7 Clive and Ken are trying to move a box of mass 50 kg on a rough, horizontal floor. As shown in Fig. 7, Clive always pushes horizontally and Ken always pulls at an angle of \(30 ^ { \circ }\) to the horizontal. Each of them applies forces to the box in the same vertical plane as described below.
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\caption{Fig. 7}
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Initially, the box is in equilibrium with Clive pushing with a force of 60 N and Ken not pulling at all.
- What is the resistance to motion of the box?
Ken now adds a pull of 70 N to Clive's push of 60 N . The box remains in equilibrium.
- What now is the resistance to motion of the box?
- Calculate the normal reaction of the floor on the box.
The frictional resistance to sliding of the box is 125 N .
Clive now pushes with a force of 160 N but Ken does not pull at all. - Calculate the acceleration of the box.
Clive stops pushing when the box has a speed of \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- How far does the box then slide before coming to rest?
Ken and Clive now try again. Ken pulls with a force of \(Q \mathrm {~N}\) and Clive pushes with a force of 160 N . The frictional resistance to sliding of the box is now 115 N and the acceleration of the box is \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
- Calculate the value of \(Q\).