8 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]
\includegraphics[alt={},max width=\textwidth]{2efbb554-fe60-42ce-9213-8c66bfdb1d85-5_255_1097_397_523}
\captionsetup{labelformat=empty}
\caption{Fig. 8.1}
\end{figure}
- 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]{2efbb554-fe60-42ce-9213-8c66bfdb1d85-5_305_1191_1050_701}
\captionsetup{labelformat=empty}
\caption{Fig. 8.2}
\end{figure} - Calculate the magnitude of the total horizontal resistance acting on the two trolleys opposing the pull.
- 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.
- 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]{2efbb554-fe60-42ce-9213-8c66bfdb1d85-5_355_1294_2156_429}
\captionsetup{labelformat=empty}
\caption{Fig. 8.3}
\end{figure} - Calculate the speed of the trolleys after 2 seconds and also the force in the rod connecting the trolleys, stating whether this rod is in tension or thrust (compression).