8 A crate, of mass 200 kg , is initially at rest on a rough horizontal surface. A smooth ring is attached to the crate. A light inextensible rope is passed through the ring, and each end of the rope is attached to a tractor. The lower part of the rope is horizontal and the upper part is at an angle of \(20 ^ { \circ }\) to the horizontal, as shown in the diagram.
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When the tractor moves forward, the crate accelerates at \(0.3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The coefficient of friction between the crate and the surface is 0.4 .
Assume that the tension, \(T\) newtons, is the same in both parts of the rope.
- Draw and label a diagram to show the forces acting on the crate.
- Express the normal reaction between the surface and the crate in terms of \(T\).
- Find \(T\).