Question

A pendulum is constructed from a string 0.0530 m long attached to a mass of 0.200 kg. When set into motion, the pendulum completes one oscillation ever 1.50 s. If the pendulum is held at rest and the string is cut, how will it take for the mass to fallthrough the distance of 2.50 m?

Answer 1

To solve this problem we will start from the pendulum period equation. From there we will find the value of gravity. Later it will be possible to apply the linear motion kinematic equations, for which we will use the value of the distance traveled and the gravity in order to find the fall time. The time period of the pendulum is

$T=2\pi\sqrt{\frac{L}{g}}$

Here,

L is the length of the pendulum

g is acceleration due to gravity.

Rearranging to find g,

$g = \frac{4\pi^2 L}{T^2}$

Replacing,

$g = \frac{4\pi^2 (0.0530)}{1.5^2}$

$g = 0.9299m/s^2$

Now using,

$x=v_0 t + \frac{1}{2} gt^2$

Here,

$v_0 =$ Initial velocity (0 because the pendulum is at rest)

t is time taken to cover the distance .

$x = \frac{1}{2}gt^2$

Replacing,

$2.5 = \frac{1}{2} (0.9299) t^2$

Solving for t

$t = 2.3188s$

Therefore it will take to fall through the distance of 2.5m around to 2.31s