Mechanics and Materials
Mechanics and materials is the A-level Physics topic covering motion, forces, work, energy, power and the deformation of materials under stress and strain. It uses the SUVAT equations, Newton's laws and Hooke's law to analyse everyday and exam-style scenarios such as braking vehicles, ramps and springs.
Method
- For constant acceleration, choose the SUVAT equation that links the quantities given and the one you need to find, being careful with signs for deceleration.
- Resolve forces into components along and perpendicular to any relevant direction (for example, parallel and perpendicular to a slope), then apply Newton's second law, F = m x a, along each direction.
- Use conservation of momentum (total momentum before = total momentum after) for collisions, and check whether kinetic energy is also conserved to decide if a collision is elastic or inelastic.
- Calculate work done (W = F x s), power (P = W/t or P = F x v) and efficiency (useful output / total input x 100%) for problems involving energy transfer.
- For projectile motion, treat the horizontal and vertical motions independently, using SUVAT vertically (with acceleration g) and constant velocity horizontally.
- For materials, use stress = force/area and strain = extension/original length to find the Young modulus from the gradient of a stress-strain graph, and use Hooke's law (F = k x x) and E = (1/2) x k x x^2 for elastic potential energy.
Worked example
A car of mass 900 kg accelerates uniformly from rest to a velocity of 24 m/s in 8.0 s while travelling along a flat, straight road. Calculate (a) the acceleration of the car, and (b) the resultant force acting on it.
- Identify the known quantities: u = 0, v = 24 m/s, t = 8.0 s.
- Use a = (v - u) / t to find the acceleration.
- Substitute: a = (24 - 0) / 8.0 = 3.0 m/s^2.
- Use Newton's second law, F = m x a, with m = 900 kg and the acceleration found above.
- Substitute: F = 900 x 3.0.
- Final answer: a = 3.0 m/s^2, resultant force F = 2700 N.
Practice questions
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Q1State the SI unit of force.Show answer
Answer: newton (N)
Q2A ball is dropped from rest and falls for 2.0 s. Calculate its velocity just before landing. (g = 9.81 m/s^2)Show answer
Answer: 19.6 m/s (v = u + g x t = 0 + 9.81 x 2.0)
Q3Calculate the work done when a force of 40 N moves an object 5.0 m in the direction of the force.Show answer
Answer: 200 J (W = F x s = 40 x 5.0)
Q4A trolley of mass 2.0 kg moving at 3.0 m/s collides with and sticks to a stationary trolley of mass 1.0 kg. Calculate their common velocity after the collision.Show answer
Answer: 2.0 m/s (momentum: 2.0 x 3.0 = 3.0 x v, so v = 6.0/3.0)
Q5A spring has a spring constant of 25 N/m. Calculate the elastic potential energy stored when it is extended by 0.20 m.Show answer
Answer: 0.50 J (E = 1/2 x k x x^2 = 0.5 x 25 x 0.20^2)
Q6A crate of weight 300 N is pulled at constant velocity up a smooth ramp inclined at 30 degrees to the horizontal by a rope parallel to the slope. Calculate the tension in the rope.Show answer
Answer: 150 N (T = W x sin(30) = 300 x 0.5, since the ramp is frictionless and the crate moves at constant velocity)
Exam-style questions
Written in the style of a A Level Science exam paper, with a full mark scheme.
A skateboarder travelling at 6.0 m/s decelerates uniformly and comes to rest after travelling 9.0 m. Calculate the deceleration.
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A 5.0 kg object falls from rest and reaches the ground with kinetic energy of 245 J, having fallen through a height h. Assuming air resistance is negligible, calculate h. (g = 9.81 m/s^2)
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This question is about the required practical to investigate Hooke's law using a spring. A student hangs a spring vertically and adds masses one at a time, recording the total extension for each added force. Describe how the student should carry out this experiment to obtain a reliable value of the spring constant, and explain how the spring constant is found from the resulting data.
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See real A Level Science past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the mechanics and materials worksheet pack - 16 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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