Finding speed using energy equations

In summary, the two masses have different potential energies at the beginning and end of the trip, but have the same speed. They both reach the ground at the same time, and the total energy is 8.854 kg.
  • #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.)

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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
 
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  • #2
asdf12321asdf said:

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
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!
 

What is the formula for finding speed using energy equations?

The formula for finding speed using energy equations is speed = √(2 * energy / mass), where energy is measured in joules (J) and mass is measured in kilograms (kg).

What is the relationship between energy and speed?

Energy and speed have a direct relationship. As the energy of an object increases, its speed also increases. This is because energy is the ability to do work, and an object with more energy has the ability to do more work, which translates to a higher speed.

Can I use any energy equation to find speed?

No, not all energy equations can be used to find speed. The energy equation must involve both kinetic energy and potential energy, such as the equation KE + PE = constant. This is because speed is a measure of an object's kinetic energy.

What are the units for speed in energy equations?

The units for speed in energy equations are meters per second (m/s). This is because speed is a measure of distance (meters) traveled over time (seconds).

Can I use energy equations to find speed for any object?

Yes, energy equations can be used to find speed for any object, as long as the object's mass and energy are known. However, for very large or very small objects, special equations may need to be used to account for factors like relativity or quantum mechanics.

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