Conservation of Mechanical Energy in rope swing

In summary, Tarzan and Jane, with a combined mass of 130.0 kg, start their swing on a 5.0 m long vine at a 30 degree angle with the horizontal. When Jane, who has a mass of 50.0 kg, releases the vine at the bottom of the arc, Tarzan continues swinging alone. Using the equations for potential and kinetic energy, it can be determined that Tarzan's maximum height on the swing is 2.5 meters.
  • #1
physicsma1391
19
0

Homework Statement



Tarzan and Jane, whose total mass is 130.0 kg, start their swing on a 5.0 m long vine when the vine is at an angle of 30 degrees with the horizontal. At the bottom of the arc, Jane, whose mass is 50.0 kg, releases the vine. What is the maximum height at which Tarzan can land on a branch after his swing continues? (Hint: Treat Tarzan's and Jane's energies as separates quanitities.)

Homework Equations



How to I calculate this?

The Attempt at a Solution



cos60=x/5
x=2.5
h=5-2.5=2.5

ME(i)=ME(f)
GPE=KE(f1)+KE(f2)
mgh=.5mv(f)^2 + .5 mv(f)^2
(130)(9.81)(2.5)=.5(50)v(f)^2 + .5(80)v(f)^2
3188.25=25v(f)^2 + 40v(f)^2

not sure if this is correct or where to go from here??
 
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  • #2
Try this out.

When the swing starts, there is only potential energy.

gh(m1+m2)

At the bottom, there is only kinetic

1/2(m1+m2)v^2. Therefore, equate these 2 quantities and solve for v. Now, Jane (m2) releases off. So the energy on the bottom becomes:

1/2(m1+m2)v^2 - 1/2(m2)v^2 = Total

Finally, this total goes into how high he can go alone.

Total = m1 g h, solve for h. Good luck!
 
  • #3




Your attempt at a solution is on the right track. To calculate the maximum height at which Tarzan can land, you need to solve for v(f) and then use that value to calculate the height using the equation h = (v(f)^2)/(2g). However, it is important to note that the conservation of mechanical energy only applies if there are no external forces acting on the system. In this case, there are other forces at play such as air resistance and friction, which may affect the accuracy of your calculation. Additionally, the angle of the vine and the release point of Jane may also affect the outcome. It is important to consider all these factors when solving for the maximum height.
 

1. What is the concept of conservation of mechanical energy in a rope swing?

The concept of conservation of mechanical energy in a rope swing refers to the principle that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another. In the case of a rope swing, the potential energy of the person at the highest point of the swing is converted into kinetic energy as they swing down, and then back into potential energy as they swing back up.

2. How does the length of the rope affect the conservation of mechanical energy in a rope swing?

The length of the rope does not affect the conservation of mechanical energy in a rope swing. As long as the rope is taut and the person is swinging within its length, the same amount of potential and kinetic energy will be conserved throughout the swing.

3. Does the weight of the person on the rope swing impact the conservation of mechanical energy?

The weight of the person on the rope swing does not have a direct impact on the conservation of mechanical energy. However, a heavier person may require more energy to start and maintain the swing, which could affect the overall conservation of energy.

4. Can friction affect the conservation of mechanical energy in a rope swing?

Friction can affect the conservation of mechanical energy in a rope swing by converting some of the energy into heat. This can cause the swing to slow down over time as energy is lost to friction. However, if the friction is minimal, the conservation of mechanical energy will still hold true.

5. Is the conservation of mechanical energy in a rope swing affected by external forces?

External forces, such as wind or other objects in the swing's path, can affect the conservation of mechanical energy in a rope swing. These forces can either add or subtract energy from the swing, altering the overall conservation of energy. However, as long as these external forces are minimal, the principle of conservation of mechanical energy will still apply.

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