Forces and Newton’s laws Worked Solutions — A-Level Maths

Fully worked, step-by-step solutions to A-Level Forces and Newton’s laws questions. See exactly how to solve problems on weight, forces, mass, newtons-second-law.

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A-Level70 questionsStep-by-step solutions
Question 1
2 markseasy
A body has mass 5 kg5\,\text{kg}. Taking g=9.8 m s−2g=9.8\,\text{m s}^{-2}, find its weight.

Worked solution

  1. Recall the connection between weight and mass

    W=mgW=mg

    Weight is the gravitational force acting on the mass.

  2. Substitute the mass and the value of g

    W=5×9.8W=5\times 9.8

    Insert the given mass and g.

  3. State the weight

    W=49 NW=49\,\text{N}

    This is the required weight.

Answer
W=49 NW=49\,\text{N}
Question 2
2 markseasy
A body has mass 12 kg12\,\text{kg}. Taking g=9.8 m s−2g=9.8\,\text{m s}^{-2}, find its weight.

Worked solution

  1. Recall the connection between weight and mass

    W=mgW=mg

    Weight is the gravitational force acting on the mass.

  2. Substitute the mass and the value of g

    W=12×9.8W=12\times 9.8

    Insert the given mass and g.

  3. State the weight

    W=117.6 NW=117.6\,\text{N}

    This is the required weight.

Answer
W=117.6 NW=117.6\,\text{N}
Question 3
2 markseasy
An object has weight 98 N98\,\text{N}. Taking g=9.8 m s−2g=9.8\,\text{m s}^{-2}, find its mass.

Worked solution

  1. Recall the connection between weight and mass

    W=mgW=mg

    Weight is mass times g.

  2. Rearrange for the mass and substitute

    m=Wg=989.8m=\frac{W}{g}=\frac{98}{9.8}

    Make the mass the subject and insert the numbers.

  3. State the mass

    m=10 kgm=10\,\text{kg}

    This is the required mass.

Answer
m=10 kgm=10\,\text{kg}
Question 4
2 markseasy
A resultant force of 20 N20\,\text{N} acts on a body of mass 4 kg4\,\text{kg}. Find the acceleration produced.

Worked solution

  1. Write Newton's second law

    F=maF=ma

    Force equals mass times acceleration.

  2. Rearrange for the acceleration and substitute

    a=Fm=204a=\frac{F}{m}=\frac{20}{4}

    Make the acceleration the subject and insert the numbers.

  3. State the acceleration

    a=5 m s−2a=5\,\text{m s}^{-2}

    This is the required acceleration.

Answer
a=5 m s−2a=5\,\text{m s}^{-2}
Question 5
2 markseasy
A resultant force of 45 N45\,\text{N} acts on a body of mass 9 kg9\,\text{kg}. Find the acceleration produced.

Worked solution

  1. Write Newton's second law

    F=maF=ma

    Force equals mass times acceleration.

  2. Rearrange for the acceleration and substitute

    a=Fm=459a=\frac{F}{m}=\frac{45}{9}

    Make the acceleration the subject and insert the numbers.

  3. State the acceleration

    a=5 m s−2a=5\,\text{m s}^{-2}

    This is the required acceleration.

Answer
a=5 m s−2a=5\,\text{m s}^{-2}

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