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Newton's Second Law (Translational Dynamics)

AP Physics 1· difficulty 4/5

θ L

A conical pendulum has length L=1.5 mL = 1.5\text{ m} and the string makes angle θ=25°\theta = 25° with vertical. What is the period? Use g=9.8 m/s2g = 9.8\text{ m/s}^2.

  • A

    1.20 s

  • B

    2.32 s

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  • C

    1.85 s

  • D

    2.95 s

Explanation

Period: T=2πLcos⁡θ/g=2π1.5×0.9063/9.8=2π0.1387≈2π×0.3724≈2.34 sT = 2\pi \sqrt{L \cos\theta / g} = 2\pi \sqrt{1.5 \times 0.9063 / 9.8} = 2\pi \sqrt{0.1387} \approx 2\pi \times 0.3724 \approx 2.34\text{ s}. Closest is 2.32 s.

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