4. Exercises

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}

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

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}.

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}.

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

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.

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.

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}}.

Four forces are shown on the diagram below.

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

b) Find the angle between the resultant force and the unit vector \displaystyle \mathbf{i} correct to the nearest degree.