the correct answer.

I'm pretty confused here and am not even sure if I am using the equation I need to be using. Any help would be greatly appreciated.

Thanks
 

Answers and Replies

  • #2
PhanthomJay
Science Advisor
Homework Helper
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Homework Statement


Two masses are connected by a light string running over a frictionless pulley as shown below. The system is initially at rest and the incline is frictionless. If m1 = 10.0 kg, m2 = 8.00 kg and the incline makes a 30o angle from the horizontal, use energy methods to find the speed of the 8.00 kg mass just as the 10.0 kg mass reaches the ground 4.00 m below. (Hint: Think about how far the second mass will rise vertically as the first mass drops 4.00 m downward.)


Homework Equations


KEf + Uf = KEi + Ui
(.5)mvf² + mgyf = (.5)mvi² + mgyi

The Attempt at a Solution


I'm really not sure what to do here. Here is one of my attempts.

(.5)(18)(vf)² +(18)(9.8)(0) = (.5)(18)(0)² + (18)(9.8)(4)

Solving for vf I get vf = 8.854, which is not the correct answer.

I'm pretty confused here and am not even sure if I am using the equation I need to be using. Any help would be greatly appreciated.

Thanks
You essentially have the right equation, but you are not correctly calculating the potential energy U correctly. For example, initially, one mass is 4 m above ground, and the other is at the ground. They have different potential energies, both initially and finaly. They do, however, have the same speed, so your Kinetic energy terms are correct.
 
  • #3
Ok I got that Yf of mass2 is 2. And if I write the equation for each mass I get:

mass1
(.5)(18)(vf)² + (18)(9.8)(0) = (.5)(18)(0) + (18)(9.8)(4)

mass2
(.5)(18)(vf)² + (18)(9.8)(2) = (.5)(18)(0) + (18)(9.8)(0)

Is that right? Does that help me at all?
 
  • #4
PhanthomJay
Science Advisor
Homework Helper
Gold Member
7,170
509
Why are you sing 18 kg as the mass of mass 1? And 18 kg as the mass of mass 2? Correct those numbers. Then add up both equations to get the total initial energy and total final energy. Otherwise your equations are correct for the y terms in your U calcs.
 
  • #5
Thanks a lot! I changed the weights and then added the two equations and solved for vf and ended up with the correct answer. I was pretty clueless as to how to solve this question initially, but now I think I am starting to get it. Thanks again!
 

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