Answer:
M = 8.5 N
Explanation:
Given:
Weight of the bar acting at the center is, [tex]W=8\ N[/tex]
Position of the fulcrum is 3 m from the left end.
Length of the bar is 5 m.
Weights on the right side of the fulcrum are 8 N and 'M' N. Weights on the left side of the fulcrum are 7 N and weight W of the bar itself.
Now, in order to balance the bar at the fulcrum, the sum of clockwise moments must be equal to sum of anticlockwise moments.
The forces on the right causes clockwise moments and forces on the left causes anticlockwise moments.
Moment of a force is given as the product of force and perpendicular distance between force and fulcrum.
Sum of clockwise moments = [tex]8\times 1+M\times 2=(8+2M)\ Nm[/tex]
Sum of anticlockwise moments = [tex]7\times 3+8\times 0.5=21+4=25\ Nm[/tex]
Now, sum of clockwise moments = sum of anticlockwise moments
[tex]8+2M = 25\\\\2M=25-8\\\\2M=17\\\\M=\frac{17}{2}=8.5\ N[/tex]
So, the unknown weight to balance the bar is 8.5 N.
