(a) State two deductions that can be made from a displacement-time graph.
(b) If the distance beween two equal masses is doubled and their individual masses are also doubled, what would happen to the force between them? Support your answer quantitatively.
(c) State two factors that affect the maximum height attained by a bullet fired from a gun.
(d) State two practical examples of mechanical resonance. A body is released from rest at the top of a plane inclined at 30° to the horizontal and 4.0 m high. If the coefficient of friction between the body and the plane is 0.3, calculate the time the body takes to reach the bottom of the plane.
Explanation
(a) From a displacement - time graph, the following can be deduced
(i) Uniform velocity
(ii) Instantaneous velocity
(iii) Initial displacement
(b) The force would remain the same Gram =
\(F_2 = \frac{Gmm}{r^2}\)
F\(_2\) = \(\frac{G2m \times 2m}{(2r)^2}\)
=\(\frac{G4m^2}{4r^2}\)
= \(\frac{Gm^2}{r^2}\)
= \(\frac{Gmm}{r^2}\)
\(F_1 = F_2\)
(c)Factors that affect maximum height of a bullet include
(i) Initial velocity / speed
(ii) Acceleration due to gravity
(iii) Angle of projection
(iv) Air resistance
(d)Practical examples of mechanical resonance include:
(i) Shattering of glass due to high pitch note.
(ii) Throwing of 2 paper rider from a vibrating stretched string
(iii) Collapse of a bridge by matching soldiers
(iv) Car bodies rattle (at very high speed)
(e)
acceleration = g sin \(\theta\) – \(\mu\) cos \(\theta\)
a =10 x sin 30 – 0.3 x 10 x cos30
=10 x 0.5 –0.3 x 10 x 0.8660
= 5 – 2.598
= 2.4m/s\(^2\)
Distance covered, s = \(\frac{4}{\sin30}\)
= \(\frac{4}{0.5}\)
= 8m
Using S = Ut + \(\frac{1}{2}\)at\(^2\)
8 =\(\frac{1}{2}\) x 2.4 x r\(^2\)
8 = 1.2\(t^2\)
\(r^2\) = \(\frac{8}{1.2}\)
= 2.58s