# Forces in Action

- Created by: CPev3
- Created on: 04-05-20 23:54

## What is a couple?

A pair of equal and opposite forces acting on a body but not in the same straight line

## What is the torque of a couple?

The product of one of the forces of a couple and the perpendicular distance between the forces

Torque = F * d

## What is a torque?

The moment of a couple

## What are the rules of the triangle of forces?

- The resultant of forces F and T must be equal in magnitude to the third force W but in the opposite direction
- Both the resultant vertical force and resultant horizontal force must be zero

## What is a triangle of forces?

- Arrows are drawn to represent each of the 3 forces end-to-end
- The triangle is closed because the net force is zero and so the object is in equilibrium

## What is density?

The mass per unit volume of a substance

ρ = m / V

## What is the density of air?

1.3 kgm^{-3 }

## What is pressure?

The normal force exerted per unit cross-sectional area

p = F / A

## What is the value of atmospheric pressure?

1.0x10^{5} Pa

## What is weight?

The gravitational force acting on an object through its centre of mass

## What is friction?

The force that arises when two surfaces rub against each other

## What is drag?

The resistive force on an object travelling through a fluid

## What is tension?

The force within a stretched cable or robe

## What is upthrust?

An upward buoyancy force acting on an object when it is in a fluid

## What is normal contact force?

A force arising when one object rests against another object

## Weight resolved into two components:

Force parallel to the slope = mgsinθ Force perpendicular to the slope = mgcosθ

## Net force equations:

Net force = m * a

Net force = normal contact force - weight

## What factors affect the magnitude of drag?

- Cross-sectional area
- Speed
- Shape
- Roughness/ texture of object
- Density of fluid

## How can you reduce the air resistance exerted agai

Smooth, streamlined shape

Increases the top speed of the car

Reduces the amount of fuel used on a journey

## What is terminal velocity?

The constant speed reached by an object when the drag force (and upthrust) is equal and opposite to the weight of the object

## What is a moment?

The product of force and perpendicular distance of the line of action of force from the axis or point of rotation

Moment = F * x

## What is the moment of a force?

The turning effect of a force about some axis or point

## The principle of moments:

When a body is in equilibrium, both the net force and net moment acting on it is zero

The sum of the anticlockwise moments about any point = the sum of the clockwise moments about that same point

## Stages of terminal velocity:

t = 0

net force = mg

a = g

mg > D

net force = mg - D

a = (mg - D) / m

mg = D

net force = 0

a = 0

## What is centre of gravity?

An imaginary point at which the entire weight of an object appears to act

## What is centre of mass?

A point through which any externally applied force produces straight-line motion but no rotation

## How do you fing the centre of gravity of an object

1) Make small holes along the edges of the object made from card

2) Insert a pin through one of the holes and hold the pin firmly in a clamp

3) Allow the object to swing freely before coming to rest with its CoG vertically below the pin

4) Hang a plumb-line from the pin

5) Draw a line along the vertical string of the plumb line

6) Repeat this process for the other holes

7) CoG = the point of intersection of the lines

## What is a fluid?

A substance that can flow

## The pressure exerted by a vertical column of liqui

W = m * g

W = (ρ * V) * g

W = ρ * A * h * g

p = (ρ * A * h * g) / A

p = h * ρ * g

## Archimedes' principle:

- The upthrust exerted on a body immersed in a fluid (fully/ partially submerged) = the weight of the fluid that the body displaces
- An object will sink if the upthrust is less than the weight of the object
- For a floating object the upthrust = the weight of the object = the weight of the fluid it displaces

## Upthrust equation:

Force at the top surface = h ρ * g * A

Force at the bottom surface = (h + x) * p * g * A

Resultant upward force (upthrust) = ((h + x) * p * g * A) - (h * ρ * g * A) = x * ρ g * A

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