Name: chair reaction forces in curvilinear motion
Uploaded: 2024-03-07T13:22:17.000Z
Duration: 1 min 24 s
Channel: JoVE

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&#176; 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.

normal and tangetial components: problem solving

Normal and Tangetial Components: Problem Solving

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&#176; angle with the horizontal. At this moment, the man has a speed of 5 m/s, increasing at a rate of 1 m/s&#178;.
<img alt="Ferris wheel physics concept, illustrating rotational motion; diagram with gondola and central axis." class="xfigimg" src="/files/ftp_upload/15576/15576_PT_figure_001.svg" data-altupdatedat="1762173717000" data-alt="Figure 1" />
As the man moves along a curvilinear path, the tangential acceleration is given as 1 m/s&#178;. 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/s&#178;, 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 ...

normal-and-tangetial-components-problem-solving

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KEY TERMS AND CONCEPTS

chair reaction forces in curvilinear motion

Chair reaction forces in curvilinear motion are found by using tangential and normal components of acceleration. A 70 kg man sits upright in a chair that is connected to a pin support by member BC. The member is 10 m long, and it makes a 45° angle with the horizontal at the instant of interest.

The man has a speed of 5 m/s, and that speed is increasing at 1 m/s². The tangential acceleration is therefore 1 m/s². The normal acceleration is then determined from the tangential speed and the radius of curvature. These values describe the man's motion along a curved path.

A free-body diagram of the man is drawn next. The forces are written in terms of the chair's horizontal and vertical reactions. The equations of motion are then set up for the tangential and normal directions. Using g = 10 m/s², two equations are formed from the given data.

Solving those equations at the same time gives the reaction forces on the man. The result is the magnitude of the horizontal and vertical forces from the chair. This method shows how normal and tangential components help analyze motion and forces in a seated curved-path problem.

Chair Reaction Forces in Curvilinear Motion

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Chair reaction forces in curvilinear motion are found by using tangential and normal components of acceleration. A 70 kg man sits upright in a chair that is connected to a pin support by member BC. The member is 10 m long, and it makes a 45° angle with the horizontal at the instant of interest. The man has a speed of 5 m/s, and that speed is increasing at 1 m/s². The tangential acceleration is therefore 1 m/s². The normal acceleration is then determined from the tangential speed and the radius...

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key terms and concepts

Use tangential and normal acceleration to solve for chair reaction forces on a 70 kg man moving on a curved path with a pin-supported member.

Chair Reaction Forces in Curvilinear Motion | JoVE K12

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Chair Reaction Forces in Curvilinear Motion

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