Question

Gravitational PE = mgh
show that the height change of the block is given by
h=L(1-cos0)

Answer 1

The height change of the block, h, can be expressed as h = L(1 - cosθ), where L is the maximum height and θ is the angle between the initial and final positions of the block.

Step-by-step explanation:

The height change of the block, h, can be expressed as h = L(1 - cosθ), where L is the maximum height and θ is the angle between the initial and final positions of the block. To prove this, we can start with the equation for gravitational potential energy (GPE): GPE = mgh. If we assume that the block starts from the lowest point of its motion, the initial height is zero, and the GPE is also zero. When the block reaches its maximum height, the GPE is at its maximum. Using the equation GPE = mgh, we can equate it to the maximum GPE at height L, which gives us mgh = mgL. Dividing both sides by mg, we get h = L. Now, if we consider the angle θ between the initial and final positions, we can use trigonometry to express the height change in terms of θ: h = L - Lcosθ = L(1 - cosθ), which is the desired expression.