Work and Power
6 marks · NormalA student with weight 500 N runs up a set of stairs 4 m high in 10 s.
Calculate the work done against gravity as the student climbs the stairs.
Calculate the student's power output while running up the stairs.
Describe one reason why the actual useful power output of the student might be less than the calculated value.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) 2000 J
(b) 200 W
(c) Because some energy is transferred to heat and sound in the body and surroundings, not all energy goes into climbing.
Also accept: Energy is lost as heat, sound, or movement not directly upwards
Common mistakes: Using mass instead of weight for work done; Missing unit conversions
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses W = F × d correctly
A1 (a) · 1 mark · Obtains correct value for work (2000 J, rounding accepted) (follow-through)
M2 (b) · 1 mark · Uses P = W/t (with answer from a) (follow-through)
A2 (b) · 1 mark · Correct power value (200 W, rounding accepted) (follow-through)
B1 (c) · 2 marks · States and explains a reason for less useful output (e.g., energy lost as heat, sound, inefficient movement)
Worked solution
a) Work done against gravity = weight × height = 500 N × 4 m = 2000 J
b) Power = work done / time = 2000 J / 10 s = 200 W
c) Not all energy produced is converted to useful work (gaining height). Some is lost as heat within muscles, sound, and extra movement.