Object A has a gravitational potential energy of 24 joules when it rests on a shelf 5 m above the ground. Object B has a mass that is three times the mass of Object A. What would be the gravitational potential energy of object B when it rests on a shelf 10 m above the ground?
o A. 72 joules
o B. 120 joules
o C. 144 joules
o D. 240 joules
24 = w x 5
w = 24/5
w = 4.8
4.8 x 3
= 14.4
gpe = 14.4kg x 10m
= 144
ISn't GPE proportional to mass x height?
144
Well, well, well, here we have some objects getting high up on shelves! I can already sense the suspense in the air. Let's break it down, shall we?
First, we need to consider that the gravitational potential energy is given by the formula P.E. = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Now, object A has a potential energy of 24 joules at a height of 5 meters. We don't know the mass, but luckily we have some information about object B. It's got a mass three times that of object A! So, let's call the mass of object A 'm' and the mass of object B '3m'.
Now, object B is at a height of 10 meters, and we want to find its potential energy. Plugging in the numbers, we get P.E. = (3m)(9.8 m/s²)(10 m), which simplifies to 294 m joules.
Aha! But hold your laughter, my friend. We're not done yet. Remember, we want to find the potential energy of object B, not in terms of 'm', but in terms of object A's potential energy, which we know is 24 joules.
So, we divide the potential energy of object B by the potential energy of object A: 294 m joules divided by 24 joules. And what do we get? A magical number? Unfortunately, no. We get 12.25.
Now, let's apply a little logic here. We can't have a fraction of an object, can we? So, we'll round it up to the nearest whole number, which is 13.
Surprise! None of the answer choices are 13 joules. But if we round down, we get 12... OH NO! There is no 12 in the answer choices either. Someone really dropped the ball on this one!
So, my friends, I'm sorry to say this, but it seems like the answer choices are playing tricks on us. None of them match our calculated value of 13 joules for object B's potential energy. It looks like we might need to have a chat with whoever wrote these options.
But hey, don't be too disappointed. At least we had some fun along the way, right? Chin up, my friend! Keep exploring the wonders of physics, and maybe one day you'll stumble upon an answer that matches your calculations. Until then, keep your clown nose high and your humor higher!
To calculate the gravitational potential energy of an object, you need to use the formula:
Gravitational Potential Energy = mass × gravitational acceleration × height
Given that the gravitational potential energy of Object A is 24 joules when it is at a height of 5 m, we can set up an equation to solve for the mass of Object A.
24 joules = mass of A × gravitational acceleration × 5 m
The given problem states that Object B has a mass three times that of Object A. So, the mass of Object B can be expressed as:
Mass of B = 3 × (mass of A)
Now, we can calculate the gravitational potential energy of Object B when it is at a height of 10 m using the same formula:
Gravitational Potential Energy of B = mass of B × gravitational acceleration × 10 m
Substituting the value from the mass of B above:
Gravitational Potential Energy of B = (3 × mass of A) × gravitational acceleration × 10 m
Since we know that Object A has a gravitational potential energy of 24 joules at 5 m, we can substitute these values into the formula:
24 joules = mass of A × gravitational acceleration × 5 m
Rearranging this equation, we get:
mass of A = 24 joules / (gravitational acceleration × 5 m)
Now, we can substitute the value of the mass of A into the formula for the gravitational potential energy of Object B:
Gravitational Potential Energy of B = (3 × mass of A) × gravitational acceleration × 10 m
Plugging in the known values:
Gravitational Potential Energy of B = (3 × (24 joules / (gravitational acceleration × 5 m))) × gravitational acceleration × 10 m
Simplifying this expression, we cancel out the gravitational acceleration term and simplify:
Gravitational Potential Energy of B = 3 × 24 joules × 2
Gravitational Potential Energy of B = 72 joules
Therefore, the gravitational potential energy of Object B when it rests on a shelf 10 m above the ground would be 72 joules. So, the correct answer is option A.