Question

A 52.1-kg skateboarder starts out with a speed of 1.71 m/s. He does 93.1 J of work on himself by pushing with his feet against the ground. In addition, friction does -213 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 7.39 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

answer)a) the change in kinetic energy= total change in energy ( work energy theorem)

so we have

dK.E=93.1-213-(PEf-PEo)

PEf-PEo=93.1-213-dK.E

dKE=1/2m(vf²-vo²)=1/2*52.1*(7.39²-1.71²)=1346.4724J

so now from eqn 1)

PEf-PEo=93.1-213-1346.4724=-1466.4 J

so the answer is -1466 J or -1470 J or 1466 J or 1470 J ( the answer is positive if they want magnitude)

b) we know the formula for potential energy

P=mgh, so we have

h=P/mg= 1466/52.1*9.8=2.87 m

so the answer is 2.87 m or 2.9 m