Which has more Gravitational Potential Energy: a 7kg lamp on a 6m high shelf or a 4kg book 2 shelves (2m) down?
Gravitational Potential Energy = m g h
higher and heavier wins
If we take the Gravitational Potential Energy equation (E=mgh) and apply it to each object, we will see that:
Lamp: E=mgh=(7kg)(9.81m/s^2)(6m)=412.02
Book: E=mgh=(4kg)(9.81m/s^2)(2m)=78.48
So clearly, the lamp has more gravitational potential energy and you didn't even need to do the formula because higher and heavier wins like R_scott said.
To calculate the gravitational potential energy of an object, you need to know its mass (m), the acceleration due to gravity (g), and the height (h) at which it is located. The formula for gravitational potential energy is:
Gravitational Potential Energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)
First, let's calculate the gravitational potential energy of the 7kg lamp on the 6m high shelf. Given that the mass (m) of the lamp is 7kg and the height (h) is 6m, and assuming the acceleration due to gravity (g) is approximately 9.8 m/s², we can use the formula to find the gravitational potential energy:
PE1 = 7kg × 9.8 m/s² × 6m
Next, let's calculate the gravitational potential energy of the 4kg book that is 2 shelves (2m) down. Given that the mass (m) of the book is 4kg and the height (h) is 2m, we can again use the same formula to find the gravitational potential energy:
PE2 = 4kg × 9.8 m/s² × 2m
Now, let's compare the two values of gravitational potential energy (PE1 and PE2) to determine which one is greater. Calculate each value and compare them:
PE1 = 7kg × 9.8 m/s² × 6m
PE1 ≈ 411.6 Joules
PE2 = 4kg × 9.8 m/s² × 2m
PE2 ≈ 78.4 Joules
Based on the calculations, the lamp on the 6m high shelf has more gravitational potential energy (411.6 Joules) compared to the book that is 2 shelves (2m) down (78.4 Joules).