Question

A block weighing 14 lb is placed on an incline plane and connected to a 10 lb block, as shown in the diagram. The pulley is frictionless. The coefficient of friction between block and plane is 1/7. For what two values of angle ? will the system move with constant velocity?

(Hint: You need the identity relating sin? and cos?; find the angles when block is sliding down and up)

Answer 1

$\dpi{120} \large \mu = \frac{1}{7} \par f = \mu R = \mu mg cos \theta \par When block is moving up; we get \par 10 g - 14 g sin \theta - \frac{14}{7} g cos \theta = 0 \par 7 sin \theta +cos \theta = 5 \par Now sin \theta = \frac{P}{H} \and \cos \theta = \frac{B}{H} \par where P is the perpendicular, B is the base and H is the hypotenuse of a right angled triangle \par Using these values in the above equation \par 7 P + B = 5 H \par Now using hit and trial method the values satisfying the above equation and \par H^2 = P^2 +B^ 2 \par for a right angled triangle comes as \par H = 5, P = 3, B = 4 \par Hence\ sin \theta = \frac{3}{5} \par \theta = 36.87^0 \\ \par When the block is sliding down, in that case we get the equation as \par 7 \sin \theta - cos \theta = 5 \par i.e. 7 P -B = 5H \par Again using hit and trial method we get the values \par H = 5, P = 4, B = 3 \par Hence sin \theta = \frac{4}{3} \par \theta = 53.12^0 \\ \par$