Question

note: use ( g = 9.81 , \text{m/s}^2 )

what would have to be the mass of a long woolen scarf if it is wrapped around a 6.7 - m - high wire and has 65 j of gpe?

report your answer to 3 decimal places. your permitted error is ( pm 0.001 , \text{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)

$$GPE = mgh$$

where \(GPE\) is the gravitational potential energy, \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height.

Step2: Rearrange the formula to solve for mass (\(m\))

$$m=\frac{GPE}{gh}$$

Step3: Substitute the given values (\(GPE = 65\space J\), \(g = 9.81\space m/s^{2}\), \(h = 6.7\space m\)) into the formula

$$m=\frac{65}{9.81\times6.7}$$

$$m=\frac{65}{65.727}$$

$$m\approx0.989\space kg$$

Answer:

\(0.989\)