Further Mechanics and Thermal Physics
Further mechanics and thermal physics is the A-level Physics topic covering momentum in collisions, circular motion, simple harmonic motion (SHM) and the kinetic theory of gases, including specific heat capacity and the ideal gas equation. It extends the mechanics met earlier in the course to periodic and molecular-scale motion.
Before you start
Make sure you're comfortable with these topics first:
Method
- Apply conservation of momentum (total momentum before = total momentum after) to collisions, then compare kinetic energy before and after to classify a collision as elastic or inelastic.
- For circular motion, use a = v^2/r for centripetal acceleration, and identify which force (tension, friction, gravity, normal reaction) provides the centripetal force in a given scenario.
- Recognise SHM from its defining condition: acceleration is proportional to displacement from equilibrium and always directed towards it, then use v(max) = omega x A and a(max) = omega^2 x A for the maximum speed and acceleration.
- Use T = 2 x pi / omega together with T = 2 x pi x sqrt(m/k) for a mass-spring system, or T = 2 x pi x sqrt(l/g) for a simple pendulum, to find the period of oscillation.
- For thermal physics, use Q = m x c x (change in temperature) for specific heat capacity calculations and p x V = n x R x T for the ideal gas equation, being careful to convert temperature to kelvin.
- Distinguish free, forced and damped oscillations, and explain resonance as the large-amplitude response that occurs when the driving frequency matches the system's natural frequency.
Worked example
A mass of 0.40 kg on a spring oscillates with simple harmonic motion of amplitude 0.15 m and period 1.2 s. Calculate the maximum speed and maximum acceleration of the mass.
- Calculate the angular frequency: omega = 2 x pi / T = 2 x pi / 1.2.
- Evaluate: omega = 5.24 rad/s.
- Use v(max) = omega x A to find the maximum speed: v(max) = 5.24 x 0.15.
- Evaluate: v(max) = 0.785 m/s.
- Use a(max) = omega^2 x A to find the maximum acceleration: a(max) = (5.24)^2 x 0.15.
- Final answer: v(max) = 0.785 m/s, a(max) = 4.11 m/s^2.
Practice questions
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Q1State the two conditions required for a system to undergo simple harmonic motion.Show answer
Answer: Acceleration is proportional to displacement from equilibrium, and is always directed towards the equilibrium position.
Q2A trolley of momentum 6.0 kg m/s collides with and sticks to a stationary trolley, giving a combined momentum of 6.0 kg m/s immediately after. State what this shows about momentum in the collision.Show answer
Answer: Momentum is conserved (unchanged) in the collision, as expected for a closed system.
Q3A car of mass 1000 kg travels around a circular bend of radius 50 m at a constant speed of 10 m/s. Calculate the centripetal acceleration.Show answer
Answer: 2.0 m/s^2 (a = v^2/r = 10^2/50)
Q4A mass-spring system has period 0.50 s and spring constant 80 N/m. Calculate the mass, using T = 2 x pi x sqrt(m/k).Show answer
Answer: 0.507 kg (m = k x (T/(2pi))^2 = 80 x (0.50/6.283)^2)
Q5A block of mass 0.50 kg is heated by a 20 W heater for 60 s, causing its temperature to rise from 20 degrees C to 44 degrees C. Calculate the specific heat capacity of the block, assuming no heat losses.Show answer
Answer: 100 J/(kg degrees C) (Q = P x t = 20 x 60 = 1200 J; c = Q/(m x change in T) = 1200/(0.50 x 24))
Q6A fixed mass of gas at pressure 1.0 x 10^5 Pa and volume 2.0 x 10^-3 m^3 is at temperature 300 K. Calculate the number of moles of gas present, using p x V = n x R x T. (R = 8.31 J/(mol K))Show answer
Answer: 0.0802 mol (n = pV/(RT) = (1.0 x 10^5 x 2.0 x 10^-3)/(8.31 x 300))
Exam-style questions
Written in the style of a A Level Science exam paper, with a full mark scheme.
A ball of mass 0.20 kg moving at 4.0 m/s collides head-on with a stationary ball of mass 0.60 kg. After the collision the two balls move off together. Calculate their common velocity.
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A mass on a spring undergoes SHM with angular frequency 6.0 rad/s and amplitude 0.080 m. Calculate the speed of the mass when its displacement from equilibrium is 0.050 m, using v = omega x sqrt(A^2 - x^2).
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This question is about the required practical to determine the spring constant of a spring using SHM. A student measures the period of oscillation of different masses on a spring and plots a graph of T^2 against m, using T^2 = (4 x pi^2 / k) x m. Describe how the student should measure each period accurately, and explain how the spring constant k is found from the graph.
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See real A Level Science past-paper questions, with official mark schemes →
Free printable worksheet
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