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}}.