Problem $1(10$ points$)$

A door weighs $85$ lb and is prevented from opening by the strut C$,$ which is a two$-$force member whose upper end is secured under the doorknob and whose lower end is attached to a rubber cup which does not slip on the floor. Of the door hinges A and B$,$ only B can support force in the vertical z$-$direction. Determine the compressive force in the strut and the reactions at hinges A and B when a horizontal force $P=30lb$ is applied normal to the plane of the door as shown in the diagram below.

Problem $1(10$ points$)$

A door weighs $85$ lb and is prevented from opening by the strut C$,$ which is a two$-$force member whose upper end is secured under the doorknob and whose lower end is attached to a rubber cup which does not slip on the floor. Of the door hinges A and B$,$ only B can support force in the vertical z$-$direction. Determine the compressive force in the strut and the reactions at hinges A and B when a horizontal force $P=30lb$ is applied normal to the plane of the door as shown in the diagram below.

Problem $1(10$ points$)$

A door weighs $85$ lb and is prevented from opening by the strut C$,$ which is a two$-$force member whose upper end is secured under the doorknob and whose lower end is attached to a rubber cup which does not slip on the floor. Of the door hinges A and B$,$ only B can support force in the vertical z$-$direction. Determine the compressive force in the strut and the reactions at hinges A and B when a horizontal force $P=30lb$ is applied normal to the plane of the door as shown in the diagram below.