Core Ideas
What is a gravitational field?
A region in which a mass experiences a gravitational force.
In which direction do gravitational field lines point around an isolated spherical mass?
Radially inwards, towards the centre of the mass.
State the equation connecting gravitational force F, mass m and gravitational field strength g.
F = mg
State the SI unit of gravitational field strength.
N kg⁻¹
What happens to the weight of an object when g decreases but its mass remains constant?
Its weight decreases because W = mg. Its mass remains unchanged.
Define gravitational field strength, g, at a point.
The gravitational force per unit mass acting on a small test mass at that point: g = F/m.
What does the spacing of gravitational field lines represent?
Closer lines represent a stronger field. Wider spacing represents a weaker field.
Calculate the gravitational force on a 3.5 kg object where g = 9.5 N kg⁻¹.
F = mg = 3.5 × 9.5 = 33.25 N, so F = 33 N to 2 significant figures.
What is the equivalent acceleration unit for N kg⁻¹?
m s⁻²
Describe the gravitational field lines near a small region of Earth’s surface when the local density is uniform.
They are approximately straight, parallel, equally spaced and directed vertically downwards.
State the direction of gravitational field strength at a point.
The direction of the force that would act on a small test mass placed at that point.
Describe the field-line pattern in a uniform gravitational field.
The lines are straight, parallel, equally spaced and point in the same direction.
Calculate the gravitational force on a 100 kg object where g = 1.6 N kg⁻¹.
F = mg = 100 × 1.6 = 160 N.
Show that N kg⁻¹ is equivalent to m s⁻².
1 N = 1 kg m s⁻². Therefore, N kg⁻¹ = (kg m s⁻²)/kg = m s⁻².
Why can Earth’s gravitational field be treated as uniform close to its surface, even though the complete field is radial?
Over a region much smaller than Earth’s radius, the radial field lines are nearly parallel and their spacing changes very little.
Explain why gravitational field strength is a vector quantity.
It has both magnitude and direction. Its direction is the direction of the gravitational force on a test mass.
Explain the difference between a radial field and a uniform field.
Radial field lines converge towards the centre and field strength changes with distance. Uniform field lines are parallel and equally spaced, so field strength is constant.
An object of mass 2.5 kg experiences a gravitational force of 40 N. Calculate g.
g = F/m = 40/2.5 = 16 N kg⁻¹.
Demonstrate that the acceleration of a freely falling object is equal to g.
For free fall, F = mg. From Newton’s second law, F = ma. Therefore ma = mg, so a = g.
As an object moves farther from Earth, what happens to the field-line spacing and gravitational field strength?
The field lines become farther apart and the gravitational field strength decreases.
Distinguish between gravitational field strength and gravitational force.
Field strength g is a property of the field and is force per unit mass. Force F acts on a particular mass and is given by F = mg.
A large mass of dense material lies beneath part of Earth’s surface. Describe how nearby gravitational field lines are affected.
The field lines bend towards the dense mass and become closer together near it, showing that the local gravitational field is stronger.
An 18 kg object experiences a force of 72 N. A 30 kg object is placed at the same position. Calculate g and the force on the second object.
g = 72/18 = 4.0 N kg⁻¹. For the second object, F = mg = 30 × 4.0 = 120 N.
At a point where g = 3.7 N kg⁻¹, an object is released from rest. Ignore air resistance. State its acceleration and calculate its speed after 4.0 s.
a = g = 3.7 m s⁻² towards the attracting body. Using v = u + at: v = 0 + 3.7 × 4.0 = 14.8 m s⁻¹.
An object weighs 490 N where g = 9.8 N kg⁻¹. Calculate its mass and its weight where g = 1.6 N kg⁻¹.
m = F/g = 490/9.8 = 50 kg. At the new position, F = mg = 50 × 1.6 = 80 N.