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Two blocks, A and B, with masses 10 kg and 15 kg respectively, are placed side-by-side on a horizontal surface. A horizontal force of 200 N is applied to block A. The coefficient of friction between t

Physics

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Answer

(b)\text{(b)}

Step-by-step solution

6 steps
  1. Identify the given values.

    Mass of block A, mA=10 kgm_A = 10 \text{ kg}
    Mass of block B, mB=15 kgm_B = 15 \text{ kg}
    Applied horizontal force, Fapplied=200 NF_{applied} = 200 \text{ N}
    Coefficient of friction between the blocks and the surface, μ=0.2\mu = 0.2
    Acceleration due to gravity, g=10 m/s2g = 10 \text{ m/s}^2

  2. Calculate the total mass of the system.

    Since the blocks are in contact and move together, we can treat them as a single system.
    Total mass, M=mA+mBM = m_A + m_B

    M=10 kg+15 kg=25 kgM = 10 \text{ kg} + 15 \text{ kg} = 25 \text{ kg}
  3. Calculate the total normal force.

    The normal force (NN) acting on the system is equal to its total weight.

    N=M×gN = M \times g N=25 kg×10 m/s2=250 NN = 25 \text{ kg} \times 10 \text{ m/s}^2 = 250 \text{ N}
  4. Calculate the total friction force.

    The friction force (ffrictionf_{friction}) opposing the motion is given by μN\mu N.

    ffriction=μ×Nf_{friction} = \mu \times N ffriction=0.2×250 N=50 Nf_{friction} = 0.2 \times 250 \text{ N} = 50 \text{ N}
  5. Calculate the net force acting on the system.

    The net force (FnetF_{net}) is the applied force minus the friction force.

    Fnet=Fapplied−ffrictionF_{net} = F_{applied} - f_{friction} Fnet=200 N−50 N=150 NF_{net} = 200 \text{ N} - 50 \text{ N} = 150 \text{ N}
  6. Calculate the acceleration of the system.

    Using Newton's second law, Fnet=M×aF_{net} = M \times a, where aa is the acceleration of the system.

    a=FnetMa = \frac{F_{net}}{M} a=150 N25 kga = \frac{150 \text{ N}}{25 \text{ kg}} a=6 m/s2a = 6 \text{ m/s}^2

    The acceleration of the system is 6 m/s26 \text{ m/s}^2. This matches option (b).

    The final answer is (b)\text{(b)}.

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