4. Exercises
From Mechanics
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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}} | </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}} | ||
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| + | ===Exercise 4.6=== | ||
| + | <div class="ovning"> | ||
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| + | The diagram shows two forces and the unit vectors i and j. | ||
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| + | a) Express each force in the form <math>a\mathbf{i}+b\mathbf{j}</math>. | ||
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| + | b) Find the magnitude of the resultant of these two forces. | ||
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| + | c) Find the angle between the resultant force and the unit vector <math>\mathbf{i}</math>, and draw a diagram to show the direction of the resultant force. | ||
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| + | </div>{{#NAVCONTENT:Answer a|Answer 4.6a|Answer b|Answer 4.6b|Answer c|Answer 4.6c|Solution a|Solution 4.6a|Solution b|Solution 4.6b|Solution c|Solution 4.6c}} | ||
Revision as of 18:12, 8 September 2009
| Theory | Exercises |
Exercise 4.1
The diagram shows a force and the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}
Express the force in terms of the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}
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Exercise 4.2
Express each of the forces given below in the form \displaystyle a\mathbf{i}+b\mathbf{j}
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}.
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}.
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}
Exercise 4.6
The diagram shows two forces and the unit vectors i and j.
a) Express each force in the form \displaystyle a\mathbf{i}+b\mathbf{j}.
b) Find the magnitude of the resultant of these two forces.
c) Find the angle between the resultant force and the unit vector \displaystyle \mathbf{i}, and draw a diagram to show the direction of the resultant force.
