3 A trolley C of mass 8 kg with rusty axle bearings is initially at rest on a horizontal floor.
The trolley stays at rest when it is pulled by a horizontal string with tension 25 N , as shown in Fig. 8.1. \begin{figure}[h] \end{figure}

1. State the magnitude of the horizontal resistance opposing the pull. A second trolley D of mass 10 kg is connected to trolley C by means of a light, horizontal rod.
   The string now has tension 50 N , and is at an angle of \(25 ^ { \circ }\) to the horizontal, as shown in Fig. 8.2. The two trolleys stay at rest. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{f5f9b9b7-6766-4f8e-b011-506051104123-3_297_1180_971_741} \captionsetup{labelformat=empty} \caption{Fig. 8.2}
   \end{figure}
2. Calculate the magnitude of the total horizontal resistance acting on the two trolleys opposing the pull.
3. Calculate the normal reaction of the floor on trolley C . The axle bearings of the trolleys are oiled and the total horizontal resistance to the motion of the two trolleys is now 20 N . The two trolleys are still pulled by the string with tension 50 N , as shown in Fig. 8.2.
4. Calculate the acceleration of the trolleys. In a new situation, the trolleys are on a slope at \(5 ^ { \circ }\) to the horizontal and are initially travelling down the slope at \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistances are 15 N to the motion of D and 5 N to the motion of C . There is no string attached. The rod connecting the trolleys is parallel to the slope. This situation is shown in Fig. 8.3. \begin{figure}[h]
   \includegraphics[alt={},max width=\textwidth]{f5f9b9b7-6766-4f8e-b011-506051104123-3_351_1285_2038_466} \captionsetup{labelformat=empty} \caption{Fig. 8.3}
   \end{figure}
5. Calculate the speed of the trolleys after 2 seconds and also the force in the rod connecting the PhysicsAptMaths, statter \&REther this rod is in tension or thrust (compression).