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?
Pe1 = 1.5 * g * h
Pe2 = 4.5 * g * h
so Pe2 = (4.5/1.5) (7)
To find the gravitational potential energy of the second object, we need to use the formula:
Gravitational Potential Energy = mass * g * height
where:
- "mass" is the mass of the object
- "g" is the acceleration due to gravity (approximately 9.8 m/s^2)
- "height" is the height above the reference point (in this case, the shelf)
Given that the gravitational potential energy of the first object is 7 joules, and its mass is 1.5 kg, we can use these values to find the height.
7 J = 1.5 kg * 9.8 m/s^2 * height
Dividing both sides of the equation by (1.5 kg * 9.8 m/s^2), we get:
height = 7 J / (1.5 kg * 9.8 m/s^2)
height ≈ 0.476 m
Now, we can use the height we just calculated along with the mass of the second object (4.5 kg) in the same formula to find its gravitational potential energy.
Gravitational Potential Energy = 4.5 kg * 9.8 m/s^2 * 0.476 m
Gravitational Potential Energy ≈ 20.7 joules
Therefore, the gravitational potential energy of the second object is approximately 20.7 joules.