2 Unit AS 2: Applied Mathematics
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Question 281
A plank ABABAB, of length 2 m and mass M M\,M kg, rests with the end A A\,A against a rough vertical wall. The plank is held in a horizontal position by a rope attached to B B\,B and to the wall at the point CCC.
A small block of mass 2M 2M\,2M kg is placed on the plank at PPP, where AP=1.5AP = 1.5AP=1.5 m. The angle between the rope and the plank is α\alphaα, where tanα=34\displaystyle \tan\alpha = \frac{3}{4}tanα=43.
The plank is modelled as a uniform rod, the block as a particle and the rope as a light inextensible string.
a.[3]
Find, in terms of M M\,M and ggg, the tension in the rope BCBCBC.
b.[3]
Find the direction of the force exerted on the plank at AAA.