Analysing Forces in Equilibrium

Analysing forces in equilibrium

Vector Addition of Forces

1. A resultant force is a single force that represents the combined effect of two or more  
  forces in magnitude and direction. The direction of the forces have to be taken into  
  consideration when forces are added.

2. If the forces act in the same straight line, the resultant is found by simple addition or  
  subtraction as shown in figure 2.1

  Resultant force, F = F1 – F2

  Figure 2.1

3. The resultant of forces that do not act in the same straight line can be determined by 
  using the parallelogram law.


4. The parallelogram law states that if two forces acting at a point are represented in size  
  and direction by the sides of a parallelogram drawn from the point, their resultant is 
  represented in size and direction by the diagonal of the parallelogram drawn from the 
  point.

Forces in Equilibrium

1. An object is said to be in equilibrium if the object is at rest or is moving with a constant velocity in a straight line.

2. The resultant force that acts on an object is zero if it is in equilibrium. In other words, the forces that act on the object are balanced in all directions.

3. If object is in equilibrium, the resultant force that acts is zero.

4. For two forces acting in the same direction or opposite direction, if the force is not zero, then the object is not in equilibrium.

Impulse and Impulsive Force

Impulse and impulsive Force

1. Impulse is defined as the change momentum

How to derive impulse?

2. From, F= ma, a = (v-u)/t

  Ft=mv-mu (change of momentum)

3. Impulse is the product of the force F acting on a body and the time t for which the force acts.
Hence, impulse = Ft = mv – mu

4. The SI unit of impulse is kg m s⁻1 or N s.
5. Impulsive force is the rate of change of momentum.
  Impulsive force = Impulse / time
6. The SI unit of impulse is kg m s⁻² or N.

The Effect of Time on an impulsive Force
1. From the formula for impulsive force, we get
Ft = mv – mu
F =  (mv - mu) / t
This shows that the time of action is very important factor in the calculation of the impulsive force.
2.When the time of action is prolonged, the impulsive force will decrease.
3. On the other hand, if the time of action is shortened, the impulsive force will increase.


Ways to Reduce Impulsive Forces
The Design of a car

1. A car is mainly designed for the safety of the driver.
2. The front and the rear parts of the car are made of soft metal so that the car is easily crumpled during an accident.
a) During collision, the time taken for the change in speed (from a high speed to zero) is prolonged. Since the impulsive force
= Distance / Time , the force will decrease when the time increase.
b) This will decrease the impulsive force on the passengers and the driver.
3. The seats of the passengers are strengthened to protect the passengers.
4. Safety belts:
a) Passengers have to fasten the safety belts. When the car stops suddenly, the inertia of the passengers will result in the passengers being flung to the front and hitting the windscreen of the car.
b) Hence, safety belts will slow down the motion of the passengers.
5. Airbags are built in some cars. When an accident happens, the airbags will be filled with air. This will prolong the time of action and reduce the impulsive force on the passenger.

Ways to utilize impulsive force

Material arts player break a few pieces of bricks
- A martial arts player ia able to break a pile of bricks with ease.
- This is because the hand of the player moves very fast and stops when it hits the top brick.
- Hence, the time of contact of the hand with the brick is short and this will increase the impulsive force on the bricks.
- The bricks are easily broken because of the big impulsive force.

The pestle and mortar
- The pestle and mortar are made of hard materials.
- During pounding or grinding, the pestle moves very fast. The mortar stops the motion of the pestle in a short time.
- A strong impulsive force is produced and the food can be broken into pieces easily.

The pile and the pile driver
- A pile driver is made of hard steel alloy.
- The pile driver is released very fast hit the hard pile.
- The time taken to hit the pile is short because both surfaces are hard.
- Hence, a big impulsive force is produced on the pile and it will be driven into the ground to support the foundation of the structure of a tall building.