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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.

(a) I figured the KE at point XA is zero so the total energy would be all PE. I used the formula U = mgh to get the potential energy. U = (24.5)(9.8)(-.130) = 31.2. (b) Again, at point XC, I figured KE to be zero. Since I figured out the total energy in part A, I took that into part b to find the new height. 31.2 = (24.5)(9.8)(h). For part (c) I used the same formula and figured the height to be -.130 - 0 since that's the change in height from point a to point b. Then I put that into the formula KE = (1/2)mv^2. I got v = 1.60 m/s. For (d) I took the formula U = (1/2)kx^2. 31.2 = (1/2)(2.40x10^4)(x^2). Finally, for part (e) I took U=mgh and got U = (24.5)(9.8)(-.130+.130).

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.

I know that F = -kx. I got F to be -15. I know the normal force is mg. I got n to be 34.3. So finally I took the formula F=(mu)(n). -15 = (mu)(34.3). That makes the coefficient of friction to be .437. I know I'm missing something because I didn't account for the 37 degree incline, though.