GRAVITATIONAL POTENTIAL ENERGY

Gravitational Potential Energy (PEgrav) is the energy possessed by an object by virtue of its position with respect to the ground. Objects that are raised to a certain height possess gravitational potential energy. 

Every material object on earth is attracted to the earth's gravitational pull. When lifting a box, for example, you spend energy to raise it to a certain height. Thus, you perform work on the box. Work is a process of transferring energy. The amount of work ( Work = Force x displacement) you perform on the box is equal to the potential energy gained by the box. 

While a box is lifted, it goes against the pull of gravity. This makes the box of a particular weight (weight = mass x gravity) more difficult to be lifted as height increases. In effect, since more work is needed to raise an object at a higher position, the more gravitational potential energy is gained by that object. The gravitational energy of an object is computed by PEgrav = mgh. 

Gravitational potential energy is equal to the product of the mass of the object, the acceleration due to gravity (g = 9.81 m/s2) and the height at which the object is raised. Comparing the potential energies of two objects that are on the same position with respect to the ground, an object with more mass have greater gravitational potential energy. Consider two stones of different masses are dropped at the same time from the same height. Following the physics of free-falling objects, the two stones will hit the ground at the same. However, which of the two stones will cause greater impact as they hit the ground?

As a result of the direct relationship between mass and PEgrav , the more massive object gives more impact force as it hits the ground. 

As the two stones are falling to the ground, what happens to their PEgrav? Take note that as height decreases, potential energy also decreases. So as these two stones fall, their potential energies are converted into another form of energy - the energy in motion known as Kinetic Energy. Work is a process of transferring energy, as said. When objects falls to the ground, the earth's gravitational pull is performing work on the objects transforming PE into KE!

Consider the following problems.

Problem 1. An object with mass of 50 kilograms is raised to a height of 4 meters from the ground. What is the potential energy of the object?


Given: 

Mass = 50 kg

Height = 4 meters

Acceleration due to gravity = 9.8 m/s2


Required: PE


Equation: PE = mgh


Solution: 

PE = (50 kg) (9.8 m/s2) (4 m)

PE = 1960 Joules



Problem 2. What is the Potential Energy of an object that has a weight of 500N on earth when raised to a height of 40 m?


Given: 

Weight (m ∙ g) = 500 N

Height = 40 m

 

Required: Potential Energy

 

Equation: PE = mgh

 

Solution: 

PE = (500 N) (40 m)

PE = 20,000 Joules



Problem 3. What is the mass of the object whose potential energy is 3,400 J at height of 30 meters?


Given: 

Potential Energy = 3,400 Joules

Height = 30 m

Acceleration due to Gravity = 9.8 m/s2


Required: mass


Equation: 

m = PE / gh


Solution:

m = 3,400 J / [(9.8 m/s2)(30 m)]

m = 11.56 kg



Problem 4: Calculate the potential energy on an object of mass 10 kilograms raised to a height of 10 m. Compare it to the potential energy of another object of mass 20 kilograms raised at the same height.

 

Given :

Mass of object 1 = 10 kg

Mass of object 2 = 20 kg

Height of object 1 = 10 m

Height of object 2 = 10 m

Acceleration due to gravity = 9.8 m/s2

 

Required: 

PE of object 1

PE of object 2

 

Equation: 

PE = mgh

 

Solution

PEOBJECT 1 = m1hg

PEOBJECT 1 = (10 kg) (9.8 m/s2) (10 m)

PEOBJECT 1 = 980 joules

 

PEOBJECT 2 = m2hg

PEOBJECT 2 = (20 kg) (9.8 m/s2) (10 m)

PEOBJECT 2 = 1960 J

 

Since the mass of object 2 is twice the mass of object 1, the Potential Energy of object 2 is twice the Potential Energy of object 1



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