Question

A horizontal spring with spring constant $750$ N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it $5.0$ cm. How hard is the athlete pushing?

Short answer

The force when the athlete pushing is$F=37.5$N

Step-by-step solution

Step 1. Given Information

A horizontal spring with spring constant $750$N/m is attached to a wall.

and compressing it$5.0$cm

Step 2. Relationship between the restoring force and the displacement

When a spring is compressed, a force is exerted by its material to restore it to its equilibrium position and its force is called restoring force $F_{sp}$

Hooke's Law states the relationship between the restoring force and the displacement $∆s$that is occurred to the spring and it is given by equation

$F_{sp}=-k∆s$

where $k$is the force constant and the negative sign shows the direction

so, he exerts a force in the negative sign of the restoring force is given by $F=-F_{sp}=k∆s$

Now, put the values

$$\begin{gathered} F=k∆s \\ =(750N/m)(\times 0.05m) \\ =37.5N \end{gathered}$$