4. Exercises

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b) Find the angle between the force and the unit vector <math>\mathbf{i}</math>.
b) Find the angle between the force and the unit vector <math>\mathbf{i}</math>.
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</div>{{#NAVCONTENT:Answer|Answer 4.4|Solution a|Solution 4.4a|Solution b|Solution 4.4b}}
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===Exercise 4.5===
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<div class="ovning">
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</div>{{#NAVCONTENT:Answer|Answer 4.4|Solution a|Solution 4.4a|Solution b|Solution 4.4b}}
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For each force given below find its magnitude and the angle between the force and the unit vector <math>\mathbf{i}</math>.
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a)
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<math>\left( 4\mathbf{i}+3\mathbf{j} \right)\text{ N}</math>
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b)
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<math>\left( 4\mathbf{i}-3\mathbf{j} \right)\text{ N}</math>
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c)
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<math>\left( -2\mathbf{i}+8\mathbf{j} \right)\text{ N}</math>
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d)
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<math>\left( -5\mathbf{i}-7\mathbf{j} \right)\text{ N}</math>
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</div>{{#NAVCONTENT:Answer a|Answer 4.5a|Answer b|Answer 4.5b|Answer c|Answer 4.5c|Answer d|Answer 4.5d|Solution a|Solution 4.5a|Solution b|Solution 4.5b|Solution c|Solution 4.5c|Solution d|Solution 4.5d}}

Revision as of 17:53, 8 September 2009

       Theory          Exercises      


Exercise 4.1

The diagram shows a force and the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}

Image:E4.1.GIF

Express the force in terms of the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}

Answer
Answer 4.1
Solution
Solution 4.1


Exercise 4.2

Express each of the forces given below in the form \displaystyle a\mathbf{i}+b\mathbf{j}

Image:E4.2.GIF

Answer a
Answer 4.2a
Answer b
Answer 4.2b
Answer c
Answer 4.2c
Answer d
Answer 4.2d
Answer e
Answer 4.2e
Answer f
Answer 4.2f


Exercise 4.3

a) Find the magnitude of the force 6 \displaystyle \mathbf{i}\displaystyle + 8 \displaystyle \mathbf{j} N, where \displaystyle \mathbf{i} and \displaystyle \mathbf{j} are perpendicular unit vectors.

b) Find the angle, to the nearest degree, between the force and the unit vector \displaystyle \mathbf{i}.


Answer
Answer 4.3
Solution a
Solution 4.3a
Solution b
Solution 4.3b


Exercise 4.4

A force is expressed as 9 \displaystyle \mathbf{i}\displaystyle + 10 \displaystyle \mathbf{j} N.

a) Calculate the magnitude of this force.

b) Find the angle between the force and the unit vector \displaystyle \mathbf{i}.

Answer
Answer 4.4
Solution a
Solution 4.4a
Solution b
Solution 4.4b

Exercise 4.5

For each force given below find its magnitude and the angle between the force and the unit vector \displaystyle \mathbf{i}.

a) \displaystyle \left( 4\mathbf{i}+3\mathbf{j} \right)\text{ N}

b) \displaystyle \left( 4\mathbf{i}-3\mathbf{j} \right)\text{ N}

c) \displaystyle \left( -2\mathbf{i}+8\mathbf{j} \right)\text{ N}

d) \displaystyle \left( -5\mathbf{i}-7\mathbf{j} \right)\text{ N}


Answer a
Answer 4.5a
Answer b
Answer 4.5b
Answer c
Answer 4.5c
Answer d
Answer 4.5d
Solution a
Solution 4.5a
Solution b
Solution 4.5b
Solution c
Solution 4.5c
Solution d
Solution 4.5d
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