Gravitational Potential and Kinetic

Energy

Define gravitational potential energy.

The energy an object has because of its position in a gravitational field.

What is the symbol for gravitational potential energy?

E₍grav₎ or GPE.

What is the unit of gravitational potential energy?

Joules (J).

What equation is used to calculate gravitational potential energy near the Earth's surface?

E₍grav₎ = mgh.

What does m represent in E₍grav₎ = mgh?

Mass in kilograms (kg).

What does g represent in E₍grav₎ = mgh?

Gravitational field strength in N kg⁻¹.

What does h represent in E₍grav₎ = mgh?

Height in metres (m).

What value of gravitational field strength is normally used near the Earth's surface?

g = 9.81 N kg⁻¹.

What equation calculates the change in gravitational potential energy?

ΔE₍grav₎ = mgΔh.

What does Δh represent in ΔE₍grav₎ = mgΔh?

The change in height.

What happens to gravitational potential energy when an object is raised?

It increases.

What happens to gravitational potential energy when an object falls?

It decreases.

What factors determine the change in gravitational potential energy?

Mass, gravitational field strength and change in height.

A 2.2 kg object is raised by 1.24 m. How much gravitational potential energy does it gain?

ΔE₍grav₎ = 2.2 × 9.81 × 1.24 = 26.8 J.

Is gravitational field strength exactly constant near the Earth?

No, but over the small height changes encountered in everyday situations it can usually be approximated as 9.81 N kg⁻¹.

How does gravitational field strength change with distance from the centre of a planet?

It decreases as distance from the planet increases.

Define kinetic energy.

The energy an object has because of its motion.

What is the symbol for kinetic energy?

Eₖ.

What is the unit of kinetic energy?

Joules (J).

What equation is used to calculate kinetic energy?

Eₖ = ½mv².

What does m represent in Eₖ = ½mv²?

Mass in kilograms (kg).

What does v represent in Eₖ = ½mv²?

Speed in metres per second (m s⁻¹).

How does kinetic energy depend on mass?

Kinetic energy is directly proportional to mass if speed is constant.

How does kinetic energy depend on speed?

Kinetic energy is proportional to the square of the speed.

What happens to kinetic energy if an object's speed doubles?

It becomes four times greater.

What happens to kinetic energy if an object's speed triples?

It becomes nine times greater.

What happens to kinetic energy if an object's mass doubles while its speed stays constant?

It doubles.

Why must speed usually be converted to m s⁻¹ before calculating kinetic energy?

The equation Eₖ = ½mv² uses SI units.

How do you convert km h⁻¹ to m s⁻¹?

Divide by 3.6.

What is 900 km h⁻¹ in m s⁻¹?

250 m s⁻¹.

How many kilograms are in one tonne?

1000 kg.

What is 400 tonnes in kilograms?

4.00 × 10⁵ kg.

What is the principle of conservation of energy?

Energy cannot be created or destroyed; it can only be transferred between energy stores.

What happens to energy during an energy transfer in an ideal system?

The total amount of energy remains constant.

What energy transfer occurs when an object falls?

Gravitational potential energy is transferred to kinetic energy.

What energy transfer occurs when an object is projected vertically upwards?

Kinetic energy is transferred to gravitational potential energy.

If air resistance is negligible, how are lost gravitational potential energy and gained kinetic energy related?

They are equal.

What equation represents the transfer from gravitational potential energy to kinetic energy?

mgΔh = ½mv².

Why can mass be cancelled from mgΔh = ½mv²?

The same mass appears on both sides of the equation.

After cancelling mass, what equation relates speed and change in height?

gΔh = ½v².

What equation gives the speed of an object after falling through a vertical height Δh?

v = √(2gΔh).

Does the final speed of a freely falling object depend on its mass if air resistance is ignored?

No.

Why do objects of different masses fall at the same rate when air resistance is ignored?

Mass cancels from the energy equation, giving v = √(2gΔh).

What assumption is required when using mgΔh = ½mv² for a falling object?

No significant energy is transferred to other stores, such as by air resistance.

What happens if air resistance is significant during a fall?

Some gravitational potential energy is transferred to thermal energy rather than kinetic energy.

Why would the actual final speed of a falling object be lower than predicted by v = √(2gΔh)?

Air resistance transfers some energy to the surroundings.

How can the maximum height reached by an object projected vertically upwards be calculated using energy?

Set its initial kinetic energy equal to its gain in gravitational potential energy.

What energy equation applies to an object projected upwards until it momentarily stops?

½mv² = mgΔh.

What equation gives the maximum height gained by an object projected upwards at speed v?

Δh = v²/(2g).

Why does mass not affect the maximum height in Δh = v²/(2g)?

Mass cancels from both sides of the energy equation.

At the maximum height of a vertically projected object, what is its kinetic energy?

Zero, because its instantaneous speed is zero.

At the maximum height of a vertically projected object, what has happened to its initial kinetic energy if air resistance is ignored?

It has been transferred to gravitational potential energy.

A coin is dropped from a height of 830 m. What equation could estimate its impact speed if air resistance is ignored?

v = √(2gΔh).

Why would using v = √(2gΔh) for an object falling from a very large height be unrealistic?

Air resistance may be significant, so not all gravitational potential energy becomes kinetic energy.

What equation links gravitational potential energy and kinetic energy for a falling object starting from rest?

mgh = ½mv².

What equation can be rearranged from mgh = ½mv² to find gravitational field strength?

g = v²/(2h).

How can gravitational field strength be investigated using energy conservation?

Drop an object from known heights, measure its speed after falling, and use the relationship v² = 2gΔh.

What graph can be plotted to determine gravitational field strength experimentally?

Plot v² on the y-axis against Δh on the x-axis.

What relationship should a graph of v² against Δh show?

A straight-line relationship because v² = 2gΔh.

What is the gradient of a graph of v² against Δh?

2g.

How can g be found from the gradient of a v² against Δh graph?

g = gradient/2.

Why are multiple measurements and a graph preferable to calculating g from one measurement?

They reduce the effect of random uncertainty and produce a more reliable result.

What is an important assumption in an experiment using energy conservation to determine g?

Air resistance and other energy losses are negligible.