A box of mass m is initially at rest on a horizontal surface. A constant horizontal force of 2 mg is applied to the box, directed to the right. The coefficient of friction changes with the distance

Question

A box of mass m is initially at rest on a horizontal surface. A constant horizontal force of $\frac{mg}{2}$ is applied to the box, directed to the right. The coefficient of friction changes with the distance pushed as $μ = μ_{0} x$ , where x is the distance from initial location. For what distance is the box pushed until it comes to rest again.

Options:

Answer:

B

Solution:

Work-energy until the box stops again:

$\frac{m g}{2} x = \int_{0}^{x} μ_{0} x^{'} m g d x^{'} = \frac{m g μ _{0} x ^{2}}{2}$

$x = \frac{1}{μ _{0}}$

Ans. (B)

TestHub · Accepted Answer

Work-energy until the box stops again: 2 m g ​ x = ∫ 0 x ​ μ 0 ​ x ′ m g d x ′ = 2 m g μ 0 ​ x 2 ​ x = μ 0 ​ 1 ​ Ans. (B)

Physics - W.E.P. Question with Solution | TestHub

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