Question

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do an amount of work of 79.0 J when you compress the springs a distance of 0.190 m from their uncompressed length.(a) What magnitude of force must you apply to hold the platform in this position?

Answer 1

Explanation:

The given data is as follows.

         Work done by the force, (W) = 79.0 J

         Compression in length (x) = 0.190 m

So, formula for parallel combination of springs  equivalent is as follows.

           $k_{eq} = K_{1} + K_{2}$

                    = 2k

Hence, work done is as follows.

             W = $\frac{1}{2}k_{eq} \times x^{2}$

           $k_{eq} = \frac{2W}{x^{2}}$

                       = $\frac{2 \times 79}{(0.19)^{2}}$

                       = $\frac{158}{0.0361}$

                       = 4376.73 N/m

Hence, magnitude of force required to hold the platform is as follows.

               F = $k_{eq}x$

                  = $4376.73 N/m \times 0.19 m$

                  = 831.58 N

Thus, we can conclude that magnitude of force you must apply to hold the platform in this position is 831.58 N.