7 A train consists of a locomotive pulling 17 identical trucks.
The mass of the locomotive is 120 tonnes and the mass of each truck is 40 tonnes. The locomotive gives a driving force of 121000 N . The resistance to motion on each truck is \(R \mathrm {~N}\) and the resistance on the locomotive is \(5 R \mathrm {~N}\).
Initially the train is travelling on a straight horizontal track and its acceleration is \(0.11 \mathrm {~ms} ^ { - 2 }\).

1. Show that \(R = 1500\).
2. Find the tensions in the couplings between
   (A) the last two trucks,
   (B) the locomotive and the first truck. The train now comes to a place where the track goes up a straight, uniform slope at an angle \(\alpha\) with the horizontal, where \(\sin \alpha = \frac { 1 } { 80 }\). The driving force and the resistance forces remain the same as before.
3. Find the magnitude and direction of the acceleration of the train. The train then comes to a straight uniform downward slope at an angle \(\beta\) to the horizontal.
   The driver of the train reduces the driving force to zero and the resistance forces remain the same as before.
   The train then travels at a constant speed down the slope.
4. Find the value of \(\beta\).