Question

A 56 kg student stands on top of a spring in an elevator accelerating upward at 3.5 m/s2m/s2. The spring constant is 2900 N/mN/m. Part A By how much is the spring compressed

Answer 1

Given data,

Mass,

`m=56\text{ kg}`

Acceleration,

`a=3.5m/s^2`

Spring constant,

`k=2900\text{ N/m}`

Given acceleration is upward, hence

`\begin{gathered} (g+a)=9.8m/s^2+3.5m/s^2 \\ (g+a)=13.3m/s^2 \end{gathered}`

Consider the equation of force,

`\begin{gathered} F=kx \\ m(g+a)=kx \\ x=(m(g+a))/(k) \end{gathered}`

Substitute the given and calculated values.

`\begin{gathered} x=\frac{56\text{ kg}*13.3m/s^2}{2900\text{ N/m}} \\ x=25.6\text{ cm} \end{gathered}`

Hence, the spring compressed is 25.6 cm.