4. Exercises

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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
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