13.3 : 法向分量和切向分量：解决问题

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.