(6) A force F is applied on bar BC at B through rod AB as shown. If the t-component of the force is F₁ = 50 lb, determine the n-, x-, and y-components of the force F. The t- axis is directed along bar BC, and the n-axis is perpendicular to the bar BC. Ans: Fn = 284 lb, Fx = -271 lb, Fy = -98.5 lb -30°4 F A 20°

(4) Two parallel forces, each of magnitude F = 35 lb, are applied on the handlebars for the position indicated. Both n-axes shown are perpendicular to the left handlebar. Determine the couple created by the two forces. Ans: M=952 lb-in CW 15° " 10° 30" OA = OB 15° B F 10°

4. Determine the resultant of the forces: F, = 440 N [N29°E] and F, = 275 N [S23°E]. Answer:

Two rescue vessels are pulling a broken-down motorboat toward a boathouse with forces of 840 lbs. and 960 lbs. The angle between these two forces is 24.5°. Determine the angle between the resultant vector and the 840-lb force (x). Find the magnitude and direction ( e) of the equilibrant. r = r =₁ x=1 8=₁ -r :: cos(24.5°) (840)² + (960)² - 2(840)(960) :: 400 lbs :: 1790 lbs e :: 77 :: 169 O 840 lbs 960 lbs. :: cos(167.75°) :: 1759 lbs :: 11° :: 139 :: 103° :: 167 :: cos(155.5°) O

Find the magnitude of the resultant force and the angle it makes with the positive x-axis. y4 200 N Magnitude: 300 N 60° Angle:

Find the work done by a force of 18 lbs acting in the direction N35°E (this means start by pointing North, then turn 35° toward East) in moving an object 6 ft due east.

Two construction workers are lifting a beam using ropes. Worker A pulls with a force of 500 newtons at an angle of 40°with the positive x-axis. Worker B is on the opposite side pulling with a force of 380 newtons at an angle of 115 ° with the positive x- axis. Find the (a) magnitude and (b) direction angle of the resultant force. (Round to the nearest hundredths)

On the graph to the right, draw a coordinate axis. Draw in the two force vectors. Show by adding the vectors graphically that the net force on the central ring is zero. Verify this algebraically by showing that the sum of the. components is also zero. L +) = N the position. Now, notice that you can slide the ring back and forth along the r axis, placing it at any distance, and the ring will stay in place. This means that every point along the r axis is an equilibrium point. Explain why this is the case. The forces Cancel it does not matter FYEN Now we're going to change the axes. Remove the two pulleys, and place them at angles of 90° and 270°, respectively. Keeping the z axis along = 0, we've now placed the forces along the y axis. Repeat the earlier analysis with the new forces. 1D Trial 2 Results Force Magnitude (N) Direction (6) 0297 F₁ F₂ 0.48A/ 1 80 13 JEN Vector 0.294160 GrMB.NK 1800 F 11800

Part A F₂= 260 N 5 13 12 A O R = 421 N, 0 = 112.3° OR = 251 N, 0 = 85.5° O R = 421 N, 0 = 67.7° OR = 251 N, 0 = 94.5° 30 F₁ = 300 N Determine the magnitude and direction of the resultant force. Give the direction as an angle measured counterclockwise from the positive x-axis.

A precast concrete wall is temporarily kept in its vertical position by ropes (see figure). Find the total force exerted on the pin at position A. The tensions in AB and AC are 420 pounds and 650 pounds, respectively.