- A suitcase of mass 40 kg is being dragged in a straight line along a rough horizontal floor at constant speed using a thin strap. The strap is inclined at \(20 ^ { \circ }\) above the horizontal. The coefficient of friction between the suitcase and the floor is \(\frac { 3 } { 4 }\). The strap is modelled as a light inextensible string and the suitcase is modelled as a particle. Find the tension in the strap.
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\caption{Figure 1}
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A metal girder \(A B\), of weight 1080 N and length 6 m , rests in equilibrium in a horizontal position on two supports, one at \(C\) and one at \(D\), where \(A C = 0.5 \mathrm {~m}\) and \(B D = 2 \mathrm {~m}\), as shown in Figure 1. A boy of weight 400 N stands on the girder at \(B\) and the girder remains horizontal and in equilibrium. The boy is modelled as a particle and the girder is modelled as a uniform rod.
- Find
- the magnitude of the reaction on the girder at \(C\),
- the magnitude of the reaction on the girder at \(D\).
(6)
The boy now stands at a point \(E\) on the girder, where \(A E = x\) metres, and the girder remains horizontal and in equilibrium. Given that the magnitude of the reaction on the girder at \(D\) is now 520 N greater than the magnitude of the reaction on the girder at \(C\),
- find the value of \(x\).