An object has a gravitational potential energy of 24 joules when it rests on a shelf 3 m above the ground. What would be its gravitational potential energy when it is lowered to a shelf 1 m above the ground?
To calculate the gravitational potential energy of an object, you can use the formula:
Gravitational Potential Energy (GPE) = mass × acceleration due to gravity × height
In this case, the mass and acceleration due to gravity remain constant. The only thing changing is the height. Let's assume the mass and the acceleration due to gravity are known and do not change. Given that the gravitational potential energy of the object is 24 joules when it's 3 m above the ground, we can use this information to find the gravitational potential energy when it is lowered to a shelf 1 m above the ground.
Step 1: Write down the known information.
- Gravitational Potential Energy at height 1 (GPE1) = ?
- Gravitational Potential Energy at height 2 (GPE2) = 24 J
- Height at 1 (h1) = 3 m
- Height at 2 (h2) = 1 m
Step 2: Substitute the values into the gravitational potential energy formula.
GPE1 = mass × acceleration due to gravity × h1
GPE2 = mass × acceleration due to gravity × h2
Step 3: Equate the two equations to find the gravitational potential energy at height 1.
GPE1 = GPE2
mass × acceleration due to gravity × h1 = mass × acceleration due to gravity × h2
Step 4: Cancel out mass × acceleration due to gravity on both sides of the equation.
h1 = h2
Step 5: Substitute the given values into the equation.
3 = 1
Step 6: Simplify the equation.
Therefore, the gravitational potential energy at a height of 1 m would still be 24 joules, the same as when it was at a height of 3 m.
So, the gravitational potential energy of the object when it is lowered to a shelf 1 m above the ground would still be 24 joules.