1. The Mechanics of Forces
Lesson Objective:
Understand Newton’s first law and be able to solve problems in context that involve objects in equilibrium

2. Eg 1
A reliant robin car of mass 1000 kg is driving at a constant speed along a horizontal road. If the total resistance forces acting on the car are 200N, what is the driving force of the car and what is the Normal Reaction force of the car with the road?

3. A mass of 3kg is pulled at a constant speed along a rough horizontal surface using a light inelastic rope at an angle of 40 degrees to surface. If the force applied to the rope is 8N, find the Normal Reaction force on the block and the size of the friction force.

9. A sign of mass 10kg is to be suspended by two strings arranged as shown in the diagram below. Find the tension in each string.
30o
45o

10. One end of a string 0.5 m long is fixed to a point A and the other end is fastened to a small object of weight 8 N. The object is pulled aside by horizontal force P, until it is 0.3 m from the vertical through A. Find the magnitudes of the tension T in the string and the magnitude of the force P.
A small block of weight 20 N is suspended by two strings each of length 0.8 m, from two points 1 m apart on a horizontal beam. Find the tension in each string.
A particle of weight 10N rests in equilibrium on a rough plane, inclined at 30° to the horizontal. Calculate the magnitude of the frictional force, and of the normal reaction of the plane.

11. One end of a string 0.5 m long is fixed to a point A and the other end is fastened to a small object of weight 8 N. The object is pulled aside by horizontal force P, until it is 0.3 m from the vertical through A. Find the magnitudes of the tension T in the string and the magnitude of the force P.
A small block of weight 20 N is suspended by two strings each of length 0.8 m, from two points 1 m apart on a horizontal beam. Find the tension in each string.
A particle of weight 10N rests in equilibrium on a rough plane, inclined at 30° to the horizontal. Calculate the magnitude of the frictional force, and of the normal reaction of the plane.

14. DO THIS WITHOUT A CALCULATOR!
A and B are two fixed points on a horizontal line. Two light inextensible strings are attached to A and B and the other ends are attached to a particle C of mass 5 kg. AC = 3 cm, BC = 4 cm and angle C = 90°. The strings are holding particle C in equilibrium.
Find the tensions in the two strings in terms of g. A B C

15. By Pythagoras’ Theorem, AB = 5 cm.
The two angles marked  are alternate as are the two angles marked .
Note that  = 90 - 
Using trigonometry,
sin =
and cos = ;
sin =
and cos = .

16. Resolving horizontally, T1cos = T2cos
Resolving vertically, T1cos(90 – ) + T2cos(90 – ) = 5g T1sin + T2sin = 5g
Therefore T2 = 3g and T1 = 4g.

17. A crate of mass 300 kg is hanging from a rope
A crate of mass 300 kg is hanging from a rope. Two dockers are pulling it downwards and to one side using a second rope, with a combined force of 1000 N. If the rope the crate is hanging from makes an angle of 15° to the vertical and the system is in equilibrium, find:
(i) the angle which the second rope makes to the horizontal,
(ii) the magnitude of the tension in the rope from which the crate is
hanging.
15o