Gravitational Potential Energy | A-level Physics | OCR, AQA, Edexcel

Summary

In this video, the concept of gravitational potential energy (GPE) is explained in relation to both uniform and radial gravitational fields. The video compares GPE to elastic potential energy, explaining how work done against gravity can store energy. It details how GPE changes with height in a uniform field, using an example of an apple falling from a tree. The video also covers how GPE is negative in a radial field and how to calculate GPE between two objects based on their masses and separation distance. Engaging examples and a clear formula breakdown make the topic accessible to viewers.

Takeaways

• 😀 Gravitational potential energy is the energy stored due to the position of an object in a gravitational field.
• 😀 Gravitational potential energy behaves similarly to elastic potential energy, like when an elastic band is stretched.
• 😀 When an object is raised, work is done against gravity, and this work is stored as gravitational potential energy (GPE).
• 😀 If an object is released from a height, the stored GPE is converted into kinetic energy as it falls.
• 😀 Gravitational potential energy is negative, as gravitational force is attractive and work is done on the object by the field.
• 😀 The change in gravitational potential energy in a uniform field is calculated as the object's mass times the gravitational field strength and the change in height.
• 😀 Near Earth's surface, the gravitational field strength is constant (9.81 N/kg), which simplifies calculations of GPE changes.
• 😀 When an object is moved in a uniform gravitational field, it loses GPE as it moves closer to the source of gravity (e.g., Earth).
• 😀 In a radial field, gravitational potential energy between two objects is determined by their masses and the distance between their centers.
• 😀 The formula for GPE in a radial field is: GPE = - (G * m1 * m2) / r, where G is the gravitational constant, m1 and m2 are the masses, and r is the separation between the objects.
• 😀 A practical example for calculating GPE in a radial field is the Earth-Moon system, where the gravitational potential energy is approximately -6.2 x 10^29 joules.

Q & A

What is gravitational potential energy (GPE)?

Gravitational potential energy is the energy stored between two masses due to the gravitational force between them. It is similar to elastic potential energy, where work is done to stretch an elastic object, storing energy.

How is work done to lift an object related to gravitational potential energy?

When an object is lifted against gravity, work is done on the object, which gets stored as gravitational potential energy. This energy is later converted into kinetic energy if the object is released.

Why is gravitational potential energy always negative?

Gravitational potential energy is always negative because gravity is an attractive force. The work done by the gravitational force to bring an object closer to the source of the field results in negative energy.

What does a negative change in gravitational potential energy indicate?

A negative change in gravitational potential energy indicates that the object has moved closer to the source of the gravitational field, losing potential energy as it moves downward.

How do we calculate the change in gravitational potential energy in a uniform field?

The change in gravitational potential energy in a uniform field can be calculated using the formula: ΔE_p = m * g * Δh, where m is the object's mass, g is the gravitational field strength, and Δh is the change in height.

In the example of the falling apple, how do we calculate the change in potential energy?

For the 0.5 kg apple falling from a height of 2 meters, we calculate the change in potential energy using the formula: ΔE_p = m * g * Δh = 0.5 * 9.81 * (-2), which gives ΔE_p = -9.8 joules.

What happens to an object’s gravitational potential energy when it is moved to a higher point in the field?

When an object is moved to a higher point in the field, it gains positive gravitational potential energy, meaning the value of ΔE_p is positive.

What is the formula for gravitational potential energy between two objects in a radial field?

The formula for gravitational potential energy between two objects in a radial field is: E_p = - (G * m1 * m2) / r, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers.

How do we calculate the gravitational potential energy between the Earth and the Moon?

To calculate the gravitational potential energy between the Earth and the Moon, we use the formula E_p = - (G * m1 * m2) / r. Substituting the values for the masses of the Earth and Moon, and the distance between their centers, we get E_p = - 6.2 * 10^29 joules.

What does the negative sign in the gravitational potential energy formula for two objects in a radial field signify?

The negative sign in the formula indicates that gravitational potential energy is negative, reflecting the attractive nature of gravity. The energy is lower (more negative) when the objects are closer together.