Question

3 the acceleration due to gravity is smaller on mars than it is on earth. if a 2 kg object were held 0.75 m above the surface of mars, it would have 5.7 j of gravitational potential energy. what is the acceleration due to gravity on mars? a 0.26 m/s² b 1.2 m/s² c 3.8 m/s² d 8.6 m/s²

Explanation:

Step1: Recall 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 of the object, \(g\) is the acceleration due to gravity, and \(h\) is the height.
We need to solve for \(g\), so we can rewrite the formula as \(g=\frac{U}{mh}\).

Step2: Substitute the given values into the formula

Given that \(U = 5.7\space J\), \(m = 2\space kg\), and \(h=0.75\space m\).
Substitute these values into \(g=\frac{U}{mh}\):
\(g=\frac{5.7}{2\times0.75}\)
First, calculate \(2\times0.75 = 1.5\).
Then, \(g=\frac{5.7}{1.5}=3.8\space m/s^{2}\)

Answer:

C. \(3.8\space m/s^{2}\)