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
- Show that \(\mu = 0.83\)
[0pt]
[4 marks]
Question 16 continues on the next page
16 - 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 - Draw a diagram to show the forces acting on the box as it moves.
16
- (ii) Find the tension in the string as the box accelerates up the slope at \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
[0pt]
[7 marks]