1. Calculate the change in potential energy of a 93.3kg man when he takes an ele

Question

1. Calculate the change in potential energy of a 93.3kg man when he takes an elevator from the first floor to 38th floor, if the distance between floors is 4.05m.

2. A spring has k = 93.2N/m. Determine the work needed to stretch it from x = 3.54cm to x = 5.68cm, where x is the displacement from its unstretched length.

3. A 1276 g mass is on a horizontal surface with mu-k = 0.390, and is in contact with a massless spring with a force constant of 745 N/m which is compressed. When the spring is released, it does 0.93 J of work on the mass while returning to its equilibrium position. Calculate the distance the spring was compressed.

Explanation / Answer

1) Change in PE = m*g*h = 93.3*9.81*4.05*38 = 137153.65 J

2) Wprk done is W = 0.5*k*x^2 = 0.5*93.2*(5.68-3.54)^2*10^-4 = 0.02134 J

3) Work done by the frictional force = 0.5*k*x^2 - Work done by the spring force

-mu_k*m*g*x = (0.5*745*x^2) - 0.93

(0.5*745*x^2) - 0.93 + (0.39*1.276*9.81*x) = 0

x = 0.0438 m = 4.38 cm

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