6.12 - Sample problem: potential energy and Niagara Falls
Variables
What is the strategy?
- Use the definition of power as the rate of work done to define an equation for the power of the falls.
- Use the fact that work done by gravity equals the negative of the change in gravitational potential energy to solve for the power.
Physics principles and equations
Power is the rate at which work is performed.
Change in gravitational PE
ǻPE = mgǻh
Work done by gravity
W = íǻPE
Step-by-step solution
We start with the definition of power í work done per unit time í and then substitute in the definition of work done by gravity and the definition
of gravitational potential energy to solve the problem.
This is the theoretical maximum power that could be generated. A real power plant cannot be 100% efficient.
In its natural state, an average of
5.71×10^6 kg of water flowed per
second over Niagara Falls, falling
51.0 m. If all the work done by gravity
could be converted into electric power
as the water fell to the bottom, how
much power would the falls generate?
height of falls h = 51.0 m
magnitude of acceleration due to gravity g= 9.80 m/s^2
potential energy PE
mass of water over falls per unit time m/t = 5.71×10^6 kg/s
power P
work done by gravity W