Weight Force and Friction Force

Table of Contents

Gravity as a Force

Weight = mass x Gravity 

Weight and Mass

W=mg

Gravity - Specific Learning Objectives 

Gravity  x  Mass  =  Weight



You already know there is a relationship between these things.

Think about it - you are weightless on the moon. You are weightless in space. What is weight?

We stand on our bathroom scales to see our weight, but they lie, the bathroom scales lie, the Briscoes woman who sold you the scales....she lied to us!! They don't tell you your Weight! They tell you your MASS!!!!!!

What is the difference? 

Mass is the stuff of an object. It's the quantity of matter within the object. If you go into space, you would be weightless, but you would not be massless. To be massless is not to exist.

If you add more matter to your body and eat more McDonalds, your mass increases.

If you reduce the amount of matter in your body by replacing McDonald's with a carrot, your mass will decrease.

Your mass is how many Kilograms of matter your body consists of. 

Your mass will be the same if you teleported to any part of the Universe

However.

Your weight will change depending on where in the Universe you are. 

On the moon, you weigh only 1/6th of what you weigh on Earth

On the international space station, you weigh nothing

Mr Cowley Lectures

Mr Cowley Lecture - Weight, Mass and Gravity

The difference between the Moon, the International Space Station and Earth is GRAVITY. 

Well what is gravity

Gravity is the force of attraction between objects. All objects!

You and that person over there are attracted to each other - even if you aren't - because of gravity

Gravity is a very weak force. (luckily)

If I put my chocolate cup, and my coffee cup 1 cm apart on a highly varnished desk and left them their for 10 years, then they will be....... still 1 cm apart. 

It is a weak force. If you stood on the Mars Moon Deimos, which is twice the size of Mount Everest, then you did a running jump, you would launch yourself into space and never return. 

The more massive the object, the more gravity it generates, but it needs to be really massive for it to be noticeable. 

The earth is massive. It is large enough to have cleared it's orbit of all other rocky matter. 

The earth is so massive, that it pulls you onto it. No matter how hard you jump, it will always pull you back. 

The Earth's gravity will always pull you down. And the bigger you are the harder you'll fall. 

But as the earth pulls you down, you push back - with an equal and opposite force. You know this innately, because if you stand for a long time, you will eventually feel tired and want to sit.  

The interaction between the force the earth pulls on you and your mass is called weight

To calculate it take your mass and times it by the force of gravity which on earth is 9.81N/ kg. 

This 9.81N/kg means that each kg is pulled towards the earth with a force of 9.81 Newtons

The more kilograms of matter an object has, the more downward force will be applied by gravity (and the more upward force, or Normal, will need to be generated to oppose it)

We can calculate that downward force, by taking the force exerted on each Kilogram and multiplying that by how many Kilograms there are. 

The formula for this is: Weight = Mass x Gravitational Force

W = mg

G can either be:

 9.81N/kg, which means that each kg is pulled towards the earth with a force of 9.81Newtons. 

Or, because a 1Newton is equal to 1kg accelerated at a rate of 1m/s per second, you could cancel the kg and have:

9.81m/s/s

The value for Weight is Newtons, since it is the downward Force generated by the interaction between a mass and gravity


Wait.... Weight Questions


 





Answers (1, 2, 3) 

1. Luka's mass is 40kg, and Earths gravity is 9.81ms/s/s so:

w = m*g w = 40kg * 9.81m/s/s w = 392.4 N

Lukas weight is 392.4N


2. My mass is 80kg, Earths G is 9.81m/s/s 

w = m*g w = 80kg *9.81 w = 784.8 N


3. Lukas mass is 40kg, and the Moon's gravity is 1.625m/s/s

w = m*g w = 40kg*1.625 w = 65N


4. My weight on the ISS. My mass is 80kg. G on the ISS is 0m/s/s (relative to the ISS)

w = m*g w = 80kg x 0 w = 0N


Answers (5 and 6) 

5. Cars weight is 18305N, what is its mass?

w = m*g "isolate m" m = w/g

m= w/g m = 18305N / 9.81

m = 1866kg


6. Lunar Rover 341.25N on Moon. Moons gravity is 1.625m/s/s

w = m*g

(Simple maths to rearrange  the formula, say 6 = 2*3, so to isolate 2 you'd go 6/3= 2. Then apply this arrangement to the formula)

  w = m*g m = w/g

m = w/g m = 341.25N/1.625

m = 210kg

Gravity vs objects moving Straight Up

Up and Down with Gravity- Specific Learning Objectives 

For something to move upwards a force must be acting on it which is at least equal to the downward force of gravity. 

If the object starts from the ground, then the force to lift the object in the air must be greater than gravity, as gravity is accelerating the object downwards. And for the object to change motion, from at rest to moving, a force must be acted upon it which is greater than the force holding it in place, so that the forces are unbalanced. 

Once the object is moving upwards, it only needs to equal the downward force of gravity to maintain constant velocity - so the upward or thrust force must be a constant 9.81N/kg. However, if you want the object to accelerate, the upwards force needs to be greater than gravity. 

If an upward force is not maintained, then the object will decelerate until it stops moving upwards. It will then start to accelerate back towards the earth. Gaining velocity at a rate of 9.81m/s per second. 

Mr Cowley Lectures

Mr Cowley Lecture - Gravity vs Straight-up movement

Take the example of the Bottle rocket above. 

In the first 1 second of its journey, its velocity changes from 0 m/s to 38 m/s. 

In other words, the bottle goes from 0 km/h to 136.5 km/h in 1 second!

During this first second, the upwards thrust force from the bottle is 5 times that of Gravity. This is upwards unbalanced force causes the bottle to accelerate upwards at a rate of 38m/s/s.  

After this first second, there is no more water to be expelled from the bottle. So it has no more upward thrust force. The bottle is at its maximum velocity of 38m/s. 

Now that there is no more thrust, the force of gravity is the greater force. This unbalanced force acts to accelerate the rocket back towards the earth. However, as the rocket is traveling at 38m/s. Gravity first causes the rocket to decelerate at a rate of 9.81m/s per second. 

This deceleration eventually causes to rocket to stop moving upwards, this is the apex of the rockets journey. It then starts to accelerate back towards the earth. It gains speed as it falls, accelerating at a rate of 9.81m/s per second. 

The graphs illustrate the journey of the rocket. Showing the rapid acceleration at the start of the journey, propelling the rocket skyward. Then, once their is no water propellant left, the constant acceleration in the opposite direction due to gravity. The graphs show how this constant acceleration due to gravity causes the rockets velocity to change, along with the rockets distance from the earth

The effect of gravity accelerating objects towards the earth at 9.81m/s per second is also shown in the clips below. The example of the bullet is the same as the bottle rocket. Gravity opposes the vertical motion of the bullet, slowing it down till it stops going upwards. The bullet then comes back down, accelerating towards the earth and thus gaining velocity.

 The SpaceX Thrusters example are very good examples of unbalanced forces. They use a brief upwards force to slow their rate of decent. They apply force greater than gravity, an unbalanced force. Thus, causing acceleration in the opposite direction of the fall and thus reducing their downward velocity. 

Below are examples of SpaceX Falcon Thrusters returning to earth, and bullets being fired directly up

Air Resistance - Friction - Drag - Terminal Velocity 

Air Resistance - Friction Specific Learning Objectives 

Everything falls towards the ground at the same rate. 

This is discussed above with the objects going straight up, then accelerating back down to earth

This should mean that if you drop a coin off the Skytower, or the Empire State Building, then by the time it hits the ground it should be going fast enough that it'd be a lethal weapon. However, it's not! 

As the Penny falls to the ground, it falls through the air. When you are in the car and put your arm out the window it is pushed back by the air. The faster you are going, the more the air pushes against your arm. This force is the force of the atoms of the air slamming into your arm and then being pushed out of the way. The same as if you put your arm in water while on a rowing boat. The air molecules cause friction with your arm. Likewise, with the penny, as it falls the air pushes against it. The faster it goes the more air pushes against it. 

The harder air pushes against the penny the the greater the Force of Drag. The Force of Drag increases with the velocity of the penny. During this time the Force of Gravity remains constant, however as the Force of Drag increases the Net Force towards the ground reduces, meaning that the rate of acceleration towards the ground decreases

Eventually, the Force of Drag on the penny is equal to the Force of Gravity. Thus their is no more acceleration. The point at which the Force of Drag is equal to the Force of Gravity is called Terminal Velocity. At this point there is no more acceleration. The object will continue to travel towards the ground, but with Constant velocity. 

The graph below uses data from Aerospaceweb for a penny dropped from the Empire State Building. I've converted it into graphs so that you can see how its motion. The Empire State Building is a bit taller than the Skytower, and the penny is about the same mass as a 10 cent coin. 

Drag is the Force caused by air friction. This force opposes movement through air. The faster you move through the air, the more drag force their is. You'll notice that in the first 'second' the force of drag doesn't have a lot of an effect. So, initially the acceleration is the same as that of gravity 9.81m/s/s. 

In the following second, the force of drag has increased as the penny is moving through the air. this reduces the rate of acceleration, so the velocity graph states to curve. 

By the fifth second the drag is equal to the downward force of gravity. The downward force of gravity is gravity time mass. This is the same equation as w*mg. So the downward force of gravity is equal to weight and is given in newtons. 

Because the force of drag is now equal to the force of gravity the net force is 0 Newtons. 

If we look back to the equation F = ma We can rearrange to get a = F/m

a = F/m then a = 0N/0.0025g then a = 0 m/s/s

So, there is now more acceleration. This is shown in the acceleration graph, with acceleration being 0 m/s/s. This zero acceleration means that Velocity is now constant, as shown in the Velocity time graph. This constant velocity is called Terminal Velocity.  

Because the coins velocity is constant, the distance time graph is linear. 

If we take that Terminal Velocity of 10.99m/s and make it big to km/h then we'll times it by 3.6 and we'd get 40km/h. So, if you were under the coin, then the 2.5 gram coin would hit you at 40km/h. It'd hurt, but you'd be ok :-)

Mr Cowley Lectures

Mr Cowley Lecture - Drag and Air Friction

Air Friction and Drag on Vehicle Design

As you can see in the photo above, the vehicle designers have tried to make it easier for the vehicle to push air molecules out of the way. They have tried to improve the aerodynamics of the truck and thus reduce Drag. This will then reduce the thrust required to maintain a constant highway velocity and will thus reduce fuel consumption. 

The larger the area of the surface entering the air, the greater the drag. Consider an Cab over truck and a Ferrari. The cab over has a larger surface than the Ferrari so it has to push more air molecules out of the way. The more air molecules (Nitrogen, Oxygen and Carbon Dioxide) that the vehicle needs to push out of the way, the more air friction and thus more Drag. 

Because a greater drag force, will mean that a greater thrust force is required to balance the drag force and thus maintain a constant highway velocity. 

Cab-over trucks have their cabs over the engine. They do this because their are legal limits to the total length of the truck and trailer. By moving the cab over the engine, the trailer can be longer. But this then means that they are Not very aerodynamic. The more aerodynamic a vehicle, the easier it can push through the air, as the angle at which the air molecules are pushed is less. (Think of your hand out the window of a car - the as you change the angle at which it encounters the air molecules, the force exerted on your hand changes.  

Terminal velocity for a person jumping out of a plane. 

Terminal Velocity is the velocity of an object when the force of gravity is equal to the drag force created by air friction, thus net force is zero and acceleration therefore zero.

The point at which drag force is equal to the force of gravity is dependent on how much frontal surface area in contact with the air. If you are skydiving minimize frontal surface area, by diving head first, then your terminal velocity is around 250km/h. 

If you decide reduce your velocity, you can increase the frontal surface area. Thus, this will increase Drag until the forces are once again balanced. Then you will be at Terminal Velocity again. You can do this by lying in a belly to the earth position. By assuming a lying down position, The fronal surface area is at its maximum. So to is your Drag. Your new terminal Velocity will be around 180km/h.

This is still much faster than a survivable landing speed. So when you are ready, you pull out your parachute. The parachute has much more Frontal surface area than your body does. This results in the drag force being larger than the gravitational force. Because the forces are unbalanced, you will accelerate in the direction that is opposite to your velocity. In other words you will decelerate.  This deceleration will reduce your velocity. As Drag force is also affected by your velocity, the lower the velocity the lower the drag force. So Drag force will reduce until it is again the same size as gravity. At this point the deceleration effect stops and your velocity once again becomes constant. This new constant velocity is your new Terminal Velocity. The terminal Velocity for a person attached to a deployed and functional parachute is around 20km/h. At this low speed, collison with the earth is survivable and injury free. 

In the graph below, acceleration and deceleration only occur because of unbalanced forces.

At steady speed, or constant velocity, the forces are balanced and thus there is no acceleration and terminal velocity occurs

Projectile Motion

If we drive a car off a cliff it is not moving straight up and down, but rather it has movement in 2 axis - forward and down, or x and y. 

This motion is called projectile motion - motion in multiple directions simultaneously

If we look at 2 direction motion, we can think of throwing a ball, driving a car off a cliff or doing a running jump off a building. 

If we take Neo's jump, both Morpheus's jump is fake, as is Neo's. He looses forward momentum to quickly, and falls straight down. 

If we watch the car off the cliff you'll see that forward momentum continues even once they have left the ground. 

This forward momentum is also seen in the Cliff Jump over road clip. Likewise, this forward momentum or inertia is seen in the Red Bull Rampage clip. 

Due to the force of drag, the forward momentum is decreasing. As Drag against forward motion is an unbalanced force one you leave the cliff. However, the strength of this force, and thus its deceleration effect (backwards acceleration) is over estimated in the Neo Jump. 

So what would happen if you did a Neo Jump? 

Well, lets get The Hulk to do the jump, as he'd survive. 

So, The Hulk Takes a running Jump from the QBE Tower on Que (next to the Burger King). That building, is 106 meters tall, but well round to 105 meters tall to make the maths easier. We will also ignore Drag Force and assume this is done in a Vacuum. And, we will round 9.81 to 10, to make the maths simpler. 

The calculations and data are shown in the table below.

As you can see, the total distance forward is 36 meters!. This places in the building on the other side of the road. If his impact doesn't break the windows then he'll land on the sidewalk across the road from the QBE Toward

This makes a lot more sense if you watch Tom Cruise doing his stunt. You can see all that momentum, and you can see why Neo's fall is so wrong and why The Hulk would go so far. 

Looking at the data in the table below, we can see: 

That Hulk runs with a constant rate of acceleration of 2m/s/s. Thus his Forward Velocity increases. 

The second (3s) he steps of the building he is no longer accelerating in the Forward Direction. With Forward Acceleration at zero, his Forward Velocity stays at 6 m/s.

When he is running along the top of the building, his Downward Acceleration due to gravity is equaled by the Supportive force of the building, or 'Normal'. As the forces are balanced, there is no acceleration in the vertical plane. Once Hulk leaves the ledge of the building the supportive force of Normal is no-longer present. Thus the Force of Gravity is unbalanced and the Hulk accelerates towards the earth. The rate of Acceleration is constant 9.81m/s/s. Here it is rounded to 10m/s/s. You can see that this causes a linear increase in velocity and an exponential increase in total distance. 

The Hulk impacts the ground with a forward velocity of 6 m/s and a downward velcocity of 60m/s. 

If we times it by 3.6 then we will see that the Forward Velocity at the moment of impact is 21.6km/h. And the Downward Velocity is 216km/h. At which point, he has traveled vertically downwards by 105 meters and horizontally, across the street by 36 meters. This distance, or displacement, is seen graphically in the final graph below. 

Mr Cowley Lectures

Friction

Friction - Specific Learning Objectives 

When ever two objects are in contact, friction occurs. Friction is the force caused by the interaction of the two surfaces. Friction opposes motion. Friction is what causes you not to fall over when walking. Reduced friction is what causes you to fall over if you walk with normal shoes on Ice. 

We talk about friction everyday - we say careful that is slippery - meaning there is reduced friction. We say that our new shoes have good grip - meaning that friction has been increased. 

I saw the Mythbusters phone-book experiment in person when Jamie and Adam came to Auckland. The friction between the two phone-books was strong enough to lift a person off the ground. In other words, the Force of Friction was equal and balanced with the Force of Gravity. Allowing a lady to be lifted into the air. 

There are 4 types of Friction

Mr Cowley Lectures

Mr Cowley Lecture - Friction - Part 1


Mr Cowley Lecture - Friction Part 2

Static Friction 

Static friction - this has the highest frictional force of the 4 types of friction. You innately know this because when you have to push something that does not have wheels over a surface - it is harder to get it moving than to keep it moving. Now, this is mostly because of inertia (force required to change motion), however a small amount of it is due to the difference between static friction and kinetic friction. 

The difference between Static and Kinetic is that gravity forces accelerates objects downwards, acceleration is a function of movement and time. Thus, once an object is stationary, it can accelerate or move towards the earth until the force is balanced. The more time, the more movement can occur. For this reason, if you push your bookshelf along the carpet to its new location, and then go to move it a few days later, it is hard to get it moving, because it has slowly moved downwards, pushing air out of the carpet and underlay, effectively sinking into the carpet. When you go to move it, you need to push it out of the cavity it now sits in. This sinking is different with different surfaces. If the bookshelf was on a wooden floor, it would be much easier to push because it would't have sunken as much so the cavity wont be as deep. 

Likewise, if you have a cement seat in the garden, it will be easier to move if it has been siting on the cement driveway. However, if it has been sitting on the soil, it will sink somewhat, until the soil underneath is compressed to the point that the force of normal is equal to the force of gravity. 

You already know this from everyday life. If something heavy is left on the dirt, it'll be harder to move than if it is on the concrete. Things slide easier on a wooden floor than on carpet - even you in your socks!

This "Intuition on Static and Kinetic Friction" by Khan Academy is the best ever - Watch it!



Rolling Friction

Rolling friction  is the halfway between static friction and sliding friction. With it the 'contact patch' between two surfaces is 'lifted' away whilst a new contact patch is created. Between the leading edge and exit edge of the contact patch the two surfaces are effectively static. 

Rolling friction will still generate heat, as the surfaces slide downwards and upwards into their contact patch position, and as the wheel deforms . This is why tires on a car glow hot on Infra-Red cameras during night time police chases.

Sliding Friction

Sliding Friction generates more a lot of heat energy. This is because the molecules in both surfaces are colliding with each other then moving due to the collisions. Just like in a microwave, energy is released from these moving molecules as heat energy. So kinetic energy is converted or transformed into heat energy. 

This transformation of kinetic energy into heat energy is why your hands get warm when you rub your hands together

It is also the transformation of kinetic energy into heat energy due to sliding friction which allows you to start a fire by rubbing wooden sticks together

Sliding Friction vs Rolling friction

Rolling friction generates greater connection between the objects than does sliding friction. This is because as the tire surface is lowered onto the road surface, and then lifted out. While generating greater connection, The contact patch has high frictional force, this is why traction control is used in powerful cars, as it gives you better acceleration and better traction going around corners. In other words, you have higher frictional force in the contact patch, so the cornering force can be higher.

Sliding friction generates more heat and less contact patch frictional force.  This sounds counter intuitive. However, when sliding the tire contact patch is not lifted and lowered into place, rather as it is sliding, it pushes against the contact surface causing the parts to slam into each other. This slamming causes the molecules to move relative to each other, molecular movement converts kinetic energy into heat energy. On a larger scale, this slamming can cause some of the road to break and some of the tire rubber to break off. This is why sliding and skidding on your bike wears down the rubber. Likewise, sliding, skidding and burnouts all remove rubber from your car tires. Furthermore, this slamming can cause compression and then expansion within the wheel, causing the wheel to bounce. This bouncing reduces contact between the two surfaces. You can feel the bounce if you 'floor it' at the lights and your drive wheels spin. You can also feel the bounce if you turn off ABS and lock-up your wheels when coming to a stop. This reduction in contact patch frictional force reduces the force required to cause your car to slide off the road. This is why locking up your brakes going into a corner can result in a crash. This is also why ABS or Anti-lock braking system is used in all cars

Are Burn-outs Static Friction, Rolling Friction or Sliding Friction?

Fluid Friction

Fluid Friction also generates heat in the air (both gases and liquids are fluids). When space travel objects re-enter earths atmosphere, they do so at about 28000km/h. They move through the air so quickly that the friction of the air causes the outer shell of the object to get very hot. 

Fluid Friction also causes heat to be generated with very fast planes, such as spy jets and the Blackbird SR-71 - the worlds fastest plane. 

Fluid Friction also generates heat. Heat is generated when water flows through pipes - but because of the heat capacity of water, there is generally no change in temperature. 

SciPad

Pages 42, 43,  44, 45

The Fastest Car in the world

This is the Bloodhound Jet powered car. It is being used in a British attempt to break the land speed record. It has already hit a top speed of 1010km/h. The current record is 1227km/h so they still have some work to do. This work involves a lot of Motion and Forces physics. 

I recommend watching this clip as part of your revision.  As it gives you an opportunity to apply your Mechanics knowledge. 

All of the Mr Cowley Force Lectures

Mr Cowley Lecture 1 - Balanced and Unbalanced

Mr Cowley Lecture 3 - Contact and Non-contact

Mr Cowley Lecture 5 - Net Force

 Mr Cowley Lecture 2 -  F = ma

Mr Cowley Lecture 4 - Force Diagrams

Mr Cowley Lecture 6 - Newton's 3 Laws of Motion

Mr Cowley Lecture 7 - Newtons Laws Continue

Mr Cowley Lecture 9 - Gravity vs Straight-up movement

Mr Cowley Lecture 8 - Weight, Mass and Gravity

Mr Cowley Lecture 10 - Drag and Air Friction

Mr Cowley Lecture 11 - Projectile Motion

Mr Cowley Lecture 13 - Friction Part 2

Mr Cowley Lecture 12 - Friction - Part 1

Revision 

These are some scanned pages from the ABA Y11 Science, aspects of Mechanics book. Reading over them can be good for clarifying your understanding, and seeing the ideas from different perspectives or angles if you are so inclined