Question

how high would a wire that has a 0.6 kg long woolen scarf wrapped around it have to be in order for the scarf to have 80 j of gpe?
report your answer to 3 decimal places. your permitted error is ±0.001 j. if your answer is negative, please make sure to include the negative sign.
answer

Explanation:

Step1: Recall the formula for gravitational potential energy (GPE)

The formula for GPE is \(GPE = mgh\), where \(m\) is the mass, \(g\) is the acceleration due to gravity (\(g = 9.81\ m/s^{2}\)), and \(h\) is the height. We need to solve for \(h\). Rearranging the formula gives \(h=\frac{GPE}{mg}\).

Step2: Substitute the given values into the formula

We are given that \(GPE = 80\ J\), \(m = 0.6\ kg\), and \(g = 9.81\ m/s^{2}\). Substituting these values into the formula \(h=\frac{GPE}{mg}\), we get \(h=\frac{80}{0.6\times9.81}\).

Step3: Calculate the value of \(h\)

First, calculate the denominator \(0.6\times9.81 = 5.886\). Then, \(h=\frac{80}{5.886}\approx13.592\).

Answer:

\(13.592\)