How much work would it take to push a # 5 kg # weight up a # 4 m # plane that is at an incline of # pi / 4 #?
The explanation below includes two possible approaches to this calculation. The answer (in some ways the least interesting bit!) is
There are at least two different ways to calculate the answer to this problem.
The first uses the formula
The distance traveled up the slope will be
The second uses the fact that doing work on something changes its energy. In this case, sliding the object up the ramp increases its height, and therefore its gravitational potential energy.
Calculating the height uses trigonometry and the definition of sine: