Learning Object: Simple Pendulum
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The child sitting on the swing has a mass of 24.0 kg. The length of the chain is 2.3 m. At an angle of 45 degrees between the equilibrium and current position, the displacement of the swing is 1.81 m. Using the relationships that the tension and radial component of weight are equal at any point, and that displacement is equal to length times angle, the tension acting on the chain at this point is calculated to be 166.31 N.
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Learning Object: Simple Pendulum
- 1. T H E S I M P L E P E N D U L U M LEARNING OBJECT 2
- 2. PROBLEM • A child with a mass of 24.0 kg sits on a swing with a chain length of 2.3 m. At a certain point, the angle between the swing’s position at equilibrium and the position somewhere during its motion is 45°. What is the displacement of the swing? At this point, what is the tension acting on the chain?
- 3. FIRST STEP: DRAW IT OUT! L m = 45° = /4 s mg mgcos mgsin T m = 24.0 kg mg = - 235.2 N L = 2.3 m KNOWN VALUES:
- 4. SECOND STEP: SOLVE FOR DISPLACEMENT s = L = (2.3)*(/4) = 1.81 m Therefore, the swing’s displacement is 1.81 metres!
- 5. THIRD STEP: SOLVE FOR TENSION Remember: tension and radial components of the weight are equal! T = mgcos = (24)(9.8)cos(/4) = 166.31 N Therefore, the tension acting on the chain is 166.31 N!