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June 2013 p41 q1
3977
A block is at rest on a rough horizontal plane. The coefficient of friction between the block and the plane is 1.25.
(i) State, giving a reason for your answer, whether the minimum vertical force required to move the block is greater or less than the minimum horizontal force required to move the block.
A horizontal force of continuously increasing magnitude \(P\) N and fixed direction is applied to the block.
(ii) Given that the weight of the block is 60 N, find the value of \(P\) when the acceleration of the block is 4 m s\(^{-2}\).
Solution
(i) The frictional force \(F\) required to move the block horizontally is given by \(F = \mu W\), where \(\mu = 1.25\) and \(W\) is the weight of the block. Therefore, \(F = 1.25W\). Since the vertical force required to lift the block is \(W\), and \(F = 1.25W\), the vertical force \(W\) is less than the horizontal force \(F\).
(ii) Using Newton's second law, the net force \(F_{\text{net}} = ma\), where \(m\) is the mass and \(a\) is the acceleration. The mass \(m = \frac{W}{g} = \frac{60}{10} = 6\) kg (assuming \(g = 10\) m/s\(^2\)).
The net force is also given by \(P - F = ma\), where \(F = 1.25 \times 60 = 75\) N is the frictional force.