Question

A 57.8-kg skateboarder starts out with a speed of 1.98 m/s. He does 82.3 J of work on himself by pushing with his feet against the ground. In addition, friction does -232 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 8.47 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give the absolute value.

Answer 1

here,

the mass of skateboarder , m = 57.8 kg

the initial velocity , u = 1.98 m/s

the work done by him , W1 = 82.3 J

the work done by friction , Wff = - 232 J

final velocity , v = 8.47 m/s

using Work energy theorm

W1 + Wff + Wg = 0.5 * m * ( v^2 - u^2)

82.3 - 232 + (- dUg) = 0.5 * 57.8 * (8.47^2 - 1.98^2)

dUg = - 2110 J

the change in gravitational potential energy is - 2110 J

b)

the vertical height of the skater changed , h = dUg /(m * g)

h = - 2110 /(57.8 * 9.81) m

h = - 3.72 m