4. Exercises
From Mechanics
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</div>{{#NAVCONTENT:Answer|Answer 4.7|Solution a|Solution 4.7a|Solution b|Solution 4.7b}} | </div>{{#NAVCONTENT:Answer|Answer 4.7|Solution a|Solution 4.7a|Solution b|Solution 4.7b}} | ||
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| + | ===Exercise 4.8=== | ||
| + | <div class="ovning"> | ||
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| + | A force | ||
| + | <math>{\mathbf{F}_{1}}</math> | ||
| + | = (<math>9\mathbf{i}+12\mathbf{j}</math>) N and a second force <math>{\mathbf{F}_{2}}</math> = (<math>-4\mathbf{i}+\mathbf{j}</math>) N act on a particle. | ||
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| + | (a) Find the magnitude of | ||
| + | <math>{\mathbf{F}_{1}}</math>. | ||
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| + | (b) Draw a diagram to show the direction of | ||
| + | <math>{\mathbf{F}_{1}}</math>, and calculate the | ||
| + | angle between | ||
| + | <math>{\mathbf{F}_{1}}</math> | ||
| + | and <math>\mathbf{i}</math>. | ||
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| + | |||
| + | (c) Find the resultant of | ||
| + | <math>{\mathbf{F}_{1}}</math> | ||
| + | and <math>{\mathbf{F}_{2}}</math>. | ||
| + | |||
| + | |||
| + | </div>{{#NAVCONTENT:Answer a|Answer 4.8a|Answer b|Answer 4.8b|Answer c|Answer 4.8c|Solution a|Solution 4.8a|Solution b|Solution 4.8b|Solution c|Solution 4.8c}} | ||
Revision as of 15:25, 9 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 \displaystyle \mathbf{i} and \displaystyle \mathbf{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.
Exercise 4.7
The diagram shows 3 forces and the perpendicular unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}.
a) Express each force in terms of the unit vectors \displaystyle \mathbf{i} and \displaystyle \mathbf{j}.
b) Find the magnitude of the resultant of the 3 forces.
Exercise 4.8
A force \displaystyle {\mathbf{F}_{1}} = (\displaystyle 9\mathbf{i}+12\mathbf{j}) N and a second force \displaystyle {\mathbf{F}_{2}} = (\displaystyle -4\mathbf{i}+\mathbf{j}) N act on a particle.
(a) Find the magnitude of \displaystyle {\mathbf{F}_{1}}.
(b) Draw a diagram to show the direction of
\displaystyle {\mathbf{F}_{1}}, and calculate the
angle between
\displaystyle {\mathbf{F}_{1}}
and \displaystyle \mathbf{i}.
(c) Find the resultant of
\displaystyle {\mathbf{F}_{1}}
and \displaystyle {\mathbf{F}_{2}}.
