Conical pendulum
A 0.25 kg ball is attached to a light string of length 0.80 m. The ball moves in a horizontal circle at constant speed while the string makes an angle of 35° with the vertical. Take g = 9.81 m s⁻².
Calculate:
a) the radius of the circular path;
b) the tension in the string;
c) the speed of the ball.
Worked answer
Solution
- Step 1
Radius:
r = 0.80 sin 35° = 0.459 m. - Step 2
Vertical equilibrium:
T cos 35° = mg. - Step 3
T = 0.25 × 9.81 / cos 35° = 2.99 N. - Step 4
The horizontal component provides the centripetal force.
- Step 5
tan 35° = v² / rg. - Step 6
v = √(rg tan 35°) = 1.78 m s⁻¹.
Final answer
Radius = 0.459 m; tension = 2.99 N; speed = 1.78 m s⁻¹.
Common mistake
Treating the entire tension force as the centripetal force rather than its horizontal component.
Concepts tested
- circular motion
- force components
- centripetal force
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