Question

you have recently been abducted by aliens and taken to their home planet. you happen to have a pen, paper clips, and a small ruler. you attach 20 g of paperclips to the spring in your pen (previous investigations have allowed you to determine the spring constant is 10 n/m) and notice it stretches 2.1 cm. what is the gravitational acceleration of your new home in m/s^2?

Explanation:

Step1: Convert units

Convert mass \(m = 20g=0.02kg\) and stretch \(x = 2.1cm = 0.021m\).

Step2: Use Hooke's law and equilibrium condition

At equilibrium, the force due to gravity \(F_g=mg'\) (where \(g'\) is the gravitational acceleration of the new planet) is equal to the spring force \(F_s = kx\). So \(mg'=kx\).

Step3: Solve for \(g'\)

Rearrange the equation \(g'=\frac{kx}{m}\). Substitute \(k = 10N/m\), \(x=0.021m\), and \(m = 0.02kg\) into the formula: \(g'=\frac{10\times0.021}{0.02}\).

First, calculate \(10\times0.021 = 0.21\). Then, \(\frac{0.21}{0.02}=10.5\).

Answer:

\(10.5\)