 # Applied Force

Force is a push or a pull on a mass. Nature gives us lots of examples of forces causing things to move. To create a force we require energy.

Isaac Newton was a scientist in the 17th century in England. He studied how objects move, and wrote his discoveries in three laws called Newton's Laws of Motion. These are still used today in all sciences and engineering. Every machine ever built relies on an understanding of Newton's Laws to predict its behaviour. Forces are never alone. Whenever one force is applied, there are always other forces involved. To use Newton's laws we need to calculate first the 'resultant force', or net force. The acceleration of a mass will be proportional to the sum of all forces acting on that mass:

\$F_R = F_1 + F_2 + F_3 + ....\$

The unit of force is newton (N), in honour of the great scientist. When two forces are pulling in the same direction, the total force is the sum of the two: 12.0 N + 8.0 N = 20.0 N.

## Resultant Force

An important thing to understand about forces is that when a force is applied to a mass, there is nearly always at least one other force trying to prevent the mass from moving or changing its behaviour. The only exception to this is a frictionless situation, such as in space. But, on Earth, trying to move an object on any surface will result in friction making the job harder or impossible. The resultant (or net) force (\$F_R\$) is the total of all the forces acting on a mass. Since friction (\$F_F\$) always pulls in the opposite direction to the applied force (\$F_A\$), it is negative:

\$\$F_R = F_A - F_F\$\$

Since friction is created by the applied force, friction can never be greater than the applied force. If friction equals the applied force, the force is insufficient to move the object. You need more force than the friction to move something.

## Hanging Masses

Engineers are always interested in how the force of gravity works on objects they want to stand up or hang from something. The force of gravity (\$F_g\$) acting on an object is its weight, and is equal to the mass (m) times the acceleration of all objects in the Earth's gravitational field (\$g = 9.81 m/s^{2}\$):

\$F_g = m⋅g\$

The resultant force on a suspended mass is the applied force upwards (\$F_A\$) minus the weight of the object:

\$F_R = F_A - F_g\$

Example In the example: a mass of 1.8 kg is pulled upwards with a force of 42.0 N. What is its acceleration?

The force resisting the upwards force is the weight of the object: \$F_g = m⋅g = 1.8 ⋅ 9.81 = 17.7 N\$

The resultant force is therefore: \$F_R = F_A - F_g = 42.0 - 17.7 = 24.3 N\$

Newton's Second Law of Motion states that
F = ma, so \$a = F/m = {24.3}/{1.8} = 13.5 m/s^2\$ upwards.

## Equilibrium of Forces

Equilibrium is the state where there are forces which cancel each other out, so the net force is zero.

Vectors describe quantities which can have magnitude and direction. Vectors indicate the magnitude and direction of quantities, such as the forces of weight and tension in rope. In equilibrium, the sum of these force vectors equals zero.

For example, a weight suspended by two ropes has forces in equilibrium. This means there is no net force acting, so the mass does not accelerate in any direction.

The forces may be drawn in a free-body diagram, where the relative strengths of the forces are indicated by the lengths of the vector, as well as their direction. If the force vectors are added together, they will result in a zero vector.

## Balanced Forces

Newton's First Law of Motion states that a body at rest will stay at rest, and a body moving at constant velocity will continue to move at that constant velocity, in a straight line, unless a net force acts upon it.

In reality, there is no situation where there is no force. Even in outer space, there is some gravity or radiation force on all matter. Since the world is full of objects that are not moving, there is a cancellation of forces in different directions.

If an object is travelling at constant speed, it would continue at that speed, unless a force is applied to change its speed. In practice, a car needs constant force from the engine to keep it moving at constant speed because air resistance and tyre friction acts to slow it down.

If an object is in equlibrium, it has a zero net force: an object at rest will stay at rest, and a moving object will continue to move at the same velocity.

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