16 In this question use \(g = 9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
The diagram shows a box, of mass 8.0 kg , being pulled by a string so that the box moves at a constant speed along a rough horizontal wooden board. The string is at an angle of \(40 ^ { \circ }\) to the horizontal.
The tension in the string is 50 newtons.
\includegraphics[max width=\textwidth, alt={}, center]{a57b0526-cf9c-44d6-a349-cac392f85a70-26_334_862_884_575} The coefficient of friction between the box and the board is \(\mu\)
Model the box as a particle.
16

1. Show that \(\mu = 0.83\)
   [0pt] [4 marks] Question 16 continues on the next page 16
2. One end of the board is lifted up so that the board is now inclined at an angle of \(5 ^ { \circ }\) to the horizontal. The box is pulled up the inclined board.
   The string remains at an angle of \(40 ^ { \circ }\) to the board.
   The tension in the string is increased so that the box accelerates up the board at \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
   \includegraphics[max width=\textwidth, alt={}, center]{a57b0526-cf9c-44d6-a349-cac392f85a70-28_385_858_778_577} 16
3. 1. Draw a diagram to show the forces acting on the box as it moves. 16
4. (ii) Find the tension in the string as the box accelerates up the slope at \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
   [0pt] [7 marks]