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Kinetic and Static Friction

AP Physics 1· difficulty 3/5

A 10 kg10~\text{kg} box on a rough floor (μk=0.20\mu_k = 0.20) is pulled by a rope at 37∘37^\circ above horizontal with 80 N80~\text{N} tension (sin⁡37∘=0.60\sin 37^\circ = 0.60, cos⁡37∘=0.80\cos 37^\circ = 0.80, g≈10 m/s2g \approx 10~\text{m/s}^2). Acceleration is closest to

  • A

    3.4 m/s23.4~\text{m/s}^2

  • B

    5.4 m/s25.4~\text{m/s}^2

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  • C

    1.0 m/s21.0~\text{m/s}^2

  • D

    8.0 m/s28.0~\text{m/s}^2

Explanation

Horizontal pull: 80(0.80)=64 N80(0.80) = 64~\text{N}. Normal: N=mg−80(0.60)=100−48=52 NN = m g - 80(0.60) = 100 - 48 = 52~\text{N}. Friction: μkN=10.4 N\mu_k N = 10.4~\text{N}. Net: 64−10.4=53.664 - 10.4 = 53.6. a=5.36≈5.4 m/s2a = 5.36 \approx 5.4~\text{m/s}^2.

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