Question

A 55-kg hiker starts at an elevation of 1600 m and climbs to the top of a 3100-m peak. (a) What is the hiker's change in potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be more than this? Explain why.

Answer 1

Answer

given,

mass of hiker = 55 Kg

elevation at start, h₁ = 1600 m

elevation at top , h₂ = 3100 m

a) change in potential energy

    $\Delta P = m g (h_2 - h_1)$

    $\Delta P = 55 \times 9.8 \times (3100-1600)$

    $\Delta P = 55 \times 9.8 \times 1500$

             ΔP = 808500 J

b) The minimum work required by the hiker will be equal to the change in potential energy.

The minimum work done

  W = Δ PE

      = 808500 J

c) Yes, work done can be more than this because hiker will exert more force to balance the force due to gravity.