Energy, Work and circular motion

[quick]

ok this first one is rated as a fairly tough problem.

1) A pendulum is formed from a small ball of mass m on a string of length L. As the figure shows, a peg is height h = L/3 above the pendulum's lowest point. From what minimum angle theta must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?

http://s93755476.onlinehome.us/knight.Figure.10.54.jpg

so far i have set up the equation T + W = mv^2/R. since the tension of the rope is so that there is no slack, T = 0. so i get mv = mv^2/R and the masses cancel. for V, i found out that the minimum velocity is just sqrt(r*g). R = 2L/3 and h = L - Lcos(theta). however when i tried plugging all the data in, i get L-Lcos(theta) = 1/2*(2L/3). so then solving for theta i get arccos((2/3)*L/L) but when i try it, it says it doesn't depend on L or h. it wants the answer in degrees which i don't see how that's possible.
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2) A 23.0 kg box slides 4.0 m down the frictionless ramp shown in the figure, then collides with a spring whose spring constant is 150 N/m. At what compression of the spring does the box have its maximum velocity?

http://s93755476.onlinehome.us/knight.Figure.10.69.jpg

i know i have to take the derivative of something and set equal to 0 to find the maximum. but of what equation I am not sure.

 

[ponjavic]

Let's look at 1)
You're very close
sin(a)=1/3L/L
a=arcsin(1/3)
Or in your case arccos(2/3)
You only missed that L/L=1 :P so the angle is arcsin(1/3)

 

[Doc Al]

Regarding problem #1:

so far i have set up the equation T + W = mv^2/R. since the tension of the rope is so that there is no slack, T = 0. so i get mv = mv^2/R and the masses cancel. for V, i found out that the minimum velocity is just sqrt(r*g).

Right, but you'll have an easier time of it if you think in terms of energy, not speed.

R = 2L/3 and h = L - Lcos(theta). however when i tried plugging all the data in, i get L-Lcos(theta) = 1/2*(2L/3).

Now you lost me. For one, R = L/3. What does h need to be to give the mass its needed speed as it reaches the top of its motion? (Hint: What is the height of the mass at the top of the motion?)

Regarding problem #2:

i know i have to take the derivative of something and set equal to 0 to find the maximum. but of what equation I am not sure.

Use conservation of energy to get an expression for the kinetic energy as a function of spring compression. That's what you need to maximize.