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 thats possible. ====================================================== 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 im not sure.