(a) State the triangle law of vector addition.
(b) Name the four physical quantities that are associated with the equationq of linear motion.
(c) Using the same set of axes, sketch and label two graphs to illustrate the variation of potential energy and kinetic energy with time for a body in simple harmonic motion.
(d)
A light spiral spring of force constant K lies on a horizontal frictionless surface and has one end fixed to a vertical wall. A block P of mass 2.0 kg placed against the free end of the spring is pushed a distance 5 cm towards the wall with 10J of energy as illustrated in the diagram above. The block is released and after 0.25s, it collides inelastically with a stationary block Q of mass 4.0 kg. Calculate the:
(i) value of k;
(ii) force used to compress the spring;
(iii) acceleration of the block p after release;
(iv) common speed after collision of the blocks.
Explanation
(a) Triangle law of vector addition states that if three forces are in equilibrium, they can be represented in magnitude and direction by the three sides of a triangle taken in order.
(b) Physical quantities associated with equations of motion are:
- time
- speed/ velocity
- distance or displacement and acceleration.
(c)
(d)
W = \(\frac{1}{2}Ke^2\)
K = \(\frac{2W}{e^2} = \frac{2 \times 10}{\frac{5}{100}} = 8000 NM^{-1}\)
(ii) F = Ke = 800 x \(\frac{5}{100}\)
= 400N
(iii) F = Ma
a = \(\frac{F}{M} = \frac{400}{2}\) = 200 ms\(^{-2}\)
(iv) Initial velocity U\(_p\) of the block
P = 200 x 0.25
= 50 ms\(^{-1}\)
but \(M_pU_p + M_qU_q = (M_p + M_Q)\)
2 x 50 + 4 x 0 = V(2 + 4)
V = \(\frac{100}{6} = 16.7 ms^{-1}\)