Calc Angle of Rope Swing for 82kg Man, 1450kg Car

[ganondorf29]

Homework Statement

The rope of a swing is 2.90 m long. Calculate the angle from the vertical at which a 82.0 kg man must begin to swing in order to have the same KE at the bottom as a 1450 kg car moving at 1.11 m/s (2.48 mph).

Homework Equations

k=(m*v^2) / 2
U = mgh

The Attempt at a Solution

I first found the kinetic energy of the car. 1/2*[(1450)*(1.11^2) = kcar. I found kcar to be 893.273 J. Than I used U=mgh to find the height the man must be to have the same amount of kinetic energy. Kcar = 82*9.8*h. I found the height to be 1.11m. Than I set up a triangle and tried cos^-1 = (1.11/2.9) to find theta. I got 67.5 deg, but that's wrong. Any suggestions?

 

[phyguy321]

How do you know that's wrong? Do you have the answer? Is it 22.5?

 

[Hootenanny]

Homework Statement

The rope of a swing is 2.90 m long. Calculate the angle from the vertical at which a 82.0 kg man must begin to swing in order to have the same KE at the bottom as a 1450 kg car moving at 1.11 m/s (2.48 mph).

Homework Equations

k=(m*v^2) / 2
U = mgh

The Attempt at a Solution

I first found the kinetic energy of the car. 1/2*[(1450)*(1.11^2) = kcar. I found kcar to be 893.273 J. Than I used U=mgh to find the height the man must be to have the same amount of kinetic energy. Kcar = 82*9.8*h. I found the height to be 1.11m. Than I set up a triangle and tried cos^-1 = (1.11/2.9) to find theta. I got 67.5 deg, but that's wrong. Any suggestions?

You're very nearly there, just one small mistake. Does his height really make up one of the sides of the triangle that you need?

 

[phyguy321]

Try again

 

[ganondorf29]

I understand what I did wrong now, but how do I apply that to fix them problem?

 

[Hootenanny]

I understand what I did wrong now, but how do I apply that to fix them problem?

Well if the height isn't the adjacent side of the triangle, then what is? Look at the sketch that phyguy provided.

 

[philsfan]

I am actually working on a problem very similar to this one and I found the height of the person, but I am stuck on how you find the angle. I looked at the image given in this thread but it was the same image I had already drawn out in my attempt at solving the problem. My thinking is that if the energy is conserved then at the bottom of the swing there would not be any potential energy, it would be all kinetic, implying that the height at the bottom of the swing would be zero. Therefore the adjacent side of the large triangle would be the length of the rope, but I am not sure how you find the hypotenuse of the triangle when you know the height and the length of the rope. I would appreciate help regarding this question, thanks!