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A boat is being pulled by 3
ropes as shown. Determine
the point on the surface CD
where single force would
produce the same effect. Also
find the magnitude and
direction of single equivalent
force?
ropes as shown. Determine
the point on the surface CD
where single force would
produce the same effect. Also
find the magnitude and
direction of single equivalent
force?
Most Upvoted Answer
A boat is being pulled by 3 ropes as shown. Determine the point on the...
Introduction
To determine the point on surface CD where a single force would replicate the effect of three ropes pulling a boat, we must evaluate the net force and its point of application.
Step 1: Analyze the Forces
- Identify the forces exerted by the three ropes, labeled as F1, F2, and F3.
- Each force has a specific direction and magnitude, contributing to the overall effect on the boat.
Step 2: Calculate the Resultant Force
- Use vector addition to find the resultant force (R).
- R = F1 + F2 + F3, considering both magnitude and direction for each force.
Step 3: Determine the Point of Application
- The point on surface CD where the single force should act can be derived from the concept of moments.
- Calculate the moments about a chosen point (point O).
- Ensure that the moment produced by the equivalent force (R) about point O equals the total moment produced by the three ropes.
Step 4: Find the Magnitude and Direction of the Equivalent Force
- The magnitude of the equivalent force is the resultant force R calculated earlier.
- The direction of the equivalent force should align with the resultant direction obtained from the vector addition.
Conclusion
The single equivalent force that replicates the effect of the three ropes can be represented as both a magnitude and a directional vector, acting at the calculated point on surface CD. This simplification allows for easier analysis and application in practical scenarios.
To determine the point on surface CD where a single force would replicate the effect of three ropes pulling a boat, we must evaluate the net force and its point of application.
Step 1: Analyze the Forces
- Identify the forces exerted by the three ropes, labeled as F1, F2, and F3.
- Each force has a specific direction and magnitude, contributing to the overall effect on the boat.
Step 2: Calculate the Resultant Force
- Use vector addition to find the resultant force (R).
- R = F1 + F2 + F3, considering both magnitude and direction for each force.
Step 3: Determine the Point of Application
- The point on surface CD where the single force should act can be derived from the concept of moments.
- Calculate the moments about a chosen point (point O).
- Ensure that the moment produced by the equivalent force (R) about point O equals the total moment produced by the three ropes.
Step 4: Find the Magnitude and Direction of the Equivalent Force
- The magnitude of the equivalent force is the resultant force R calculated earlier.
- The direction of the equivalent force should align with the resultant direction obtained from the vector addition.
Conclusion
The single equivalent force that replicates the effect of the three ropes can be represented as both a magnitude and a directional vector, acting at the calculated point on surface CD. This simplification allows for easier analysis and application in practical scenarios.
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A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force?
Question Description
A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force?.
A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boat is being pulled by 3 ropes as shown. Determine the point on the surface CD where single force would produce the same effect. Also find the magnitude and direction of single equivalent force?.
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