A block of mass m is pushed against a spring of constant k by a distance x on a rough horizontal surface with coefficient of friction mu. When released, the block travels a distance d before coming to rest. What is the value of d?

A. kx^22 mg — Apply the work-energy theorem. The initial potential energy stored in the spring is converted into work done against friction over the total distance traveled.

JEE Main · PhysicsHard

$A block of mass m is pushed against a spring of constant k by a distance x on a rough horizontal surface with coefficient of friction μ . When released, the block travels a distance d before coming to rest.$

A. $\frac{k x ^{2}}{2 μ m g}$
B. $\frac{k x ^{2}}{μ m g}$
C. $\frac{k x}{μ m g}$
D. $\frac{k x ^{2}}{4 μ m g}$

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Correct answer: A — $\frac{k x ^{2}}{2 μ m g}$

Solution

The initial energy stored in the spring is U = \frac{1}{2} k x^{2} . This energy is dissipated by friction over the total distance d . Thus, \frac{1}{2} k x^{2} = μ m g d, which gives d = \frac{k x ^{2}}{2 μ m g} .

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A block of mass m is pushed against a spring of constant k by a distance x on a rough horizontal surface with coefficient of friction μ. When released, the block travels a distance d before coming to rest.

Solution

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More Laws of Motion practice questions

$A block of mass m is pushed against a spring of constant k by a distance x on a rough horizontal surface with coefficient of friction μ . When released, the block travels a distance d before coming to rest.$