Question

a 6 kg weight is lifted off the ground to a height that gives it 70.56 j of gravitational potential energy. what is its height? acceleration due to gravity is ( g = 9.8 , \text{m/s}^2 ).

a. 3.2 m
b. 0.09 m
c. 1.2 m
d. 11.8 m

Explanation:

Step1: Write the formula for gravitational potential energy

The formula for gravitational potential energy is \(U = mgh\), where \(U\) 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 height \(h\)

From \(U = mgh\), we can solve for \(h\) by the formula \(h=\frac{U}{mg}\).

Step3: Substitute the given values into the formula

Given \(U = 70.56\space J\), \(m = 6\space kg\), and \(g=9.8\space m/s^{2}\).
Substitute these values into \(h=\frac{U}{mg}\), we get \(h=\frac{70.56}{6\times9.8}\).
First, calculate \(6\times9.8 = 58.8\).
Then, \(h=\frac{70.56}{58.8}=1.2\space m\).

Answer:

C. \(1.2\space m\)