A block with mass 0.50 kg is forced against a horizontal spring of negligible mass, compressing the spring a distance of 0.20 m (fig). When released, the block moves on a horizontal table top for 1.00 m before coming to rest. The spring constant k is 100 N/m. What is the coefficient of kinetic friction, μk, between the block and the table?

Question

A block with mass 0.50 kg is forced against a horizontal spring of negligible mass, compressing the spring a distance of 0.20 m (fig). When released, the block moves on a horizontal table top for 1.00 m before coming to rest. The spring constant k is 100 N/m. What is the coefficient of kinetic friction, μk, between the block and the table? <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/448fe126852208d2e8c6421615ae8da6-.png" /> (A) 0.40 (B) 0.50 (C) 0.25 (D) None of these

Tardigrade Admin · Accepted Answer

The initial and final kinetic energies are both zero, so the work done by the spring is the negative of the work done by friction,
or

\frac{1}{2} k x^{2} = μ_{k} m g l,

where

l

is the distance the block moves. Solving for

μ_{k},

μ_{k} = \frac{( 1/2 ) k x ^{2}}{m g l}

= \frac{( 1/2 ) ( 100 N / m ) ( 0.20 m ) ^{2}}{( 0.50 k g ) ( 10 m / s ^{2} ) ( 1.00 m )}

= 0.40

0.40

0.50

0.25

None of these

The initial and final kinetic energies are both zero, so the work done by the spring is the negative of the work done by friction, or 21​kx2=μk​mgl, where l is the distance the block moves. Solving forμk​, μk​=mgl(1/2)kx2​ =(0.50kg)(10m/s2)(1.00m)(1/2)(100N/m)(0.20m)2​ =0.40