Newton’s Second Law — WJEC GCSE Science (Double Award) - Physics Revision Notes & Topical Questions

Section 1 of 9The law and equation

Newton's second law

Newton's second law the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass.

Equation

• F = ma.
  What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s⁻²)
• F is the resultant force in N, m is mass in kg and a is acceleration in m/s².

Rearranged forms

• Rearranged forms a = F/m and m = F/a.

Direction

• Direction the acceleration is in the same direction as the resultant force.

Newton

• 1 N is the force that gives a mass of 1 kg an acceleration of 1 m/s², so 1 N = 1 kg m/s².

Section 2 of 9Effects of force and mass

Effects of force and mass

Doubling the resultant force on a given mass doubles the acceleration.

Doubling the mass for the same force halves the acceleration.

If the resultant force is zero, a

0 (the first law).

Graph of a against F for fixed mass

• Graph of a against F for fixed mass a straight line through the origin with gradient 1/m.

Graph of a against m for fixed force

• Graph of a against m for fixed force a curve showing an inverse relationship.

Section 3 of 9Always use the resultant force

F in F

F in F ma is the resultant (net) force.

Draw a force diagram first and find the resultant with direction.

Driving force minus friction and drag gives the resultant for a car.

Using the driving force alone is a common error.

Section 4 of 9Weight and free fall

Weight W

Weight W mg gives acceleration a = F/m = mg/m = g.

The mass cancels, so all objects fall with the same acceleration when air resistance is negligible.

With upward air resistance R the resultant is mg − R, so the acceleration is less than g.

Section 5 of 9Investigating the law

1

Pull a trolley along a bench with a string attached to a hanging weight.

2

Measure the acceleration with light gates or a ticker-timer.

3

To test a against F, move masses from the trolley to the hanger so the total mass stays constant.

4

To test a against m, keep the force constant and add masses to the trolley.

5

Compensate for friction by tilting the track slightly until the trolley moves at constant speed when pushed.

Section 6 of 9Problem-solving routine

Problem-solving routine

Write down the known quantities.

Find the resultant force with its direction.

Apply F = ma and check the units.

1If speeds and times are given, find a

Δv/Δt first, then the force.

2If force and mass are given and a speed or time is needed, find a and then use v

If force and mass are given and a speed or time is needed, find a and then use v u + at.

Section 7 of 9More from the specification

1Elastic proportional limit

• Elastic proportional limit applied tensile forces produce linear extension according to Hooke's law until reaching the characteristic elastic limit.

2Extension

• Increase in length over the original length.

3Length

• Resistance is directly proportional to the length of a wire.

4Velocity

• Rate of change of displacement.

5Balanced

• Having equal and opposite moments.

6Elastic

• Returns to original shape when force is removed.

7Spring constant

• Stiffness k in N/m.

8Constant velocity

• Zero acceleration.

9Circular motion

• Motion along a circular path with a force towards the centre.

10One acceleration

• One acceleration an object may have several forces acting on it, but it has only one acceleration, set by the resultant force.

Section 8 of 9Key terms

Term	Meaning
Newton's second law	F = ma; acceleration is proportional to the resultant force and inversely proportional to mass.
Newton	Force that gives 1 kg an acceleration of 1 m/s².
Resultant force	Net force found by vector addition.
Acceleration	Rate of change of velocity, in m/s².
Mass	Amount of matter and a measure of inertia.

Section 9 of 9Exam technique

1

Using the driving force instead of the resultant force — subtract friction and drag first.

2

Forgetting to convert grams to kilograms — mass must be in kg.

3

Saying acceleration is larger for a larger mass — it is smaller for the same force.

4

Leaving out weight in vertical problems — include it in the resultant.