# Two cables BG and BH are attached to the frame ACD as shown.Knowing that the tension in cable BG is 450N, determine the components of the force exerted by cable BG on the frame at B.

Question
Complex numbers

Two cables BG and BH are attached to the frame ACD as shown.Knowing that the tension in cable BG is 450N, determine the components of the force exerted by cable BG on the frame at B.

2020-12-25
From fig
$$\displaystyle{O}{B}={1}{i}+{1.5}{k}$$
$$\displaystyle{O}{G}={1.85}{j}+{0.7}{k}$$
$$\displaystyle{B}{G}={O}{G}-{O}{B}=-{i}+{1.85}{j}-{0.8}{k}$$
$$\displaystyle{\left|{B}{G}\right|}=\sqrt{{{1}^{{2}}+{1.85}^{{2}}+{0.8}^{{2}}}}={2.25}$$
$$\displaystyle\lambda={\frac{{{B}{G}}}{{{\left|{B}{G}\right|}}}}={\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}$$
$$\displaystyle\vec{{{F}}}={F}\times\lambda$$
Where F=450 N
Find $$\displaystyle\vec{{{F}}}$$
But, $$\displaystyle\vec{{{F}}}={F}_{\xi}+{F}_{{y}}{j}+{F}_{{z}}{k}$$
$$\displaystyle\vec{{{F}}}={450}\times{\left({\frac{{-{i}+{1.85}{j}-{0.8}{k}}}{{{2.25}}}}\right)}$$
$$\displaystyle=-{200}{i}+{370}{j}-{160}{k}$$
$$\displaystyle{F}_{{x}}=-{200}$$ N
$$\displaystyle{F}_{{y}}={370}$$ N
$$\displaystyle{F}_{{z}}=-{160}$$ N

### Relevant Questions

Boom AB is held in the position shown by three cables. Knowing that the tensions in calbe AC and AC are 900lb and 1200lb,respectively, determne (a) the tension in cable AE if the resultant of thettensions exerted at point A of the boom must be directed along AB, (b) the corresponding magnitude o the resultant.
A person bending forward to lift a load "with his back" rather than"with his knees" can be injured by large forces exerted on themuscles and vertebrae. A person is bending over to lift a200-N object. The spine and upper body are represented as auniform horizontal rod of weight 350 N, pivoted at the base of thespine. The erector spinalis muscle, attached at a pointtwo-thirds of the way up the spine, maintains the position of theback. The angle between the spine and this muscle is 12degrees. Find the tension in the back muscle and thecompressional force in the spine.

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as shown in the figure. The sum of the forces $$\displaystyle{F}_{{A}}$$ and $$\displaystyle{F}_{{B}}$$ exerted on the unit by the horizontal cables is parallel to the line L, and $$\displaystyle{F}_{{A}}={4200}$$ N. Determine $$\displaystyle{F}_{{B}}$$? Determine the magnitude of $$\displaystyle{F}_{{A}}+{F}_{{B}}$$?

Write each complex number in standard form. $$2(\cos 30^{\circ} + i \sin 30^{\circ})$$

In the figure a worker lifts a weight $$\displaystyle\omega$$ by pulling down on a rope with a force $$\displaystyle\vec{{{F}}}$$. The upper pulley is attached to the ceiling by a chain,and the lower pulley is attached to the weight by another chain.The weight is lifted at constant speed. Assume that the rope,pulleys, and chains all have negligible weights.

A) In terms of $$\displaystyle\omega$$,find the tension in the lower chain.
B) In terms of $$\displaystyle\omega$$,find the tension in upper chain.
C) In terms of $$\displaystyle\omega$$,find the magnitude of the force $$\displaystyle\vec{{{F}}}$$ if the weight is lifted at constant speed.
When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure (a). The total gravitational force on the body, vector F g, is supported by the force vector n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure (b), where vector T is the force exerted by the Achilles tendon on the foot and vector R is the force exerted by the tibia on the foot. Find the values of vector T , vector R , and θ when vector F g = 805 N. (Do not assume that vector R is parallel to vector T .)
A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 $$\displaystyle\frac{{m}}{{s}^{{2}}}$$, moving it a distance of 20 m, horizontally.How much work is done by the force?
A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?
A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?
A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?
What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?
A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?
A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).
A paraglider is flying horizontally at a constant speed.Assume that only two forces act on it in the vertical direction,its weight and a vertical lift force exerted on its wings by theair. The lift force has a magnitude of 1800 N.
(a) What is the magnitude and direction of the force that theparaglider exerts on the earth ?
(b)If the lift force should suddenly decrease to 1200 N, whatwould be the vertical acceleration of the glider ? For bothquestions, take the upward direction to be the + y direction.
The person weighs 170 lb. Each crutch makes an angle of 22.0 with the vertical. Half of the person's weight is supported by the cruches, the other half by the vertical forces exerted by the roundon his feet. Assuming that he is at rest and that the force exerted by the ground on the crutches acts along the crutches,determine
a) the smallest possible coefficient of friction between crutches and ground and
b) the magnitude of the compression force supported by each crutch.
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$$
where A is the cross-sectional area of the vehicle and $$\displaystyle{C}_{{d}}$$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $$\displaystyle\vec{{{v}}}$$. Find the power dissipated by form drag.
Express your answer in terms of $$\displaystyle{C}_{{d}},{A},$$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $$\displaystyle{P}_{{0}}$$. Suppose that the maximum speed of thee car, $$\displaystyle{v}_{{0}}$$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $$\displaystyle{P}_{{1}}$$ is 10 percent greater than the original power ($$\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $$\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
...