(1) A square foundation mat supports the four columns and each column carries a vertical load shown. Determine the location on the mat of the point of application of the single resultant force of the four loads. Ans: x = 3.5 ft, z=3 ft 20 kips 40 kips 6 ft B 8 kips 12 kips 5 ft

(5) A force T is applied at the tip of the rod as shown. If the n- component of the force is T, = 35 lb, determine the t-, x-, and y-components of the force T. The t-axis is directed along the rod, and the n-axis is perpendicular to the rod. Ans: T₁ =-130.6 lb, Tx=-103.6 lb, Ty = -86.9 lb T n 40° O 55°

At a county fair, there is a contest to see who can pull a heavy crate along the ground with the shortest piece of rope. The rope is attached to the crate at the bottom. By digging in his heels, Albert can pull on a rope with a force of 500 NEwtons. In order to budge the crate, Albert has calculated that he needs to use a force of 425 Newtons horizontally (parallel to the ground). When Albert is in his best pulling position, his hands are 95 cm above the ground.

A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The hoist weighs 430 N. The ropes, fastened at different heights, make angles of 50° and 38° with the horizontal. Find the tension in each rope and the magnitude of each tension (in N). (Let T, and T3, represent the tension vectors corresponding to the ropes of length 2 m and 3 m respectively. Round all numerical values to two decimal places.) 38° 50° 3 m 2 m T2 X N |T2l X N T3 X N = |T3| = X N

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)

NAME: 1. Express the follow situation as a vector in component form: a. A boat is traveling at a bearing of 260° at 35 mph. 15⁰. ID: BLOCK: Applications of Vectors b. A plane is traveling at 300 mph as it begins to descend for landing at an angle of depression of lbs. DATE: c. A cart full of children is being pulled up a ramp at an angle of elevation of 3° with a force of 5 1600 lbs. d. A rope is being horizontally pulled by a truck due west of a car stuck in a ditch with a force of

ABCD is a rectangle with AB and AD of lengths 2a and a respectively. Forces of magnitudes 2 N, 3 N and 3/5 act along AB, AD and AC respectively, in the directions indicated by the order of the letters. Find the force which would need to be applied to A to maintain equilibrium.