Question

A 1.45-kg block is pushed against a vertical wall by means of a spring (k = 860 N/m). The coefficient of static friction between the block and the wall is 0.36. What is the minimum compression in the spring to prevent the block from slipping down? g

Answer 1

Answer:

The minimum compression in the spring is  $d=0.0459m$

Explanation:

From the question we are told that

                     The mass of the block is $m_b = 1.45kg$

                     The spring constant is $k =860 N/m$

                      The coefficient of static friction is  $\mu = 0.36$

The mathematical relationship between the wight of the block and the force exerted by the spring is    

                        $W_b = F_s$

Where $W_b$ is mathematical represented as $W_b = mg$ and

           $F_s$ is mathematically represented as $F_s = \mu * k *d$

Where d is minimum length of compression in the spring to prevent the block from slipping

              Now the relation can be wrtten as

                          $mg = \mu *k * d$

making d the subject we have

                   $d = \frac{mg}{\mu * k}$

                      $= \frac{1.45* 9.8 }{0.36 *860}$

                      $d=0.0459m$