Question

What average mechanical power (in W) must a 64.5 kg mountain climber generate to climb to the summit of a hill of height 285 m in 49.0 min? Note: Due to inefficiencies in converting chemical energy to mechanical energy, the amount calculated here is only a fraction of the power that must be produced by the climber's body.

Answer 1

Answer:61.275 W

Explanation:

Given

Mass of climber $m=64.5 kg$

Height to climb $h=285 m$

Time taken $t=49 min \approx 2940 s$

Now Using  Work-energy Theorem work done is given by

$W=m g h$

$W=64.5\times 9.8 \times 285$

$W=180148.5 J$

$W=180.148 kJ$

Now  Average Mechanical Power is given by

$P=\frac{W}{\Delta t}$

$P=\frac{180.148}{2940}=0.0612 kW$

$P=61.275 W$