a uniform rod 100cm long and weighing 50N is supported in a horizontal position on a fulcrum with weights 80N and 100N suspended from its end. compute the position of a fulcrum.draw the illustration.
Muajy khod nahi ata
To find the position of the fulcrum, we need to consider the equilibrium of moments acting on the rod. The condition for equilibrium is that the sum of the clockwise moments is equal to the sum of the counterclockwise moments.
First, let's draw the illustration to visualize the situation:
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80 cm 20 cm
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In the figure, the rod is denoted by a horizontal line. The fulcrum is represented by a vertical line cutting the rod into two sections. The lengths indicated are the distances from the fulcrum to the forces acting on the rod.
Next, let's compute the position of the fulcrum.
Clockwise moments (M1):
M1 = 80N * 80cm = 6400 N⋅cm
Counterclockwise moments (M2):
M2 = 100N * 20cm = 2000 N⋅cm
M2 = 50N * 100cm = 5000 N⋅cm
Since the moments are balanced, M1 = M2:
6400 N⋅cm = 2000 N⋅cm + 5000 N⋅cm
Simplifying, we get:
6400 N⋅cm = 7000 N⋅cm
Now, we can find the position of the fulcrum by dividing the total moment by the total weight:
Position of fulcrum = Total moment / Total weight
Position of fulcrum = 7000 N⋅cm / 130N
Position of fulcrum ≈ 53.85 cm
Therefore, the position of the fulcrum is approximately 53.85 cm from the left end of the rod.