Question

Sarah is going sledding! She starts at the top of a hill that is 1.5 m above the ground. She has a mass of 30 kg. What is her gravitational potential energy? Group of answer choices 41.3 J 45 J 33.75 J 441 J

Answer 1

Answer:

Given:

• Height (h) = 1.5 m
• Mass (m) = 30 kg
• Let 'g' or acceleration due to gravity = $\bold{9.8m/s^{2}}$

Question:

        Find the gravitational potential energy?

Solution:

• Formula for gravitational potential energy = mgh

        Where:

• 'm' stands for the mass of the object.
• 'g'  stands for the gravitational pull applied by the celestial body
• 'h'  stands for the height away from the ground

        Derivation of the formula:

• Let 'h' be the height the object is raised up to.
• Let 'g' be the gravitational pull applied on the object.
• Let 'm' be the mass of the object.

       We know that:

• Work done (W) = Force (f) x Distance (S)
• Force (f) = Mass (m) x Acceleration (a)
• Acceleration (a) = Acceleration due to gravity (g)
• Distance (S) = Height (h)

        From the above equations:

• Replace values for force and distance in the equation

       'Work done (W) = Force (f) x Distance (S)'

        We get:

• Work done (W) = Mass (m) x Acceleration due to gravity (g) x Height (h)
• Work done (W) = Gravitational Potential Energy (P.E)
• Gravitational Potential Energy (P.E) = Mass (m) x Acceleration due to gravity (g) x  Height (h)
• Gravitational potential energy = mgh

        SI unit:

• Joule (J)
• which is defined as the work expended by a force of one newton (N) through a displacement of one metre.  

        Solving the given question with the above derived formula:

• Gravitational potential energy = mgh
• Gravitational potential energy = 30 x 9.8 x 1.5
• Gravitational potential energy = 45 x 9.8
• Gravitational potential energy = 441 J