Question

A bowling ball is attached to a 4-meter long cable and hung from the ceiling. The cable is kept taut and the ball is raised to an initial height of 1.6 meters above the classroom floor. It is released from rest and allowed to swing as a pendulum. Determine its speed (in m/s) when it is at a height of 1.23 meters above the floor.

Answer 1

In order to solve this problem, we can approach it as a problem of conservation of energy. The equation of energy on the first stage can be written as:

`E_1=m*g*h_1`

On the second stage, the energy will be:

`E_2=m*g*h_2+(m*v^2)/(2)`

Thus, equaling both we'll get:

`mgh_1=mgh_2+(mv^2)/(2)\Rightarrow gh_1=gh_2+(v^2)/(2)`

Isolating v:

`v=\sqrt[\placeholder{⬚}]{2*g*(h_1-h_2)}=\sqrt[\placeholder{⬚}]{2*9.8*(1.6-1.23)}=2.693(m)/(s)`

Then, our final velocity is 2.693 m/s