Unit 2 Summary

• In this unit, I learned about Newton's First and Third of Motion and applied them to a multitude of scenarios.  We also learned about how forces act upon objects and the Balanced Force Model.

Newton’s First Law: The first law says that an object at rest tends to stay at rest, and an object in motion tends to stay in motion, with the same direction and speed.

Newton’s Third Law: The third law says that for every action there is an equal and opposite reaction. In addition, forces are found in pairs.

Fg = 10N/kg (mass)

How do seat belts keep you safe?

Newton’s First Law of Motion says that unless an outside force acts on an object, the object will continue to move at its present speed and direction. Unless the objects inside the car are restrained they will continue moving at whatever speed the car is traveling even if the car is stopped by a crash. If the passenger is restrained by a seat-belt, their momentum is reduced more gradually by the constant and smaller force of the belt acting over a longer period of time.

Newton's First Law Applied: 

The soccer ball will remain at rest unless acted upon by an external force. The foot applies a push force to the ball and the ball will continue with constant speed and direction unless acted upon by an unbalanced force. 

To examine the forces that are being acted upon an object, we use a free-body diagram. A free-body diagram is a sketch of the object that shows all of the forces acting on the object shown.    

In this free-body diagram, we are examining the forces acting upon a football that has has been kicked into the air. The football was at rest until an unbalanced force acted upon it (the foot). As the football travels at a constant speed in the air, a normal force and a gravitational force act upon the football. The football will continue to travel at a constant speed until an unbalanced force acts upon it. 

What exactly are balanced and unbalanced forces?

• Forces occur in pairs and can be either balanced or unbalanced. Balanced forces do not cause a change in motion. They are equal in size and opposite in direction.
• Unlike balanced forces, unbalanced forces always cause a change in motion. They are not equal and opposite.

Newton's Third Law Applied: 

If someone pushes horizontally against a wall with a force of 100 N, then the wall will push horizontally against the person with a force of 100 N. 

To examine the forces that are being acted upon an object, we use a free-body diagram. 

In this free-body diagram, we are examining the forces acting upon the ball and the wall. The ball's push against the wall is equal to the wall's push force on the ball. There will always be a reaction-action pair. The ball pushes forward on the wall; the wall pushes back on the ball with an equal force. We know this because of Newton's Third Law: for every action, there is an equal and opposite reaction. 

In this example, two forces act upon the motionless cat: normal force and gravitational force. The floor provides the normal force and the earth's gravity provides the gravitational force. These forces are balanced, so the cat remains at rest.

What about objects suspended by the ceiling? 

In this example, two forces act upon this chandelier suspended by the ceiling: tension force and gravitational force. The chain attached to the ceiling provides the tension force and the earth's gravity provides the gravitational force. These forces are balanced, so the chandelier remains at rest. 

What are force diagrams?

• A force diagram is simply a diagram showing all the forces acting on an object, the force's direction and its magnitude.

Some examples: 

In each example there is a net force acting upon the object. The net force is the vector sum of all the forces that act upon an object. That is to say, the net force is the sum of all the forces, taking into account the fact that a force is a vector and two forces of equal magnitude and opposite direction will cancel each other out.    

In the examples above, the net force is determined by summing the individual force vectors that are acting upon the objects.    

INCLINED PLANES:

A box can be moved up an inclined plane with constant velocity by a push force of magnitude F1 or down the inclined plane with constant velocity by a force of magnitude F2. When creating a Force Diagram representing the forces acting upon the box, the axes should be aligned parallel and perpendicular to the hill. Rotate the coordinate axis and it will make analyzing much easier.

The box in both cases is affected by these forces:

F⃗ G - the weight of the box

F⃗ 1(F⃗ 2)- force pushing the box

N⃗  - force by which the inclined plane affects the box (the normal force)

F⃗ t - Friction force

What is the coefficient of kinetic friction?

μk: Symbol

μk   = F_k / N  (F_{k = Force of kinetic friction), (N =} Normal force or the force perpendicular to the contacting surfaces)

The motion equation for the box that moves up the hill:

F⃗ G+N⃗ +F⃗ 1+F  = 0⃗ t

The motion equation for the box that moves down the hill:

F⃗ G+N⃗ +F⃗ 2+F⃗ t=0

Force Diagrams and Component Forces: Using SOHCAHTOA

SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent.

sinθ = opp/adj, cosθ = adj/hyp, tanθ = opp/adj

Vector: A quantity possessing both magnitude and direction, represented by an arrow the direction of which indicates the direction of the quantity and the length of which is proportional to the magnitude.

In this example, need to calculate the tension in the cable that is supporting this object. The equation for the forces in the Horizontal (x) Direction: FTBx + FTAx = 0 N and the equation for the forces in the Vertical (y) Direction: Fg + FTBy + FTAy = 0 N. We know the weight of the object is equal to 25 N and that the cables make a 30 degree angle with the object. FTy = 12.5 N so we would use Sin(30°) = 12.5/FT1. We would calculate this and FT2 should equal 25 N.  The object exerts 25 N on the cable and the cable exerts 25 N on the object, representing a reaction-action pair! So the forces acting upon this object are equal, therefore the object will remain at rest unless an unbalanced force acts upon it. 

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