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1) A 110 N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy of the child--Earth system relative to the child's lowest position at the following times. (a) When the ropes are horizontal. (b) When the ropes make a 30 degree angle with the vertical. (c) When the child is at the bottom of a circular arc.

I tried the formula U = mgh, but I can't get it to work. For (a) I had (110 N)(9.8 m/s^2)(0). For (b) I figured out the hypotenuse of the triangle to be 4, and used that for length, and for (c) I used 2 for length.

2) This one has a picture with it that I'll try to explain. There's a ball at the top of a slide (point a) (height = 6.00m) that's mass is 6.50 kg. The slide dips down and then curves up, and at the top of that curve is point b which is 3.20 m high. Then it dips down again, where point (c) is, which is 2.00 m high. I'm supposed to determine the ball's speed at points b and c and then determine the net work done by the force of gravity in moving the particle from A to C.

3) A 0.408 kg ball is thrown straight up into the air and reaches a maximum altitude of 20.0 m. (a) What is its total mechanical energy? (b) What is the ratio of its kinetic energy to the potential energy of the ball-Earth system when the ball is at an altitude of 10.00 m?

I know that the change in mechanical energy is kinetic energy plus potential energy, but I don't know how to get either of those.

4) A parachutist of mass 59.0 kg jumps out of a balloon at a height of 1400 m and lands on the ground with a speed of 6.20 m/s. How much energy was lost in kJ to air friction during this jump?

5) A child's pogo stick stores energy in a spring (k = 2.40 104 N/m). At position A (xA = -0.130 m), the spring compression is a maximum and the child is momentarily at rest. At position B (xB = 0), the spring is relaxed and the child is moving upward. At position C , the child is again momentarily at rest at the top of the jump. (a) Calculate the total energy of the system if both potential energies are zero at x = 0.(b) Determine xC.(c) Calculate the speed of the child at x = 0.(d) Determine the value of x for which the kinetic energy of the system is a maximum. e) Calculate the child's maximum upward speed.

6) A block of mass m = 3.50 kg situated on a rough incline at an angle of = 37.0° is connected to a spring of negligible mass having a spring constant of 100 N/m. The pulley is frictionelss. The block is released from rest when the spring is unstretched. The block moves 15.0 cm down the incline before coming to rest. Find the coefficient of kinetic friction between block and incline.