Kinteic Energy, Potential Energy, Mechanical Energy

Question

Suzie (m=56 kg) is skiing at Bluebird Mountain. She is moving at 16 m/s across the crest of a ski hill located 34 m above ground level at the end of the run. Determine: 

a. Suzie's kinetic energy. 

b. Suzie's potential energy relative to the height of the ground at the end

of the run.  

c. Suzie's total mechanical energy at the crest of the hill. 

d. If no energy is lost or gained between the top of the hill and her initial

arrival at the end of the run, then what will be Suzie's total mechanical

energy at the end of the run? 

e. Suzie's speed as she arrives at the end of the run and prior to braking to

a stop.

Answer 1

a. E_k= 1/2 mV²= 1/2 x 56 x 162= 7,168 J

b. E_p= mgh= 56 x 9.81 x 34 = 18,678.24 J

c. E_t= 7,168 + 18,678.24= 25,846.24 J

d. Because no energy is lost or gained between the top of the hill and her initial

arrival at the end of the run, then the total mechanical energy at the end of the run would be equal to the total mechanical energy at the top of the hill or any place across the crest and at the bottom of the crest. Thus, Et= 25,846.24 J

e. Et=1/2 mV_b²

25,846.24= 1/2 x 56 x V_b²

V_b=30.38 m/s