4. Exercises
From Mechanics
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a) | a) | ||
| - | <math> | + | (<math>4\mathbf{i}+3\mathbf{j}</math> |
| + | ) N | ||
b) | b) | ||
| - | <math> | + | (<math>4\mathbf{i}-3\mathbf{j}</math> |
| + | ) N | ||
c) | c) | ||
| - | <math> | + | (<math>-2\mathbf{i}+8\mathbf{j}</math> |
| + | ) N | ||
d) | d) | ||
| - | <math> | + | (<math>-5\mathbf{i}-7\mathbf{j}</math> |
| + | ) N | ||
Revision as of 15:49, 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 4\mathbf{i}+3\mathbf{j} ) N
b) (\displaystyle 4\mathbf{i}-3\mathbf{j} ) N
c) (\displaystyle -2\mathbf{i}+8\mathbf{j} ) N
d) (\displaystyle -5\mathbf{i}-7\mathbf{j} ) 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}}.
