In this question use $g = 9.8 \, ext{ms}^{-2}$ - AQA - A-Level Maths Pure - Question 16 - 2017 - Paper 2

The diagram should accurately depict the forces acting on the box, including:

• Gravitational force, $W = mg$ directed downwards,
• Normal force $R$ acting perpendicular to the surface,
• Tension force $T$ acting along the string,
• Frictional force $F = \mu R$ opposite the direction of motion.
  Ensure all forces are labeled with arrows indicating their direction.

To find the tension, we utilize Newton's second law.
For the inclined board with an angle of 5$^{\circ}$:

• The net force is given by:
  $\sum F = ma$
  Where $a = 3 \, \text{ms}^{-2}$, hence we start with:

Step 1: Resolve Forces Parallel to Inclined Plane
The forces acting along the incline include the tension and the component of weight along the incline:

$T - mg \sin 5^{\circ} - F = ma$
With $F = \mu R$, we substitute our earlier calculated values of $R$:

Step 2: Substituting forces
Using the earlier approximation for friction, we set:
$T - 8 \times 9.8 \sin 5^{\circ} - \mu \times 78.1 = 8 \times 3$
Rearranging gives us:
$T = 8 \times 9.8 \sin 5^{\circ} + \mu \times 78.1 + 24$
Substituting values into this equation yields:
$T = 24 + 0.83 \times 78.1 + 8 \times 9.8 \sin 5^{\circ}$
Calculating this provides:
$T \approx 73.56 \, \text{N} \text{ (rounded to 2 d.p.) }$
Thus, the tension in the string is approximately $74 \, \text{N}$.