Answer :
The force applied by the left support beam to the balance beam is 19.625 N.
To find the force applied by the left support beam to the balance beam, we'll use the principle of moments. Since the balance beam's own weight is negligible, we only need to consider the vertical forces acting on it.
Step 1: Identify the forces acting on the balance beam:
- The downward force due to gravity acting at the center of the beam.
- The upward support force at the left end of the beam.
Step 2: Use the principle of moments:
The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the counterclockwise moments about that point.
Step 3: Choose a point to calculate moments:
We can conveniently choose the right end of the balance beam as the point of calculation, where the clockwise moments are positive, and the counterclockwise moments are negative.
Step 4: Calculate the moments:
The moment due to the force of gravity is zero since it acts at the center of the beam.
The moment due to the support force can be calculated as follows:
Support force (F_support) × distance from support to the right end (d) = Weight of the beam (0, since it's negligible) × distance from center to right end (1.625 m)
F_support × 1.625 m = 0
F_support = 0 N
Step 5: Determine the support force:
Since the sum of moments about the right end is zero, the support force is also zero.
Therefore, the force applied by the left support beam to the balance beam is 0 N.
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