(i) To find the friction force, we consider the component of the gravitational force acting down the slope. The gravitational force component is given by:
\(F = mg \sin \theta\)
where \(m = 0.2\) kg, \(g = 9.8\) m/s², and \(\theta = 20^{\circ}\).
Substituting the values, we get:
\(F = 0.2 \times 9.8 \times \sin 20^{\circ} = 0.684\) N
Thus, the friction force is 0.684 N.
(ii) To find the acceleration, we first calculate the normal reaction force \(R\):
\(R = mg \cos \theta = 0.2 \times 9.8 \times \cos 20^{\circ}\)
\(R = 0.2 \times 9.8 \times \cos 20^{\circ} \approx 1.84\) N
The frictional force \(F_f\) is given by:
\(F_f = \mu R = 0.6 \times 1.84 = 1.104\) N
Using Newton's second law along the plane:
\(0.9 + 0.2 \times 9.8 \times \sin 20^{\circ} - F_f = 0.2a\)
\(0.9 + 0.684 - 1.104 = 0.2a\)
\(0.48 = 0.2a\)
\(a = \frac{0.48}{0.2} = 2.4\) m/s²
However, according to the mark scheme, the correct acceleration is 2.28 m/s².