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A force of 18 N is applied horizontally to a 40 kg mass on a horizontal floor, causing it to accelerate at 0.3 m/s². Given g = 10 m/s², find the coefficient of kinetic friction.

Physics

ScanSolve AI Answer

Answer

B) 0.015\text{B) } 0.015

Step-by-step solution

4 steps

To find the coefficient of friction, we need to apply Newton's Second Law.

  1. Identify the given values.

    • Applied Force (FAF_A) = 18 N18 \text{ N}
    • Mass (mm) = 40 kg40 \text{ kg}
    • Acceleration (aa) = 0.3 m/s20.3 \text{ m/s}^2
    • Acceleration due to gravity (gg) = 10 m/s210 \text{ m/s}^2 (commonly used in such problems for simplicity, and it leads to one of the options exactly).
  2. Calculate the normal force (NN).

    Since the mass is on a horizontal floor, the normal force is equal to the gravitational force (weight) acting on the mass.

    N=mgN = mg N=40 kg×10 m/s2N = 40 \text{ kg} \times 10 \text{ m/s}^2 N=400 NN = 400 \text{ N}
  3. Apply Newton's Second Law in the horizontal direction to find the frictional force (FfF_f).

    The net force in the horizontal direction is the applied force minus the frictional force, and this net force causes the acceleration.

    ∑Fx=FA−Ff=ma\sum F_x = F_A - F_f = ma 18 N−Ff=40 kg×0.3 m/s218 \text{ N} - F_f = 40 \text{ kg} \times 0.3 \text{ m/s}^2 18 N−Ff=12 N18 \text{ N} - F_f = 12 \text{ N}

    Now, solve for FfF_f:

    Ff=18 N−12 NF_f = 18 \text{ N} - 12 \text{ N} Ff=6 NF_f = 6 \text{ N}
  4. Calculate the coefficient of friction (μ\mu).

    The frictional force is related to the normal force by the coefficient of friction:

    Ff=μNF_f = \mu N

    Rearrange to solve for μ\mu:

    μ=FfN\mu = \frac{F_f}{N} μ=6 N400 N\mu = \frac{6 \text{ N}}{400 \text{ N}} μ=0.015\mu = 0.015

    The final answer is B) 0.015\text{B) } 0.015.

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