Show all work to get credit. No credit given just for answers without work. Problem 1: Before the trunk of a large tress is felled, cables AB and BC are attached as shown. Knowing that the tensions in the cables AB and BC are 100 and 200 N, respectively, determine the moment about O of the resultant force exerted on the tree by the cables and B. (1 point) What are the coordinates of point A, B, and C (2 points) What is vector BA (1 Point) What is the magnitude of BA (2 Points) What is the unit vector along BA (2 Point) Write the tension in BA in its vector form (2 Point) What is vector BC (1 Point) What is the magnitude of BC (2 Point) What is the unit vector along BC (2 Point) Write the tension in BC in its vector form (2 Point) What is the resultant tension ‘TR’ due to tensions in cables BA and BC (1 Point) What is position vector ‘r’ that connects point O to the line of action of T R (1 Point) What formula do you use to calculate the moment due to TR about O (5 Points) What is the resultant moment vector Problem 2: Knowing that P results in a clockwise moment of 100 N-m about A, reduce to a single force and single moment at point A (1 Point) What is the value of P (1 Point) What is the x component of the 120 N force (1 Point) What is the y component of the 120 N force (1 Point) What is the x component of the 200 N force (1 Point) What is the y component of the 200 N force In the table below fill out the moments and couples created by each force and moment when moved to point A. Note: In some cases, the corresponding moment or force may be zero Force/Moment (1 Point) (1 Point) (2 Points) (2 Points) (2 Points) (2 Points) (2 Points) (1 Points) 42 N-m 40 N-m P 80 N X comp. of 120 N Y comp. of 120 N X comp. of 200 N Y comp. of 200 N Moment CW/CCW Force along X (Include sign) Force along Y (Include Sign) (1 Point) What it the resultant moment (1 Point) What is the resultant force in the X-Direction (1 Point) What is the resultant force in the Y-Direction (1 Point) What is resultant of the forces in the X and Y directions (2 Points) What is the angle the resultant force makes with the X axis? Problem 3: Knowing that the tension in the wire BD is 1000 N, determine the reaction at the fixed support C of the frame shown. (5 Points) Draw the FBD of the pole ACB (1 Points) What is the length of cable BD (2 Points) What is the component of the tension in wire BD in the x direction (2 Points) What is the component of the tension in wire BD in the y direction (1.5 Points) What are the three equations of equilibrium for any static system in 2D (2 Points) What is static equilibrium equation in the x direction for the given system (2 Points) What is the static equilibrium equation in the y direction for the given system (1 Points) What is the best point to write the moment equation about (3 Points) What is the moment equation about the best point that you choose (4.5 Points) What is the magnitude and direction of the reactions at A Problem 4: (1.5 Points) Draw the FBD of joint C (1 Points) Find the force in member CD and state if the member is in tension or compression (1 Points) Find the force in member CB and state if the member is in tension or compression (1.5 Points) Draw the FBD of joint D (1.5 Points) Find the force in member DB and state if the member is in tension or compression (1.5 Points) Find the force in member DA and state if the member is in tension or compression (1 Points) Draw the FBD of joint A (1 Points) What is the magnitude and direction of the reaction force exerted by the pin at A (1 Points) Draw the FBD of joint B (1 Points) What is the magnitude and direction of the reaction force exerted by the pin at B (1 Point) In vector algebra A + B + C = C + A + B (1 Point) What is the direction of the normal force (1 Point) A car is travelling at 100 mph. Will the motion of the car be studied under statics or dynamics? (1 Point) The objective of statics is to find the following: Check all that apply
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