Question

A 64.7-kg skateboarder starts out with a speed of 2.44 m/s. He does 119 J of work on himself by pushing with his feet against the ground. In addition, friction does -257 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 7.88 m/s. (a) Calculate the change (PE_f - PE₀) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give the absolute value.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the skateboarder = m = 64.7 kg

Initial speed of the skateboarder = V₁ = 2.44 m/s

Final speed of the skateboarder = V₂ = 7.88 m/s

Work done by the skateboarder on himself by pushing with his feet against the ground = W₁ = 119 J

Work done by friction on him = W₂ = -257 J

Initial potential energy of the skateboarder = PE_i

Final potential energy of the skateboarder = PE_f

The initial potential and kinetic energy of the skateboarder plus the work done on him by the non conservative forces is equal to the final potential and kinetic energy of the skateboarder.

PE_i + mV₁²/2 + W₁ + W₂ = PE_f + mV₂²/2

PE_i + (64.7)(2.44)²/2 + 119 + (-257) = PE_f + (64.7)(7.88)²/2

PE_f - PE_i = -1954.15 J

Vertical height of the skater changed = h

(64.7)(9.81)h - 1954.15

h = 3.079 m

a) Change in gravitational potential energy = PE_f - PE_i = -1954.15 J

b) Vertical height of the skater changed = 3.079 m