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the free body diagram shown above is for a 5 kg box on a rough surface being pulled to the right at a constant speed by a string that is at an angle of 30° above the horizontal. the coefficient of kinetic friction between the box and the surface is 0.30. the tension in this string is most nearly:

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onyebuchinnaji

The tension in the string pulling the box is most nearly 17 N.

The given parameters;

  • mass of the box, m = 5 kg
  • inclination of the string, θ = 30°
  • coefficient of kinetic friction, μ = 0.3

The tension on the string is calculated by applying Newton's second law of motion as follows.

[tex]\Sigma F = ma[/tex]

at constant speed, acceleration, a, = 0

[tex]\Sigma F = 0\\\\T_x - \mu F_n = 0\\\\Tcos(\theta) - \mu F_n = 0\\\\Tcos(\theta)= \mu F_n\\\\T = \frac{\mu F_n}{cos(\theta)} \\\\T = \frac{0.3 \times 5 \times 9.8}{cos(30)} \\\\T = 16.97 \ N\\\\T \approx 17 \ N[/tex]

Thus, the tension in the string pulling the box is most nearly 17 N.

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