Work and Energy - Mission WE2 Detailed Help

A 55-kg mountain climber ascends (climbs) 15 meters up a steep cliff in 45 seconds. The power rating of the mountain climber is ____ W.

Work (W) is calculated from knowledge of the force (F) that acts upon an object, the displacement (d), and the angle (Θ) between the F and d vectors. The formula is
W = F • d • cosine(Θ).

Power (P) is calculated from knowledge of the work done upon an object (W) and the time (t) required to do this work. The formula is

P = W / t

As is often the case in a power problem, the best strategy is to first calculate the work done; then use the work done and the time to calculate the power. See the two equations in the Formula Frenzy section.
The difficulty in this problem pertains to the absence of a stated value for the force applied by the mountain climber. If a climber is ascending a mountain (usually at a slow constant speed), then the applied force required to sustain the motion is equal to the weight of the climber. So in calculating the work done by the climber, assume a constant speed motion and use the weight of the climber. See the Formula Frenzy section.

The mass of an object is mathematically related to its weight by the equation:
Weight = mass • g

where g is the gravitational field strength. The value of g on Earth is 9.8 N/kg (approximately 10 N/kg).


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