Question

A model airplane with mass 1.3 kg hangs from a rubber band with springconstant 20 N/m. How much is the rubber band stretched when the modelhangs motionless?A. 0.78 mB. 0.23C. 0.64 mO D. 0.082 mSUBMIT

Answer 1

`x\approx0.64\text{ m}`

Explanation:

The weight of the airplane is hanging from the rubber band is represented by the multiplication between its mass (1.3 kg) and the acceleration due to gravity, which is 9.8 m/s^2.

`\begin{gathered} W=m\cdot g \\ W=1.3\cdot9.8 \\ W=12.74\text{ N} \end{gathered}`

This situation can be modeled by Hook's law, which states that the force acting on a spring is given by:

`\begin{gathered} F=kx \\ \text{where,} \\ k=\text{ spring constant} \\ x=displacement\text{ of the spring with respect to its equilibrium position} \end{gathered}`

Substituting the given values, F=12.74 N and k=20 N/m.

Isolate x and solve:

`\begin{gathered} x=(12.74)/(20) \\ x=0.637 \\ x\approx0.64\text{ m} \end{gathered}`