A uniform plank of length 3 m is supported by two wooden trestles L and M as shown in the diagram above. L exerts a force of 80n upwards and M a force of 160N upwards. M is O.5m from the centre of gravity of the plank.
calculate the weight w of the plank and by taking moments about the centre of gravity find the value of x
upward force= downward force
Weight(W)= 80N+160N
W= 240N
Value of X,
forces in one direction=forces in opp direction
160N multiplied by 0.5= 80N multiplied by X
which gives.....
80N= 80N multiplied by X
X= 80/80
X=1
i hope you get it
To calculate the weight of the plank, we can use the equation:
Weight = Force L + Force M
Given that Force L is 80 N and Force M is 160 N, we can substitute these values into the equation:
Weight = 80 N + 160 N
Weight = 240 N
So, the weight of the plank is 240 N.
To find the value of x by taking moments about the center of gravity, we can use the equation:
Sum of anticlockwise moments = Sum of clockwise moments
The sum of anticlockwise moments in this case is the moment caused by Force L, which is 80 N multiplied by the distance from the center of gravity to the point of support L. Let's call this distance "y".
The sum of clockwise moments is the moment caused by Force M, which is 160 N multiplied by the distance from the center of gravity to the point of support M, which is given as 0.5 m.
Since the plank is uniform, the center of gravity will be at the midpoint of the plank, which is 3 m / 2 = 1.5 m.
With these values, we can set up the equation:
80 N * y = 160 N * 0.5 m
Now, let's solve for y:
80 N * y = 160 N * 0.5 m
80 N * y = 80 N * 1.0 m
y = 1.0 m
Hence, the value of x is 1.0 m.
To calculate the weight (w) of the plank, we can use the fact that weight is equal to mass times gravity. We can assume the acceleration due to gravity is 9.8 m/s^2.
Weight (w) = mass × gravity
Next, we can calculate the moment for each force applied to the plank. Moment is the force multiplied by the distance from the pivot point.
For force L with a magnitude of 80 N, the distance from the center of gravity is 1.5 m.
Moment of L = 80 N × 1.5 m
For force M with a magnitude of 160 N, the distance from the center of gravity is 0.5 m.
Moment of M = 160 N × 0.5 m
Since the plank is in equilibrium, the sum of the moments must be equal to zero.
Sum of moments = Moment of L + Moment of M
0 = 80 N × 1.5 m + 160 N × 0.5 m
Now, we can solve for the weight using the equation for sum of moments.
Weight × x = Sum of moments
Weight = Sum of moments / x
Finally, we substitute the values we have:
Weight = (80 N × 1.5 m + 160 N × 0.5 m) / x
And we can calculate the value of x using the given information that M is 0.5 m from the center of gravity of the plank.