Pearson Edexcel IAL Mathematics M1.2.1 Magnitude & direction

Practise finding vector magnitudes and directions from components, diagrams and bearings, including resultant forces in i and j form.

[Maximum number: 4]

Figure 4

A particle P of mass 4 m lies on the surface of a fixed rough inclined plane.
The plane is inclined to the horizontal at an angle $\alpha$ where $\tan \alpha=\frac{3}{4}$
The particle P is attached to one end of a light inextensible string.
The string passes over a small smooth pulley that is fixed at the top of the plane. The other end of the string is attached to a particle Q of mass m which lies on a smooth horizontal plane.

The string lies along the horizontal plane and in the vertical plane that contains the pulley and a line of greatest slope of the inclined plane.

The system is released from rest with the string taut, as shown in Figure 4, and P moves down the plane.

The coefficient of friction between P and the plane is $\frac{1}{4}$
For the motion before Q reaches the pulley

find the magnitude of the force exerted on the pulley by the string.

$2 T \sin \frac{1}{2} \alpha$ oe e.g. $\sqrt{T^{2}+T^{2}-2 T^{2} \cos \alpha}$ using cos rule

Or $\frac{T \sin \alpha}{\sin \left(90^{\circ}-\frac{1}{2} \alpha\right)}$ using sine rule

Or $\sqrt{(T-T \cos \alpha)^{2}+(T \sin \alpha)^{2}}$ using components and Pythag.

M1 A1

Substitute for T and trig

M1

$\frac{8 m g \sqrt{10}}{125}$ oe, 2 m or 2.0 m or 1.98 m or 0.2 m g or better

A1

(4)

All question bank results loaded

M1.2.1 - Magnitude and direction question 1