An object of mass m When raised to height h possesses a potential energy of 12000 j. find the new potential energy: (a)if the same object is raised to height h/4. (b) if the same object if raised to height 4h
Answers
mgh/4 = 12000 * 4 = 36,000 J
(B) 4mgh = 12000/4 = 3000 J
The potential energy will be 3000J if the object is raised to height h/4 and the the potential energy will be 48000J if the object is raised to height 4h.
Given : An object of mass m When raised to height h possesses a potential energy of 12000 j.
To find : The new potential energy, if the same object is raised to height h/4 and if the same object if raised to height 4h.
Solution :
We can simply solve this numerical problem by using the following process. (our goal is to calculate the new values of potential energy)
Here, we will be using the following mathematical formula.
Potential energy = mass of the object × gravitational acceleration × height of the object from the ground
In the first given case,
- mass of the object = m (this will be constant in other cases also)
- gravitational acceleration = g (this will be constant in other cases also)
- height of the object from the ground = h
According to the data mentioned in the question,
mgh = 12000 J
(This will be our standard equation, which will be considered as a reference for upcoming calculations.)
In second given case,
- mass and gravitational acceleration are same.
- height = h/4
So,
mgh = 12000 (previously obtained equation)
m × g × h = 12000
m × g × h/4 = 12000/4 = 3000 J
Or,
Potential energy when the object raised to height h/4 = 3000 J
In third given case,
- mass and gravitational acceleration are same.
- height = 4h
So,
mgh = 12000 (previously obtained equation)
m × g × h = 12000
m × g × ( 4 × h) = 12000 × 4 = 48000 J
Or,
Potential energy when the object raised to height 4h = 48000 J
Hence, the potential energy will be 3000J if the object is raised to height h/4 and the the potential energy will be 48000J if the object is raised to height 4h.