A uniform plank measures 2 meter long from its end point A to B if the weight of the plank is 54N and it rest on a knife edge 0.50m from end B and point A is supported by a vertical string so that B balances horizontally.
(1) draw a force diagram for the arrangement
(2) Determine the tension in the string
(3) Determine the force acting on the knife edge
(1) To draw the force diagram for the arrangement, we need to consider the various forces acting on the plank.
- The weight of the plank, which acts downwards from its center of gravity.
- The tension in the string, which acts upwards towards the support point at A.
- The reaction force at the knife edge, which acts upwards and perpendicular to the edge.
- The normal force at the knife edge, which acts upwards and perpendicular to the edge in response to the weight of the plank.
Note that the horizontal forces cancel out since the plank is in equilibrium.
(2) To determine the tension in the string, we can use the principle of moments. The plank is in equilibrium, so the sum of the moments on either side of the support point must be equal.
Taking moments about point A, we have:
Weight of plank * Distance from A to center of gravity = Tension in string * Distance from A to support point B
Given that the weight of the plank is 54N, the distance from A to the center of gravity is 1 meter (half of the plank's length), and the distance from A to B is 0.50m, we can solve for the tension in the string:
54N * 1m = Tension * 0.50m
Tension = (54N * 1m) / 0.50m
Tension = 108N
Therefore, the tension in the string is 108N.
(3) To determine the force acting on the knife edge, we need to consider the reaction force and the normal force.
Since the plank is in equilibrium, the sum of the vertical forces must be zero. Therefore, the reaction force at the knife edge is equal in magnitude but opposite in direction to the weight of the plank. The force acting on the knife edge can be determined as:
Force on Knife Edge = Weight of Plank = 54N
Therefore, the force acting on the knife edge is 54N.