Example 10.4: Determine the magnitude of the restoring force for a pendulum bob of mass 100.0 g that has been pulled to an angle of 10° from the vertical.
Given Mass of the bob, m = 100.0 g = 0.1000 kg Angle, θ = 10° Gravitational acceleration, g = 9.8 ms-2 | Required Restoring force, Frest | Formula Frest = -mgsinθ |
Construction: Draw the diagram of a simple pendulum with displacement angle 10°. Analyze the forces acting on the pendulum by resolving the W force into rectangular components. See, the x-component of W balances the tension T in the string and the y-component of W = Wsinθ = mgsinθ drives the pendulum and hence called the restoring force, Frest.
Calculation: Put the values in the formula,
Frest = – 0.1000 × 9.8 sin10° ⇒ Frest = 0.1000 × 9.8 × 0.1736 = 0.170 N
