An unattended 18.0-kg shopping cart rolls downhill and crashes into a curb at th

Question

An unattended 18.0-kg shopping cart rolls downhill and crashes into a curb at the bottom. It passes a stop sign when its speed is 2.1 m/s and hits the curb at a speed of 7.9 m/s, 3.6 m below the stop sign. (a) Calculate the change in the cart's gravitational potential energy as it rolled from the stop sign to the curb. (b) Calculate the change in the cart's kinetic energy for the same interval. (c) Was the cart's mechanical energy conserved during this interval? Explain in 1-2 sentences, based on the results obtained above.

Explanation / Answer

a. The change in potential energy = mgh = 18 x 9.81 x 3.6 = 635.68 Joules

b. The change in Kinetic energy = 0.5m(v22-v12) = 0.5x18x(7.92-2.12) = 522 Joules.

c. No the energy was not conserved in this interval. Initial Energy = KE + PE = 0.5 x 18 x 2.12 + 18 x 9.81 x 3.6 = 675.37 Joules

Final Energy = Kinetic Energy = 0.5 x 18 x 7.92= 561.7 Joules. Hence initial and final energies are not same so the energy is not conserved.

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