1.17-1.18 - Newton's second law and weight

1.17-1.18 - Newton's second law and weight

Newton's second law links the unbalanced force on an object to its mass and acceleration. Weight is a particular force: the pull of gravity on a mass. In this lesson you will learn what the symbols in the two equations mean, how to choose the right relationship, and how to avoid mixing up mass, weight and gravitational field strength.

Force, mass and acceleration

Newton's second law is used when an object has an unbalanced force acting on it. In this equation, the force is the resultant force along the line of motion, not every force added without direction.

If the resultant force is larger, the acceleration is larger. If the same resultant force acts on a larger mass, the acceleration is smaller.

Unbalanced force

An unbalanced force is a resultant force that is not zero, so it can change an object's velocity.

The Edexcel relationship is:

Newton's second law

F=m×aF = m \times a

where:

  • F is the unbalanced force in newtons, N
  • m is the mass in kilograms, kg
  • a is the acceleration in metres per second squared, m/s^2

This equation also explains the size of the newton: 1 N is the force needed to give a 1 kg mass an acceleration of 1 m/s^2.

Using F = m x a

Most exam questions are not trying to trick you with new physics here. They are checking whether you choose the correct equation, substitute the values with units, and rearrange when needed.

For Newton's second law:

  • to find force: F = m x a
  • to find mass: m = F / a
  • to find acceleration: a = F / m

Worked example:

A cyclist and bicycle have a total mass of 80 kg. The resultant forward force is 120 N. Calculate the acceleration.

Use:

a=Fma = \frac{F}{m}

Substitute:

a=12080=1.5 m/s2a = \frac{120}{80} = 1.5\ \text{m/s}^2

The acceleration is 1.5 m/s^2 in the direction of the resultant force.

Be careful with the wording. If a question gives two forces acting in opposite directions, find the resultant first. For example, a forward driving force of 50 N and a backward friction force of 20 N give an unbalanced force of 30 N forwards.

Weight, mass and gravitational field strength

Mass and weight are connected, but they are not the same quantity.

Mass is measured in kilograms. It tells you how much matter an object has, and it is the same for the object unless matter is added or removed.

Weight is a force. It is the gravitational force on a mass, so it is measured in newtons.

Gravitational field strength, g, tells you the weight per kilogram of mass at a particular place. Its unit is newtons per kilogram, N/kg.

Weight

W=m×gW = m \times g

where:

  • W is weight in newtons, N
  • m is mass in kilograms, kg
  • g is gravitational field strength in newtons per kilogram, N/kg

Near the surface of Earth, questions often use a value close to 10 N/kg; use the value given in the question. On a planet or moon with a smaller gravitational field strength, the same mass has a smaller weight.

Using W = m x g

The weight equation works in the same way as other formulae: write it down, substitute, then calculate with the correct unit.

Worked example:

A student has mass 52 kg. The gravitational field strength is 9.8 N/kg. Calculate the student's weight.

Use:

W=m×gW = m \times g

Substitute:

W=52×9.8=509.6 NW = 52 \times 9.8 = 509.6\ \text{N}

The student's weight is about 510 N.

You may also need to rearrange:

  • to find mass: m = W / g
  • to find gravitational field strength: g = W / m

Worked example:

An object has weight 180 N where the gravitational field strength is 6.0 N/kg. Its mass is:

m=Wg=1806.0=30 kgm = \frac{W}{g} = \frac{180}{6.0} = 30\ \text{kg}

The mass is 30 kg. Do not write 30 N; newtons are for forces such as weight.

Choosing the right equation

The two equations have a similar shape, but they answer different questions.

Use F = m x a when the question is about an unbalanced force causing acceleration. The acceleration unit m/s^2 is the clue.

Use W = m x g when the question is about the force of gravity on a mass. The gravitational field strength unit N/kg is the clue.

The symbols also carry meaning:

  • F can be any unbalanced force on an object
  • W is specifically the object's weight
  • a is acceleration caused by an unbalanced force
  • g is gravitational field strength at a place

If weight is the only unbalanced force on an object, the two equations can connect: the weight provides the unbalanced force. For this lesson, the key skill is still to choose the equation that matches the quantity the question asks for.