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Nov 2018 p42 q2
4037
A block of mass 5 kg is being pulled by a rope up a rough plane inclined at 6° to the horizontal. The rope is parallel to a line of greatest slope of the plane and the block is moving at constant speed. The coefficient of friction between the block and the plane is 0.3. Find the tension in the rope.
Solution
First, calculate the normal reaction force, \(R\), on the block. Since the block is on an inclined plane, \(R = 5g \cos 6^{\circ}\).
Next, calculate the frictional force, \(F\), using the formula \(F = \mu R\), where \(\mu = 0.3\). Thus, \(F = 0.3 \times 5g \cos 6^{\circ}\).
Since the block is moving at constant speed, the tension \(T\) in the rope must balance the component of gravitational force down the plane and the frictional force. Therefore, \(T = 5g \sin 6^{\circ} + F\).