(a) Explain the term net force. (b) Define the principle of conservation of linear momentum...
(a) Explain the term net force.
(b) Define the principle of conservation of linear momentum and state one example of it.
(c) A ball of mass 200 g released from a height of 2.0 m hits a horizontal floor and rebounds to a height of 1.8 in. Calculate the impulse received by the floor. (g = 10 ms\(^{-2}\)).
(d) A body of mass 20 g performs a simple harmonic motion at a frequency of 5 Hz. At a distance of 10 cm from the mean position, its velocity is 200 cms\(^{-1}\). Calculate its:
(i) maximum displacement from the mean position;
(ii) maximum velocity;
(iii) maximum potential energy. (g = 10 ms\(^{-2}\) \(\pi\) = 3.14)
Explanation
(a) Net force is the effective or resultant force resulting from the actions of a system of forces on a body.
(b) The principle ofconservation of linear momentum explains that in an isolated or closed system of colliding bodies the total linear momentum in a fixed direction remains constant, e.g. the recoil of gun, colliding trolleys, rocket propulsion, etc.
(c) V\(_1^2\) = \(U_1^2 + 2gh_1\) = 0 + 2 x 10 x 2
= 40
\(V_1 = \sqrt{40}\) = 6.325m/s
\(v_2^2 = u_2^2 - 2gh_2\)
O = \(U^2_2\) - 2 x 10 x 1.8
u = \(\sqrt{36}\)
= 6ms\(^{-1}\)
Impulse Change in momentun
mv\(_1\) - (-mu\(_2\)) = m (v\(_1\) + u\(_2\))
= 0.2(6.325 + 6.000)
= 2.46 Ns
(d) v = \(\omega \sqrt{r^2 - y^2}\)
2\(\pi\)f\(\sqrt{r^2 - y^2}\)
2 = 2 x 3.14 x 5 x \(\sqrt{r^2 - 0.1^2}\)
r = 0.12m
(ii) Vmax = \(\omega\)r = 2\(\pi\)fr
= 2 x 3.142 x 5 x 0.12
= 3,77 m/s
(iii) P.E = \(\frac{1}{2}m \omega^2e^2 = \times \frac{1}{2}m(2 \pi f)^2r^2\)
= \(\frac{1}{2} \times 0.02(2 \times 3.142 \times 5)^2 \times (0.12)^2\)
= 1.42 x 10\(^{-1}J\)