Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

4. Exercises

From Mechanics

Jump to: navigation, search
       Theory          Exercises      


Exercise 4.1

The diagram shows a force and the unit vectors i and j

Image:E4.1.GIF

Express the force in terms of the unit vectors i and j

Answer | Solution


Exercise 4.2

Express each of the forces given below in the form ai+bj

Image:E4.2.GIF

Answer a | Answer b | Answer c | Answer d | Answer e | Answer f


Exercise 4.3

a) Find the magnitude of the force 6 i+8 j N, where i and j are perpendicular unit vectors.

b) Find the angle, to the nearest degree, between the force and the unit vector i.


Answer | Solution a | Solution b


Exercise 4.4

A force is expressed as 9 i−10 j N.

a) Calculate the magnitude of this force.

b) Find the angle between the force and the unit vector i.

Answer | Solution a | Solution b

Exercise 4.5

For each force given below find its magnitude and the angle between the force and the unit vector i.

a) (4i+3j ) N

b) (4i−3j ) N

c) (−2i+8j ) N

d) (−5i−7j ) N


Answer a | Answer b | Answer c | Answer d | Solution a | Solution b | Solution c | Solution d


Exercise 4.6

The diagram shows two forces and the unit vectors i and j.

Image:E4.6.GIF

a) Express each force in the form ai+bj.

b) Find the magnitude of the resultant of these two forces.

c) Find the angle between the resultant force and the unit vector i, and draw a diagram to show the direction of the resultant force.

Answer a | Answer b | Answer c | Solution a | Solution b | Solution c



Exercise 4.7

The diagram shows 3 forces and the perpendicular unit vectors i and j.

Image:E4.7.GIF

a) Express each force in terms of the unit vectors i and j.

b) Find the magnitude of the resultant of the 3 forces.


Answer | Solution a | Solution b


Exercise 4.8

A force F1 = (9i+12j) N and a second force F2 = (−4i+j) N act on a particle.

(a) Find the magnitude of F1.


(b) Draw a diagram to show the direction of F1, and calculate the angle between F1 and i.


(c) Find the resultant of F1 and F2.


Answer a | Answer b | Answer c | Solution a | Solution b | Solution c


Exercise 4.9

Four forces are shown on the diagram below.

Image:E4.9.GIF

a) Find the magnitude of the resultant of the four forces.

b) Find the angle between the resultant force and the unit vector i correct to the nearest degree.


Answer | Solution a | Solution b

Retrieved from "http://wiki.math.se/wikis/2009/bridgecoursemechanics/index.php/4._Exercises"