A gripper with 4 vacuum cups has been design to lift the aut

A gripper with 4 vacuum cups has been design to lift the automoble front window glass during car assembly. Determine the diameter in inches of each vacuum cup if the glass weights 22 pounds, the vacuum is 0.75 atmosphers, and a 35 percent safety factor is used. (Enter your answer as a number without the units.)

Solution

Vacuum from each cup = 0.75 atm = 11.02 psi

If area of each cup is A, lifting force due to vacuum of each cup = 11.02*A lb

Lifting force due to 4 cups = 11.02*A*4 lbs

Equating it with weight of glass we get,

11.02*A*4 = 22

A = 0.499 in^2

3.14/4 *d^2 = 0.499

d = 0.797 in

Considering 35% safety factor we get actual dia = 1.35*0.797 = 1.076 inches