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?
o A. 8 joules
o B. 12 joules
o C. 22 joules
o D. 72 joules
PE = mgh
Therefore m = PE/(g x h)
m = 24/(9.8 x 3)
m = 0.82kg
Now the object is moved to 1m above the ground.
PE = mgh
PE = 0.82 x 9.8 x 1
PE = 8.036
Round off to 8 (A)
Alternatively, you could divide 24J by 3, as this is the change in height difference. But you may be marked down if proper work is not shown.
Well, let me calculate that for you. When the object is lowered to a shelf 1 m above the ground, the change in height is 2 m (3 m - 1 m). Gravitational potential energy is directly proportional to height, so to find the change in gravitational potential energy, we multiply the change in height by the gravitational potential energy at the original height.
24 joules * 2 m = 48 joules
Therefore, the object would have a gravitational potential energy of 48 joules when it is lowered to a shelf 1 m above the ground.
But wait, none of the given options match 48 joules! It seems like we have a mystery on our hands here. Looks like the answer choices are playing tricks on us. I'm afraid I can't juggle these choices, so let's go with option B, 12 joules, since it's the closest to the correct answer. Although it's not the exact answer, it's the best we've got in this circus of options.
To calculate the gravitational potential energy, you can use the formula:
Gravitational Potential Energy = mass × gravitational acceleration × height.
However, in this case, the mass of the object is not given. So, we can use the simplified formula where mass is not considered:
Gravitational Potential Energy = gravitational acceleration × height.
Given that the gravitational potential energy is 24 joules when the object is at a height of 3 m, we can calculate the gravitational potential energy when it is at a height of 1 m.
Gravitational Potential Energy = gravitational acceleration × height
Gravitational Potential Energy = 9.8 m/s^2 × 1 m
Gravitational Potential Energy = 9.8 joules.
Therefore, the correct answer is A. 8 joules.
To calculate the gravitational potential energy, we can use the formula:
GPE = m * g * h
where GPE is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth), and h is the height or vertical distance.
Given that the object has a gravitational potential energy of 24 joules when it rests on a shelf 3 m above the ground, we can calculate the value of m * g * h.
24 = m * 9.8 * 3
By solving this equation, we can find the value of m * g, which is the mass of the object multiplied by the acceleration due to gravity:
24 = m * 29.4
Now, we need to find the gravitational potential energy when the object is lowered to a shelf 1 m above the ground. Using the equation:
GPE = m * g * h
and plugging in the known values:
GPE = m * 9.8 * 1
To find the gravitational potential energy when the object is 1 m above the ground, we can solve for m * g:
m * 9.8 = GPE / 1
m * 9.8 = GPE
Now, we can substitute the value of 24 joules for GPE:
m * 9.8 = 24
By solving this equation, we can find the value of m * g:
m * 9.8 = 24
m = 24 / 9.8
m ≈ 2.45 kg
Finally, we can calculate the gravitational potential energy when the object is lowered to a shelf 1 m above the ground:
GPE = m * g * h
GPE = 2.45 * 9.8 * 1
GPE ≈ 24 joules
Therefore, the gravitational potential energy when the object is lowered to a shelf 1 m above the ground is approximately 24 joules.
So, the correct answer is not listed in the options provided.