4. Exercises

From Mechanics

(Difference between revisions)
Jump to: navigation, search
Line 114: Line 114:
</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}}
 +
 +
 +
 +
===Exercise 4.8===
 +
<div class="ovning">
 +
 +
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.
 +
 +
(a) Find the magnitude of
 +
<math>{\mathbf{F}_{1}}</math>.
 +
 +
 +
(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>.
 +
 +
 +
(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}

Image:E4.1.GIF

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


Exercise 4.2

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

Image:E4.2.GIF


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}.

Image:E4.6.GIF

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}.

Image:E4.7.GIF

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}}.