13.3
Normal and Tangetial Components: Problem Solving
Consider a man with a 70 kg mass sitting in a chair. The chair is connected to a pin support via a member BC of length 10 m.
If the man is always seated upright, determine the horizontal and vertical reactions of the chair on the man when the member makes an angle of 45° with the horizontal. At this instant, the man has a speed of 5 m/s that is increasing at 1m/s2.
Here, the man travels the curvilinear path, and the tangential acceleration of the man is 1 m/s2. The normal acceleration of the man can be calculated using tangential speed and the radius of the curvature.
Next, draw a free-body diagram of the man and write the equations of motion for tangential and normal components.
Substituting the known values and assuming acceleration due to gravity to be 10 m/s2, two equations with the required reaction forces are established.
Solving them simultaneously gives the magnitudes of the reaction forces along the horizontal and vertical directions.
Consider a man with a mass of 70 kg seated in a chair connected to a pin support through a member BC. If the man maintains an upright position, the task is to determine the horizontal and vertical reactions of the chair on the man when the member makes a 45° angle with the horizontal. At this moment, the man has a speed of 5 m/s, increasing at a rate of 1 m/s².
As the man moves along a curvilinear path, the tangential acceleration is given as 1 m/s². The normal acceleration can be calculated using the tangential speed and the curvature radius. A free-body diagram of the man is then drawn, and the equations of motion for tangential and normal components are formulated.
Two equations are derived by substituting known values and assuming the acceleration due to gravity as 10 m/s², revealing the required reaction forces. Solving these equations simultaneously provides the magnitudes of the reaction forces along the horizontal and vertical directions.
This analytical approach offers a systematic method for determining the chair's reactions on the man under specific conditions, considering the dynamic aspects of the man's motion and acceleration.
Consider a man with a 70 kg mass sitting in a chair. The chair is connected to a pin support via a member BC of length 10 m.
If the man is always seated upright, determine the horizontal and vertical reactions of the chair on the man when the member makes an angle of 45° with the horizontal. At this instant, the man has a speed of 5 m/s that is increasing at 1m/s2.
Here, the man travels the curvilinear path, and the tangential acceleration of the man is 1 m/s2. The normal acceleration of the man can be calculated using tangential speed and the radius of the curvature.
Next, draw a free-body diagram of the man and write the equations of motion for tangential and normal components.
Substituting the known values and assuming acceleration due to gravity to be 10 m/s2, two equations with the required reaction forces are established.
Solving them simultaneously gives the magnitudes of the reaction forces along the horizontal and vertical directions.
- Tangential Acceleration - Acceleration component in the direction of motion.
- Normal Acceleration - Acceleration perpendicular to the direction of motion.
- Curvilinear Motion - Motion along a curved path or trajectory.
- Reaction Forces - Forces caused by interaction between two objects.
- Euler’s Laws - Framework for analyzing the motion of any body as it moves and accelerates.
- Define Tangential and Normal Acceleration - Understand their application in motion analysis (e.g., chair motion case study).
- Contrast Tangential vs Normal Acceleration - Distinguish their implications in motion (e.g., when man seated adjusts position).
- Explore Free-body Diagram - Discuss its use in resolving force vectors (e.g., detecting forces on man in chair).
- Explain Motion Equations – Understand their use in computing acceleration and speed values.
- Apply Physics in Everyday Scenarios – Analyze effects of normal and tangential components in regular activities.
- What is tangential and normal acceleration in the context of curvilinear motion?
- How are reaction forces calculated in a dynamic system?
- How to identify and analyze normal and tangential components in a real-world scenario?
From Chapter 13:
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