Quiz 01 in MECH 223

Find the x and y components of the force shown.

• Fₓ = 173.205 N & Fᵧ = 100 N

• Fₓ = 100 N & Fᵧ = 173.205 N

• Fₓ = 172.305 N & Fᵧ = 73.205 N

• Fₓ = 73.205 N & Fᵧ = 172.305 N

Find the components of the given force.

• Fₓ = 172.305 N & Fᵧ = 73.205 N

• Fₓ = 173.205 N & Fᵧ = 100 N

• Fₓ = 320 N & Fᵧ = 240 N

• Fₓ = 240 N & Fᵧ = 320 N

Determine the magnitude of the resultant force acting on the pin and its direction measured clockwise from the positive x axis.

• R = 69.6 lb and θ = 13.3°

• R = 77.6 lb and θ = 10.3°

• R = 66.7 lb and θ = 13.3°

• R = 67.6 lb and θ = 11.3°

If F₁ = 600 N and ɸ = 30°, determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis.

• R = 720 N and θ = 49.6°

• R = 702 N and θ = 44.6°

• R = 676.7 lb and θ = 31.3°

• R = 77.6 lb and θ = 33.3°

Find the x and y components of the forces P and F shown.

• Pₓ = -730 lbs & Pᵧ = -900 lbs

• Pₓ = -700 lbs & Pᵧ = -900 lbs

• Pₓ = -740 lbs & Pᵧ = -950 lbs

• Pₓ = -720 lbs & Pᵧ = -960 lbs

In a ship-unloading operation, a 3500-lb automobile is supported by a cable. A rope is tied to the cable at A and pulled in order to center the automobile over its intended position. The angle between the cable and the vertical is 2°, while the angle between the rope and the horizontal is 30°. What is the tension in the rope?

• T_AB = 3550 lb and T_AC = 154 lb

• T_AB = 3570 lb and T_AC = 144 lb

• T_AB = 3770 lb and T_AC = 174 lb

• T_AB = 3370 lb and T_AC = 134 lb

A string ABCD, attached to fixed points A and D has two equal weights of 1000 N attached to it at B and C. The weights rest with the portions AB and CD inclined at angles as shown in the figure. Find the tensions in the portions AB, BC and CD of the string, if the inclination of the portion BC with the vertical is 120°.

• T_AB = 1732 N, T_BC = 1000 N, and T_CD = 1000 N

• T_AB = 1832 N, T_BC = 1000 N, and T_CD = 1340 N

• T_AB = 1372 N, T_BC = 1200 N, and T_CD = 1340 N

• T_AB = 1332 N, T_BC = 1240 N, and T_CD = 1000 N

A light string ABCDE whose extremity A is fixed, has weights W₁ and W₂ attached to it at B and C. It passes round a small smooth peg at D carrying a weight of 300 N at the free end E as shown in the figure. If in the equilibrium position, BC is horizontal and AB and CD make 150° and 120° with BC, find (i) Tensions in the portion AB, BC and CD of the string and (ii) Magnitudes of W₁ and W₂.

• T_CD = 240 N, T_BC = 230 N, T_AB = 173.2 N, W₁ = 88.6 N, and W₂ = 254.8 N

• T_CD = 250 N, T_BC = 250 N, T_AB = 163.2 N, W₁ = 78.6 N, and W₂ = 239.8 N

• T_CD = 200 N, T_BC = 250 N, T_AB = 153.2 N, W₁ = 83.6 N, and W₂ = 229.8 N

• T_CD = 300 N, T_BC = 150 N, T_AB = 173.2 N, W₁ = 86.6 N, and W₂ = 259.8 N

A wall section of precast concrete is temporarily held by the cables shown. Knowing that the tension is 840 lb in cable AB and 1200 lb in cable AC , determine the magnitude and direction of the resultant of the forces exerted by cables AB and AC on stake A.

• R = 1450 lb, θ_x = 160.8°, θ_y = 65.1°, θ_z = 110.6°

• R = 1550 lb, θ_x = 155.8°, θ_y = 68.1°, θ_z = 105.6°

• R = 1650 lb, θ_x = 150.8°, θ_y = 64.1°, θ_z = 102.6°

• R = 1750 lb, θ_x = 140.8°, θ_y = 70.1°, θ_z = 100.6°

A transmission tower is held by three guy wires anchored by bolts at B, C, and D. If the tension in wire AB is 525 lb, determine the components of the force exerted by the wire on the bolt at B.

• F_x = +100.0 lb, F_y = +500 lb, F_z = -125.0 lb

• F_x = +50.0 lb, F_y = +250 lb, F_z = 185.0 lb

• F_x = +105.0 lb, F_y = +400 lb, F_z = -135.0 lb

• F_x = +110.0 lb, F_y = +450 lb, F_z = +125.0 lb