A plank of length l = 2m is hinged at one end to a wall. Theother end is being (temporarily) supported by a worker who isholding it up with his hand, keeping the plank horizontal. Theplank has a mass of 20kg, and there is also a toolbox of mass 5kgsitting on it, 50cm away from the worker (1.5 m away from thewall). (a) Draw a free body diagram and an extended free-bodydiagram for the plank. (b) What are the magnitudes of (1) theupwards force exerted by the worker on the plank and (2) the forceat the hinge?(c) If the worker were to let go of the plank, whatwould its angular acceleration be as it starts swinging down? Themoment of inertia is I = 1Ml2. (Note: assume the toolbox stopspressing down on the plank immediately. This is a goodapproximation, as you shall see below.)(d) Consider a point on theplank located immediately below the toolbox. As the plank swings,this point moves in a circle of radius 1.5 m. What is its linear(tangential) acceleration as it starts going down, and how does itcompare to the acceleration of gravity?
