A plank AB 3.0 long weighing 20kg and with its centre of gravity 2.0m from the end A carries a load of mass 10kg at the end A. It rest on two supports at Cand D.Show diagram and solution
Why did the plank hire a personal trainer? Because it wanted to improve its balance!
Here's a diagram to help visualize the scenario:
A--------------------B
^(load)|...................................
|.......C____________D.........
|..................................
To find the reaction forces at supports C and D, we can use the principle of moments:
Taking moments about point D (clockwise positive):
20kg * 9.8m/s² * 1.0m = 10kg * 9.8m/s² * (2.0m + 3.0m)
Simplifying, we get:
196 = 98 + 490
196 = 588
Hmmm, it seems like there's a bit of a balancing act going on here. It looks like there might be a mistake in the calculation or setup. Let's try again!
Remember that the plank has a center of gravity 2.0m from end A, so the load of 10kg at end A is adding to the moment.
Taking moments about point D again:
(20kg * 9.8m/s² * 1.0m) + (10kg * 9.8m/s² * 4.0m) = R(C) * 3.0m
Simplifying, we get:
196 + 392 = 3R(C)
588 = 3R(C)
R(C) = 196N
So, the reaction force at support C is 196 N. Now we can find the reaction force at support D by using the principle of moments again, this time taking moments about C:
(20kg * 9.8m/s² * 1.0m) + (10kg * 9.8m/s² * 2.0m) = R(D) * 3.0m
Simplifying, we get:
196 + 196 = 3R(D)
392 = 3R(D)
R(D) = 130.67N
Therefore, the reaction force at support D is approximately 130.67N. Keep in mind that these values may vary slightly due to rounding in the calculations.
I hope this helped balance out your question!
To draw the diagram, start by drawing a horizontal line to represent the plank. Label one end as A and the other end as B.
Next, mark the center of gravity on the plank by drawing a vertical line upward from the midpoint of the plank. Label this point as G.
At point A, draw a vertical line downward to represent the load of mass 10kg. Label this point as L.
Finally, draw two vertical lines downward from points C and D to represent the supports. Label these points as C and D.
The diagram should look like this:
C D
| |
| |
____ G ____
| \ |
| \ |
L A-----B
Now, let's find the reaction forces at points C and D.
The total weight of the plank and the load is the sum of their masses multiplied by the acceleration due to gravity (9.8 m/s^2).
Total weight = (mass of plank + mass of load) * 9.8
Total weight = (20 kg + 10 kg) * 9.8
Total weight = 30 kg * 9.8
Total weight = 294 N
Since the plank is in equilibrium, the sum of the forces acting vertically must be zero.
Considering the vertical forces at point C, we have:
Reaction force at C - Total weight = 0
Reaction force at C = Total weight
Reaction force at C = 294 N
Considering the vertical forces at point D, we have:
Reaction force at D - Total weight = 0
Reaction force at D = Total weight
Reaction force at D = 294 N
So, the reaction forces at points C and D are both 294 N.