8.1
Gravitational Potential Energy
Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of i…
The gravitational potential energy is the energy stored in an object due to its position in the gravitational field.
Mathematically, it is defined as the product of an object’s weight and height above the ground.
Thus, the gravitational potential energy of a ball of mass m hanging at a height y from the ground is mgy.
For example, in ice hockey, if a puck of mass m takes a parabolic path after the shot, then the gravitational potential energy at point B is mgy, where y is the height of the puck from the ground.
When the puck moves from point A to B, the change in gravitational potential energy is positive as the gravitational potential energy increases and is equal to the negative of the work done.
Similarly, when the puck moves from point B to C, the gravitational potential energy decreases, and the work done by the gravitational force is positive.
Thus, when a body moves upwards, the gravitational potential energy increases and decreases when the body moves downwards.
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Q1: What is gravitational potential energy and how is it calculated?
Gravitational potential energy is the energy stored in an object due to its position in Earth's gravitational field. It is calculated as the product of an object's mass, gravitational acceleration, and height above a reference point: PE = mgy. For example, a puck at height y has gravitational potential energy mgy, where m is mass and g is gravitational acceleration.
Q2: How does gravitational potential energy change when an object moves vertically?
When an object moves upward, gravitational potential energy increases because height increases. Conversely, when an object moves downward, gravitational potential energy decreases. The change in gravitational potential energy equals the negative of the work done by the gravitational force during the motion.
Q3: What is the relationship between work and gravitational potential energy?
The work done by gravitational force on a moving object is the negative of the change in gravitational potential energy. When an object rises, gravitational force does negative work while potential energy increases. When an object falls, gravitational force does positive work while potential energy decreases, illustrating energy conservation.
Q4: Why is Earth's motion neglected when calculating gravitational potential energy?
Earth's motion is neglected because the mass ratio of any ordinary object to Earth is vanishingly small. According to Newton's second law, the acceleration produced on Earth by an object's gravitational force is negligible. Therefore, we treat the system as a single-particle system subject to uniform gravitational force rather than considering Earth's motion.
Q5: How does gravitational potential energy depend on mass and height?
Gravitational potential energy is directly proportional to both mass and height. The formula PE = mgy shows that doubling mass or height doubles the potential energy. Near Earth's surface, the gravitational force on each object is simply its weight (mg), acting toward Earth's center, making mass and height the primary determinants of stored energy.
Q6: What types of potential energy exist in a system?
Potential energy is classified into two major categories: gravitational potential energy and elastic potential energy. Gravitational potential energy relates to an object's weight and height above the ground. The total potential energy of a system is the sum of all individual potential energies from each type of interaction present.
Q7: How does the work-energy relationship apply to gravitational potential energy?
The work done on a body by Earth's uniform gravitational force depends on mass, gravitational acceleration, and the height difference traversed. This work equals the negative of the difference in gravitational potential energy between two positions. Understanding this relationship is essential for analyzing force and potential energy in one dimension and applying energy conservation principles.