A plank AB 3.0m long weighing 20kg and with its centre of gravity 2.0m from the end A carries a load of mass 10kg at end A. It rest on two supports at C and D
I) Compute the values of the reaction forces R1 and R2 at C and D
To compute the values of the reaction forces R1 and R2 at supports C and D, we need to balance the moments about the points C and D.
First, let's draw a diagram to visualize the setup:
A---------------------------B
|<---2.0m--->|
C D
Now, let's calculate the moments about support C:
The weight of the plank (20kg) acts at its center of gravity, which is 2.0m from end A. Therefore, the moment caused by the plank's weight about C is 20kg * 2.0m = 40kg·m.
Since the load (10kg) is located at end A, it has a moment of 10kg * 3.0m = 30kg·m about C, in the opposite direction.
Next, let's consider the unknown reaction force R1 at support C. Taking moments about C, we have:
40kg·m - 30kg·m - R1 * 3.0m = 0
Simplifying the equation, we get:
10kg·m - R1 * 3.0m = 0
Solving for R1, we find:
R1 = 10kg·m / 3.0m
R1 = 3.33 kg·m/s² (rounding to two decimal places)
Now, let's calculate the moments about support D:
Since there is no load beyond support D, the only moment acting about D is the weight of the plank (20kg) multiplied by its length (3.0m):
Moment about D = 20kg * 3.0m = 60kg·m
Next, let's consider the unknown reaction force R2 at support D. Taking moments about D, we have:
R2 * 3.0m - 60kg·m = 0
Simplifying the equation, we get:
R2 * 3.0m = 60kg·m
Solving for R2, we find:
R2 = 60kg·m / 3.0m
R2 = 20 kg·m/s²
Therefore, the values of the reaction forces R1 and R2 at supports C and D are:
R1 = 3.33 kg·m/s²
R2 = 20 kg·m/s²