Question

A pendulum is made up of a metal cylinder of diameter d attached to a thin string. The pendulum passes through a photogate at the lowest point in its motion, as shown in the side view. The photogate measures the time t it takes the cylinder to pass through the photogate. Using this information, the mechanical energy of the system is obtained at its lowest position. The speed of the pendulum is calculated as dt. If the motion of the pendulum does not oscillate perpendicular to the photogate, as shown in the top view, how will this affect calculated total mechanical energy?.

Answer 1

The calculated total mechanical energy will reduce if the oscillation is not perpendicular to the photogate.

Mechanical energy at the lowest position of the pendulum

The mechanical energy at the lowest position of the pendulum is calculated as follows;

$U = K.E = \frac{1}{2}mv^2$

When the direction of the motion changes

let the velocity of the pendulum = vsin(θ)

when the velocity is perpendicular = vsin(90) = v

At any direction different from perpendicular direction, the mechanical energy reduces by;

$\Delta U = \frac{1}{2} mv^2 - \frac{1}{2} m(vsin\theta)^2\\\\\Delta U = \frac{1}{2} m(v^2 - v^2sin^2\theta)\\\\\Delta U = \frac{1}{2} mv^2(1 - sin^2\theta )$

Thus, the calculated total mechanical energy will reduce if the oscillation is not perpendicular to the photogate.

Learn more about mechanical energy here: https://brainly.com/question/24443465