Makerere University
Department of Physics
PHY1211/PHX1212: Classical Mechanics I
Test I
Date: Thursday, 02nd December, 2021
Duration: 1 hour
Answer ALL questions
1. (a)
(i) State the principle Galilean invariance.
[1]
(ii) State the two assumptions of classical mechanics.
[2]
2
~
(b) A 2 kg object moves in a force field given by F = 2t ı̂ + (3t − 1)̂ − tk̂. If at time t = 0,
~r = 0 and ~v = 0. Find the expressions for;
(i) velocity ~v at any time t.
(ii) and its position ~r.
[3]
[3]
2. (a) The potential energy function of a particle is given by
U (x) = 5x2 − 4x3 ,
where U is in joules and x is in metres.
(i) Determine the force F~ (x) acting on the particle.
[2]
(ii) Find the positions where the particle is in equilibrium and state whether they are
stable or unstable.
[3]
(b) A parachutist jumps at an altitude of 3000 m. Before the parachute opens she reaches a
terminal velocity of 30 ms−1 .
(i) Assuming that air resistance is proportional to velocity, write down an expression for
the equation of motion for the parachutist.
[2]
(ii) Find the velocity at any time t and hence find the time it takes her to reach terminal
velocity.
[5]
(iii) Derive an expression for the displacement and hence find the distance she has travelled
before reaching the terminal velocity?
[4]
(iv) Is the assumption that air resistance is proportional to speed a reasonable one? Show
that this is or is not the case using qualitative arguments.
[3]
Good luck
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