Question

A pendulum has a velocity of 2.5 m/s at the bottom of its swing. Using the law of conservation of energy, what is the maximum height of the pendulum's swing if there is no friction acting on it?

Answer 1

The maximum height of the pendulum's swing is 0.32 m

Step-by-step explanation:

The Principle Of Conservation Of Mechanical Energy

In the absence of friction, the total mechanical energy is conserved. That means that

Em=U+K is constant, being U the potential energy and K the kinetic energy

U=mgh

`\displaystyle K=(mv^2)/(2)`

At the bottom of the swing, the pendulum has zero potential energy but its kinetic energy is at maximum. At the top of the swing, the pendulum has zero kinetic energy and the potential energy is at maximum.

Thus, applying the principle of conservation of mechanical energy:

`\displaystyle mgh = (mv^2)/(2)`

Simplifying by m:

`\displaystyle gh = (v^2)/(2)`

Solving for h:

`\displaystyle h = (v^2)/(2g)`

Substituting:

`\displaystyle h = (2.5^2)/(2*9.8)`

h = 0.32 m

The maximum heigth of the pendulum's swing is 0.32 m