H2 Physics 7 - Circular Motion: Conical Pendulum

Step 1 - Set up the problem

A 0.2 kg ball on a 0.8 m string moves as a conical pendulum.

Step 1 - Set up the problem

The string makes 30 degrees with the vertical.

Step 1 - Set up the problem

Find the tension, the radius, and the speed. Take g = 9.81 m/s squared.

Step 2 - Resolve the tension vertically

No vertical acceleration - the ball stays at constant height.

Step 2 - Resolve the tension vertically

Vertically: T cos theta = mg.

Step 2 - Resolve the tension vertically

T cos 30 = 0.2(9.81), so T(0.866) = 1.962.

Step 2 - Resolve the tension vertically

T = 2.27 N.

Step 3 - Find the radius

The radius: r = L sin theta.

Step 3 - Find the radius

r = 0.8 times sin 30 = 0.8 times 0.5 = 0.40 m.

Step 3 - Find the radius

This radius defines the horizontal circle traced by the bob.

Step 4 - Apply Newton's second law radially

The horizontal component of tension supplies the centripetal force.

Step 4 - Apply Newton's second law radially

T sin theta = mv squared / r.

Step 4 - Apply Newton's second law radially

v squared = T sin theta times r / m.

Step 4 - Apply Newton's second law radially

v squared = 2.27(0.5)(0.4) / 0.2 = 2.27.

Step 5 - Find the speed and state the answers

v = 1.51 m/s.

Step 5 - Find the speed and state the answers

Period = 2 pi r / v = 2.51 / 1.51 = 1.66 s.

Step 5 - Find the speed and state the answers

Summary: T = 2.27 N, r = 0.40 m, v = 1.51 m/s.