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find hinge reaction when rod inclined at 37 degree released from rest....
Understanding the Problem
When a rod is inclined at an angle of 37 degrees and released from rest, we need to analyze the forces acting on it to find the hinge reaction.
Forces Acting on the Rod
- The weight of the rod (W) acts downwards at its center of mass.
- The hinge at the base of the rod exerts a reaction force (R) which can be resolved into horizontal (R_x) and vertical components (R_y).
Free Body Diagram
- Draw a free body diagram of the rod.
- Mark the weight (W = mg) acting at the center of the rod.
- Identify the hinge reaction R, which has components R_x and R_y.
Equations of Motion
1. Torque about the hinge:
- The rod will rotate about the hinge. The torque (τ) due to the weight is given by:
\[
τ = r \times F = \left(\frac{L}{2}\right) mg \sin(37^\circ)
\]
- Here, L is the length of the rod, and r is the perpendicular distance from the hinge to the line of action of the weight.
2. Equilibrium Conditions:
- For vertical motion:
\[
R_y - mg = 0 \quad (1)
\]
- For horizontal motion:
\[
R_x = 0 \quad (2)
\]
Calculating the Hinge Reaction
- From equation (1):
\[
R_y = mg
\]
- Since there is no horizontal motion (equation (2)), we have:
\[
R_x = 0
\]
Final Hinge Reaction
- The total hinge reaction (R) is given by:
\[
R = \sqrt{R_x^2 + R_y^2} = \sqrt{0 + (mg)^2} = mg
\]
This means the hinge reaction is equal to the weight of the rod, acting vertically upwards.
When a rod is inclined at an angle of 37 degrees and released from rest, we need to analyze the forces acting on it to find the hinge reaction.
Forces Acting on the Rod
- The weight of the rod (W) acts downwards at its center of mass.
- The hinge at the base of the rod exerts a reaction force (R) which can be resolved into horizontal (R_x) and vertical components (R_y).
Free Body Diagram
- Draw a free body diagram of the rod.
- Mark the weight (W = mg) acting at the center of the rod.
- Identify the hinge reaction R, which has components R_x and R_y.
Equations of Motion
1. Torque about the hinge:
- The rod will rotate about the hinge. The torque (τ) due to the weight is given by:
\[
τ = r \times F = \left(\frac{L}{2}\right) mg \sin(37^\circ)
\]
- Here, L is the length of the rod, and r is the perpendicular distance from the hinge to the line of action of the weight.
2. Equilibrium Conditions:
- For vertical motion:
\[
R_y - mg = 0 \quad (1)
\]
- For horizontal motion:
\[
R_x = 0 \quad (2)
\]
Calculating the Hinge Reaction
- From equation (1):
\[
R_y = mg
\]
- Since there is no horizontal motion (equation (2)), we have:
\[
R_x = 0
\]
Final Hinge Reaction
- The total hinge reaction (R) is given by:
\[
R = \sqrt{R_x^2 + R_y^2} = \sqrt{0 + (mg)^2} = mg
\]
This means the hinge reaction is equal to the weight of the rod, acting vertically upwards.
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find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)?
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find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)?.
find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for find hinge reaction when rod inclined at 37 degree released from rest. p Related: Circular Motion, Chapter Notes, Class 11, Physics (IIT-JEE & AIPMT)?.
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