5. A toy sledge of mass 4 kg is being pulled in a straight line by a light string. The resistance to its motion is 6 N . \begin{figure}[h] \end{figure} At one time, the string is horizontal and the sledge is on horizontal ground, as shown in Fig. 6.1. The acceleration of the sledge is \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) forwards.

1. Calculate the tension in the string. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{fb36606d-0ee3-4050-af31-1642e5f67a03-14_190_718_813_733} \captionsetup{labelformat=empty} \caption{Fig. 6.2}
   \end{figure} At another time, the sledge is again on horizontal ground but the string is now at \(40 ^ { \circ }\) to the horizontal, as shown in Fig. 6.2. The tension in the string is 25 N .
2. Calculate the acceleration of the sledge. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{fb36606d-0ee3-4050-af31-1642e5f67a03-16_364_465_283_479} \captionsetup{labelformat=empty} \caption{Fig. 6.3}
   \end{figure} \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{fb36606d-0ee3-4050-af31-1642e5f67a03-16_414_463_233_1226} \captionsetup{labelformat=empty} \caption{Fig. 6.4}
   \end{figure} In another situation the sledge is on a slope inclined at \(35 ^ { \circ }\) to the horizontal, as shown in Fig. 6.3. It is held in equilibrium by the light string parallel to the slope. The resistance to motion of 6 N acts up the slope.
3. Calculate the tension in the string. The sledge is now held in equilibrium with the light string inclined at \(\theta ^ { \circ }\) to the slope, as shown in Fig. 6.4. The tension in the string is 25 N and the resistance to motion remains 6 N acting up the slope.
4. (A) Show all the forces acting on the sledge.
   (B) Calculate the angle \(\theta\).
   (C) Calculate the normal reaction of the slope on the sledge. \includegraphics[max width=\textwidth, alt={}, center]{fb36606d-0ee3-4050-af31-1642e5f67a03-17_2688_1886_118_118}