2. (10 points) Thelma approaches a door (mass 30 kg, height 2.4 m, width 0.80 m,

Question

2. (10 points) Thelma approaches a door (mass 30 kg, height 2.4 m, width 0.80 m, thickness 0.030 m) and attempts to open it by exerting a 60 N force perpendicular to the door and located at the far edge of the door away from the hinges. Unknown to her, George and David are on the other side of the door, ready to exert forces perpendicular to the door and located 0.60 m away from the hinges. Thelma W E O George David a. (4 points) What magnitude force must George and David each exert in order to prevent Thelma from opening the door? Assume that they exert equal forces. b. (2 points) What is the magnitude and direction of the met horizontal force at the hinges? (Note: there are vertical forces at the hinges which cancel gravity I am not interested in that component.) c. (4 points) Thelma, after hearing the giggling on the other side of the door, suddenly increases her force to 90 N. What is the angular acceleration of the door? Assume that George and David retain their balance (for now and thus continue to exert the same forces they exerted before.

Explanation / Answer

a) Let F is the force exrted by George and David

Here Net Trque about hinge = 0

60*0.8 - 2*F*0.6 = 0

==> F = 60*0.8/1.2

= 40 N <<<<<<-----------Answer

b) Let Fx is the force exrted by hinge

net force in horizonat direction = 0

Fx - 2*40 + 60 = 0

Fx = 80 - 60

= 20 N <<<<<<-----------Answer

c) Momnet of Inertia of the door about hinge, I = m*W^2/3

= 30*0.8^2/3

= 8.2 kg.^2

Apply, Net torque = I*alfa

90*0.8 - 2*40*0.6 = 8.2*alfa

==> alfa = (90*0.8 - 2*40*0.6)/8.2

= 2.92 rad/s^2 <<<<<<-----------Answer

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