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Kinetic and Static Friction

AP Physics 1· difficulty 4/5

Block A (mass 4 kg4\,\text{kg}) sits on top of block B (mass 6 kg6\,\text{kg}), which rests on a frictionless floor. The coefficient of static friction between A and B is μs=0.40\mu_s = 0.40. A horizontal force FF is applied to block B. What is the maximum FF for which the two blocks move together (without slipping)? Use g=10 m/s2g = 10\,\text{m/s}^2.

  • A

    Fmax⁡=16 NF_{\max} = 16\,\text{N}

  • B

    Fmax⁡=60 NF_{\max} = 60\,\text{N}

  • C

    Fmax⁡=24 NF_{\max} = 24\,\text{N}

  • D

    Fmax⁡=40 NF_{\max} = 40\,\text{N}

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Explanation

Maximum acceleration of A is amax⁡=μsg=4 m/s2a_{\max} = \mu_s g = 4\,\text{m/s}^2. Both blocks move together with mass 10 kg10\,\text{kg}, so Fmax⁡=(mA+mB)amax⁡=10⋅4=40 NF_{\max} = (m_A + m_B) a_{\max} = 10 \cdot 4 = 40\,\text{N}.

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