Express the force as a cartesian vector. (figure 1)

Image for Fundamental Problem 2.17 Part A Express the force as a Cartesian vector. (Figure 1) Express your answer in ter

Answer

General guidance

Concepts and reason
Cartesian vector representation: Consider a vector A having components along x, y and z axes. Then the vector A can be written in Cartesian vector from as: A=&i+A;j+ĄK Here, , and are the components of vector A along x, y and z axes and , and are the unit vectors along x, y and z axes. Cartesian vectors are used to simplify the vector algebra in three dimensions.

Fundamentals

The Cartesian form of the force F is, F=F_i+F,j+F_K ……. (1) Here, the components of the force vector along x, y and z Fare, and respectively.

Step-by-step

Step 1 of 3

Draw the free body diagram of the system as shown below. N
F = 750lb
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-
607
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After identifying the forces acting in the system, the free body diagram of the system is drawn as shown above.

Step 2 of 3

Calculate the z component of the force using relation. F = Fsin 45° Substitute, 750 N for in relation above and calculate. F, = 750sin 45°
= 530.33 N Calculate the y component of the force using relation. F, =-F, sin 60° Substitute, 530.33 N for in relation above and calculate. F = -530.33 sin 60°
= -459.28 N Calculate horizontal component of the force on xy plane. F = F cos 45º Substitute, 750 N for in relation above and calculate. Fn = 750 cos 45°
= 530.33 N Calculate the x component of the force using relation. F = F, cos 60° Substitute, 530.33 N for in relation above and calculate. F = 530.33 cos 60°
= 265.165 N

The force along each coordinate axis are calculated as per the inclination made by the force F.

Step 3 of 3

Calculate the Cartesian vector form of force. Using equation (1), F=F_i+F,j+F_K Substitute 265.165 Nfor, -459.28 Nfor, 530.33 Nfor.

F=(265.1651 - 459.28j+530.33k) N

The Cartesian vector form of force is(265.1651 - 459.28j+530.33k) N.


The sum of the force components along each coordinate axis gives the Cartesian vector form of the given force.

Answer

The Cartesian vector form of force is(265.1651 - 459.28j+530.33k) N.

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