If the strut AC can withstand a maximum compression force of 150 lb before it fa

Question

                    If the strut AC can withstand a maximum compression force of 150 lb before it fails, determine the cart's maximum permissible acceleration. The crate has a                     weight of 150 lb with center of gravity at G, and it is secured on the platform, so that it does not slide. Neglect the platform's weight.                 

Center of gravity at G, and it is secured on the platform, so that it does not slide. Neglect the platform's weight. If the strut AC can withstand a maximum compression force of 150 lb before it fails, determine the cart's maximum permissible acceleration. The crate has a weight of 150 lb with center of gravity at G, and it is secured on the platform, so that it does not slide. Neglect the platform's weight.

Explanation / Answer

About the point B

there are 3 forces which apply torque

1) Torque due to weight = 150*2 (counter clockwise)

2) torque due to AC = T*sin(30 degrees)*3 (clockwise)

3) Torque due to psudo force = ma*2*cos(30 degrees) (clock wise)

balancing moment about the point B

==> 150*2 = T*sin(30 degrees)*3 + ma*2*cos(30 degrees)

now to determine the carts maximum acceleration value of T must be maximum which is 150 lb

==> 150*2 -150*sin(30 degrees)*3 = ma*2*cos(30 degrees)

==> 259.807*a/g=75

==> a= 75*g/259.807= 0.28867*g

now g=9.8 m/s^2

==> a= 2.829 m/s^2

also g=32.15 ft/s^2

==> a= 9.28 ft/s^2

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