# SPH4C

What happens when you hit the brakes in a car that makes you come to a blockage, or what happens to the parachutist as she jumps out of the plane that makes her fall faster and faster — this is the learn of dynamics. Dynamics is the report of the causes of the different motions : uniform and non-uniform .
In order for an object to change its travel rapidly, something needs to act on it : an object either needs to get pushed or pulled in a certain steering. Our parachutist is being pulled toward the earth by the Earth ’ s pull of graveness, causing her to go faster. When she deploys her parachute, the parachute pulls her up, causing her to go slower. And when she collides with the Earth ( hopefully, lightly ! ) the earth is, in effect, pushing on her, causing her forth movement to slow down quite quickly and stop .
These pushing and pulling interactions between objects are called forces. Any two objects, provided they are interacting with each early, will exert a impel on each other. Don ’ triiodothyronine forget, that objects preceptor ’ thymine necessarily need to be touching in order to interact, for case the earth can still exert gravity on an airplane in mid-air .
force is a vector measurement, so there is always a focus associated with it. The symbol for force is , and forces are measured in newtons — the argue for this will become apparent late in this activity !

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Throughout this activeness, we will look at six types of forces that impact us every day. To simplify, each force is defined individually, however there is about always a combination of forces acting on any given object .

Gravitational Force:

• Exists between a planet (usually the Earth) or other large body and the object in question; dependant on the object’s mass.
• Always acts on the object in the [down] direction.
• Known as an action-at-a-distance force: two objects do not need to be in contact with each other in order to experience a gravitational force.

Normal Force:

• Exists when an object is in contact with a surface (like a book sitting on a table, or a skater gliding on the ice, or a box on a ramp), usually to counteract the force of gravity.
• Always acts in the direction perpendicular to the surface upon which the object is resting.

Applied Force:

• Exists when two objects interact with each other.
• The direction of the force will depend on the situation.

Each applied force will have a different notation depending on the source of the force. For example, a person pushing on a car would have an applied force of .

Friction Force:

• Exists when two objects are in contact with each other.
• Typically acts in the opposite direction of an object’s motion (it is what slows down a skateboarder gliding down the street), or opposite an applied force on a stationary object (it is what keeps a heavy filing cabinet in place even when you are pushing on it).

Air Resistance:

• Exists when a moving object comes into contact with air (think friction, but due to the air instead of a surface).
• Always acts in the opposite direction of an object’s motion.

Tension Force:

• Exists when an object is being pulled by a string, rope, chain, etc.
• Always acts in the direction parallel to the rope.

## Questions

Can you identify the forces acting on each of the be objects ?

1. A bird, standing motionless on a branch.

• Gravitational force (pulled downward by the Earth)
• Normal force (pushed upward by the branch)
2. A curling stone, gliding forward along an ice surface.

• Gravitational force (pulled downward by the Earth)
• Normal force (pushed upward by the ice)
• Friction force (pushed backward by the roughness of the ice)
3. A toy, being dragged along the ground by a child pulling on a string.

• Gravitational force (pulled downward by the Earth)
• Normal force (pushed upward by the ground)
• Tension force (pulled by the child)
• Friction force (pulled opposite the direction of motion by the roughness of the ground)
4. A person, pushing a car that has run out of gas.

• Gravitational force (pulled downward by the Earth)
• Normal force (pushed upward by the ground)
• Applied force (pushed by the person)
• Friction force (pulled opposite the direction of motion by the roughness of the ground)

# Reflection

Give some think to the follow questions, and create a reflection to jot down your answers .

1. All of these examples include the gravitational force. Can you think of a situation where an object would NOT have a gravitational force exerted on it?
2. All of these examples also include a normal force. Can you think of a situation where an object would NOT have a normal force exerted on it?
3. Which force was NOT exerted in any of the above examples? Can you come up with a situation where an object WOULD have that force exerted on it?

now that we are keeping racetrack of what is happening to objects to cause them to move in unlike ways, it helps to describe a situation with two kinds of diagrams : system diagrams, and free-body diagrams. A system diagram is a quick sketch of the object in question, along with any other interact objects in the same environment, and an indication of the forces acting on them .
A free-body diagram is a cartoon of only the object in interrogate and the forces acting upon it. While this could still be a sketch, the emphasis is on the forces, so they must be drawn accurately. While system diagrams are useful in helping us understand the problem at hand, free-body diagram contain the quantitative information needed to solve the problem .
Let ’ s go back to our earlier examples and draw their system diagrams and free-body diagrams .
a) A shuttlecock, standing inactive on a arm .
The system diagram might look like this :

The free-body diagram, however, would look like this :

“ Hey – that bird looks a batch like a box ! ” In physics, we much represent objects as a box or a encircle in free-body diagrams to keep things simple. We are very only concern in the forces on the bird in this diagram, not what kind of bird is sitting on the outgrowth !
Each of the forces acting on the dame are represented and labelled by arrows starting at the object and moving outward. It would be incorrect to have drawn the keep up :

besides, notice the size of the arrows. In the case of the boo, the normal force of the outgrowth on the bird is precisely the lapp magnitude of the force of graveness on the boo, causing the bird to remain inactive on the ramify. We represent this by drawing the arrows the same length. The longer the arrow ( relative to the early arrows ), the stronger the force .
How did we know the normal force and the gravitational wedge would be the like magnitude ? Think back to the shuttlecock on the ramify — is it moving ? If the gravitational storm was stronger than the normal force, the dame would accelerate down, breaking the branch. If the convention impel was stronger than the gravitational storm, the shuttlecock would accelerate up. Since the bird is at respite, there is no acceleration, thus those two forces must be equal. We will learn more about this belated in the bodily process .
b) A coil stone, gliding forth along an ice surface .
Let ’ s assume the stone is moving to the right. The system diagram might look like this :

The free-body diagram would look like :

c) A play being dragged along the ground by a child pulling on a chain .
again, let us assume the play is being dragged to the right .
system diagram :

Free-body diagram :

d) A person, pushing a car that has run out of gas .
once again, assume the car is moving to the right .
system diagram :

Free-body diagram :

note that though we ’ ra giving the directions of each of the forces, we are not distinguishing between a force that pushes, and a force that pulls. Though the system diagrams for the child ’ south plaything and the stall cable car look very different, the free-body diagram for the toy and the car look very similar. even though one object is being pulled ( tension effect ) and one is being pushed ( lend oneself effect ), how the forces act on the objects is about identical .

## Questions

Try drawing some system diagrams and free-body diagrams of your own. Check your answers when finished .

1. A sign, hanging by a string.

system Diagram

Free-Body Diagram
1. A car, travelling at constant speed down a straight stretch of highway.

system Diagram

Free-Body Diagram
1. A baseball, flying through the air.

system Diagram

Free-Body Diagram

Did you have an applied push on your free-body diagram for the baseball ? That ’ s a common mistake. Once the ball leaves the throwster ’ mho hand, or leaves the bat ( if it is being hit ), there is no longer an practice force out acting on it. In other words, there is nothing continually pushing it ( or pulling it ) advancing as it flies through the breeze. The only forces acting on it are the gravitational impel ( pulling it down ) and air travel resistance ( acting opposite to the ball ’ south guidance of movement, slowing it down ) .

Imagine a box at rest in the center of a room. If you were asked to make that box accelerate, what would you do to it ?

You might think to push it ( apply force ), or attach a string to it and pull it ( tension force ). But before the box began to move, it would have to overcome the coerce of friction .
If you pushed on it a little, the box ’ s free-body diagram might look like this :

even though you are pushing on the box, your use push is not enough to overcome the clash force the box feels in liaison with the ground. In fact, when you fair push a little, the clash push and the applied force out are equal, and perfectly balanced. In this case, so are the normal force and the gravitational force out .
You will need to push hard — apply a larger force — in ordain to overcome the clash effect and get the box to accelerate :

By pushing hard, you have made forces unbalance : the applied military unit is no longer equal to the clash storm. The box feels a greater tug to the mighty, and accelerates in that direction. In general, if you want to make an object accelerate ( change its amphetamine ), you have to apply an unbalance force .
Sir Isaac Newton was one of the inaugural scientists to put this observation into words, and we know it now as  Newton’s First Law of Motion :
An object in motion (or at rest) will remain in motion (or at rest) until acted upon by an unbalanced force.

A car moving at a changeless accelerate ( consistent gesture ) has all forces acting on it balanced. In this sheath, the two backward forces ( air resistance and friction ) perfectly balance the lend oneself push of the wheels on the road in the reverse management.

The consequence you take your foot off the boast pedal, though, there is no longer an apply storm, and the forces become unbalance :

now unbalanced, those forces acting back on the car slow it down, which we besides know as negative acceleration .
Sitting on a professorship, you might find that the forces acting on you are perfectly balanced ( you are not accelerating ) .

But if person gave you a pile of heavy textbooks to hold on to, your free-body diagram might come to look like this :

That unbalanced coerce would cause you to accelerate downward, likely hurting your tailbone as you crashed through the moderate to the floor, because there was not enough up force ( i.e. normal force from the moderate ) to balance the extra mass .

Another name for Newton ’ s First Law of Motion is the Law of Inertia. Inertia is the ability for matter to remain in its existing state of movement or remainder .

What happens to passengers in a car when the car brakes abruptly ? We frequently perceive being “ thrown ” forward, feeling the strive of the seat belt keeping us in place. In reality, we are experiencing inertia : our body ( already in motion, moving forward with the car ) will remain in apparent motion until acted upon by an brainsick coerce. So we are not actually being thrown advancing — we are moving forward as we always have .
When the seat belt out pushes on us, we are feeling an unbalanced effect, causing our forward apparent motion to cease. Check out this video of a crash test dummy to see how the dummy ’ sulfur inactiveness keeps it moving forward even after the car comes to a break .

# Inertia

Think about early times in a cable car when your body seems to move in a unlike management than the car is moving. typically, these motions happen when the car moves on the spur of the moment in a certain direction .
Create a mirror image and commemorate two or three early examples of inertia you have experienced in a car. What is your body trying to do that the car ( or parts of the car, like the seat belt ) is preventing ?

Can you imagine a situation where there are many forces acting on an object, all along the same direction ? For example, five people pushing on a stall cable car to move it, or nine birds and a squirrel sitting on a telephone wire. What about eight children pulling one means on a tug-of-war r-2, and another eight children pulling the opposite way on the lapp r-2 ? Is there a way we can combine forces ?
alternatively of referring to every force stage in a problem, we frequently refer to the overall force acting on an aim, and we call that the net force. The net force is not a force unto itself — it should never show up in a free-body diagram — but preferably a total of all the forces in a certain guidance .
echo that forces are vector quantities, measured in newtons ( it was Sir Isaac Newton ’ second observations and work with forces that inspired scientists to use his name as the unit of force ) .
We can imagine two children fighting over a toy : one child pulls on the plaything with a storm of five newtons in the westward direction ( written : 5 N [ W ] ), while the other pulls on it with a force of 8 N [ E ]. In which direction would the dally accelerate ?
We can tell from the free-body diagram : the arrow to the right ( east ) is larger, so we know that the play will accelerate to the east. But what is the net violence ?

If the net force is the sum of the forces in a given steering, then we can write :

… but remember : we can only add vectors when they are in the lapp focus. We have to change the positive 5 N [ E ] to negative 5 N [ W ] .

So the web military unit on the object is 3 N [ W ], and it will accelerate in the westbound steering .
eminence that the gravitational storm and the normal pull are NOT in the lapp focus as the apply forces in this wonder. In fact, they are vertical to the lend oneself forces. Because of this, we do not take them into consideration — we are entirely refer with the direction of motion .

## Practice

1. A cable car is stuck in the mud ! In an attempt to free it, a person pushes on the back of the cable car with a force out of 27 N [ fore ], while a tow truck pulls on the car with a force of 259 N [ forward ]. The frictional force on the cable car, though, is 281N [ backward ]. Does the car come unblock ? Try this for yourself and then click on the solution below to see if you ’ ve got it .

### Solution

Given:

Required:
The car will need to accelerate in orderliness to come release of the mud. In order to accelerate, we need a positivist net wedge in the advancing steering .

Analysis:

We know that the net power is equal to the kernel of the forces in a given commission, in this lawsuit, horizontally .

### Paraphrase:

The net impel on the car is 5 newtons forth. Because of this, the car will accelerate in a ahead direction, and will likely become free of the mire .

Let’s go back to the two children pulling on the toy. When we calculated the net force, we only considered the applied forces, not the gravitational force or the normal force, as they were perpendicular to the direction of motion in which we were interested.

But what if we calculated the net income vertical impel here ? What would it be ?

recall that the gravitational effect and the normal push were precisely balanced. This is represented in our free-body diagram as arrows of the same distance, pointing inverse to each other .
If we were to calculate the total of these forces, the leave would be a net effect of zero ( they would sum to zero ). A net pull of zero indicates no acceleration in that steering, and that makes sense for the toy — in fact in the vertical steering, the toy is not moving at all .
The exemplar of the car moving at a uniform amphetamine earlier in the action shows the like :

Since the car is not accelerating, the force of air underground and the friction force must add to give the demand antonym of the applied force. The net pull here would be zero, angstrom well .
note that a net income force of nothing does NOT mean that the object is standing silent. A net military unit of zero indicates that the object is not accelerating. The car in this model is still moving, but its speed remains unaltered .

# Careers

Civil Engineering is a branch of engineering that deals with the design, construction and alimony of structures. This can include everything from roads, bridges, and railways, to canals, seaports, and dams, to energy systems and drink in water systems .
Chris, after a successful career in retail, has just finished a three-year Civil Engineering Technology plan as a mature scholar at Algonquin College in Ottawa, Ontario, where depart of his studies centred on the effects of forces on structures. One of his courses, Structural Analysis, emphasized the importance of having to consider the magnitudes and directions of forces :

“ A winder view of forces on the design of any structure is that they must be static. Every building, bridge, or even shed, has to be in chemical equilibrium. In order to verify this, you need to use a free consistency diagram to calculate all the forces affecting a body. If the calculate is imbalanced, then the body is n’t stable. In a structure this could cause break down. By calculating the weight of the structure, adding in the coke and rain load, and then factoring in the wind load, you can determine the load that the foundation must support. If it is able, then you have a stable structure. ”