An object of mass 1.5 kg rests on a shelf where it has a gravitational potential energy of 7 joules. An object of mass 4.5 kg is placed on the same shelf. What is the gravitational potential energy of this second object?
PE = mgh
Therefore H = PE/(mxg)
H = 7/(1.5 x 9.8)
H = 0.48m
PE (object 2) = 4.5 x 9.8 x 0.48
PE (object 2) = 21.17J
Isn't GPE directly proportional to mass?
So what if mass is tripled?
The gravitational potential energy of an object is given by the formula:
Potential energy = mass x gravitational acceleration x height
For the first object, the potential energy is given as 7 joules and the mass is 1.5 kg. We can rearrange the formula to solve for height:
Height = Potential energy / (mass x gravitational acceleration)
Plugging in the values:
Height = 7 J / (1.5 kg x 9.8 m/s^2)
Height ≈ 0.476 m
Now, let's find the potential energy of the second object with a mass of 4.5 kg:
Potential energy = mass x gravitational acceleration x height
Potential energy = 4.5 kg x 9.8 m/s^2 x 0.476 m
Potential energy ≈ 20.9 J
Therefore, the gravitational potential energy of the second object is approximately 20.9 joules.
Gravitational potential energy is given by the formula U = mgh, where U is the gravitational potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height at which the object is located.
In this case, we know that the gravitational potential energy of the first object is 7 joules and that its mass is 1.5 kg. Let's assume that the height at which the first object is located is h1. Therefore, we can write the equation as follows:
7 = 1.5 * g * h1 -- (Equation 1)
Now, the second object has a mass of 4.5 kg, and we want to find its gravitational potential energy. Let's assume that it is located at the same height h1. Using the same formula, we can write the equation for the second object as follows:
U2 = 4.5 * g * h1 -- (Equation 2)
Since both objects are at the same height, we can equate h1 in Equation 1 and Equation 2:
1.5 * g * h1 = 4.5 * g * h1
Now, we can solve for U2:
U2 = 4.5 * g * h1 = 4.5 * g * h1
Therefore, the gravitational potential energy of the second object is also 7 joules, assuming both objects are at the same height.