Question

A 2kg block is released 4m from a massless spring with a force constant K=100N/m that is aong a plane inlined at 30°. If the coefficient of kinetic friction between the plane and the block is 0.2, find the maximum compression.

Answer 1

Explanations & Calculations

• Refer to the sketch attached.
• Also, refer to the algebraic solution which you can substitute values into to get the required answer.

• Consider conservation of mechanical energy from location A to C. Here the energy is measured with respect to C at which we consider the level of zero potential energy.

$\qquad\qquad \begin{aligned} \small mgh&=\small \frac{1}{2}kx^2+f(d+x)\\ \small mgh&=\small \frac{1}{2}kx^2+\mu_kR(d+x)\\ \small mg([d+x]\sin\theta)&=\small \frac{1}{2}kx^2+\mu_kmg\cos\theta.(d+x)\\ \end{aligned}$

• Here R is the normal force on the block from the incline, and it is equal to the component of the weight of the box that is perpendicular to the incline.

• Here $\small d=4m$ , $\small \theta =30^0,$ $\small k=100\,Nm^{-1}$, $\small \mu_k=0.2$ and $\small x =$ the compression.
• You can substitute and get the answer, here you will get a quadratic function of x you can solve it for x.