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Newton's Three Laws of Motion:

1.  An object at rest remains at rest, and an object in motion continues in motion with constant velocity.

2.  The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass. The direction of the acceleration is the direction of the resultant force i.e. Fnet = ma; m = mass of the object, a = acceleration of the object

3.  If  two bodies interact, the magnitude of the force exerted on body 1 by body 2 is equal to the magnitude of the  force exerted on body 2 by body 1, and these two forces are opposite in direction i.e. "action-reaction"; If object A exerts a force on object B, then object B exerts an equal and opposite force, in return, on object A (that's why it hurts when you kick really hard on something rigid --like a wall--with your foot)

Now, forces are vectors, so keep that in mind when resolving problems involving forces. You can often separate the force into components (horizontal and vertical) and add or subtract them as vectors.

Concurrent Forces

When resolving forces, the most common method is vector addition and subtraction. You resolve the vector into its horizontal and vertical components and then find the net horizontal and vertical components of the force. Then combine them into the one force again by using the Pythagorean theorem.

Concurrent forces are forces that have a constructive influence on another force, meaning that when you add the components of the two forces, the net force is greater than either of the initial forces.

Weight

Weight describes the pull of gravity on mass. In fact, it is the mass of the object times the acceleration due to the gravity acting on it. Weight, thus, is the gravitational force exerted on an object.

 Fweight = mg

(just another form of F = ma)

Example: A 100 kg man slides down a rope at constant speed. (a) What minimum strength must the rope have in order to support the man? (b) If this minimum strength is the actual strength of the rope, will it support him if he tries to climb back up?

Solution:

If he is sliding down at constant speed, the rope is not breaking but he is pulling at it with the force of his weight. Therefore it supports Fw of the man.

If he is climbing back up he will have to exert an extra force to pull himself up (man's force + force due to his weight) and the rope will break.

Normal Force

Normal force is a form of the "action reaction" principle. Take the example with the book resting on the table. Gravity is pulling the book downwards with a force equal to its weight. Well...so why doesn't the book fall? No duh, there's a table supporting it. But you've got to think about it like this: the table, in response to the downward force of the books weight, has to push back up with an equal and opposite force. And this reaction force is called the normal force (pointing perpendicular from the surface on which the book is resting)

 Fnormal = -mg = N

Example: Resolving Forces

A book of weight 10N is sitting on a table. My assistant places a toolbox of 60N on top of it. What is the net force on the book?

Common sense will do in solving it. You don't see the book falling through the table nor do you see the book shooting up into the air as a result of these weight forces on it. In fact, it is not moving; it has no acceleration, thus the net force is 0 (because a = 0).

Solution:

Weight is pulling the book down with a force of 10 N. The toolbox placed on top of it exerts a downward force (weight) of 60 N, but the book resists and pushes back up with 60 N.

Frictional Force

Sometimes when you push things you feel some kind of resistance. Maybe because the tabletop or floor isn't smooth, a frictional force is created when the object has been given a tendency of motion.

Friction, the resistance to the tendency of motion, therefore acts in the opposite direction in order to hinder the motion.

Two Kinds of Frictional Forces: Static and Kinetic

When an object has a force applied to it and was not given enough force to overcome the resistance (friction) then it does not move (i.e. it remains static). The friction is present even if the object has not moved, simply because there is a force applied to it.

However, given the correct amount of force, the friction will be overcome and then the object will move. Friction is present because it is moving, and since it is moving, the friction is called kinetic friction (kinetic meaning energy from motion).

There is a difference between kinetic and static friction, besides the fact they they are present only at different stages of pushing. Static friction increases to match the force applied to push the object up until a certain point. where the maximum static friction is reached, and then the object starts to move. Even though there is still friction present, the applied force can overcome kinetic friction easier than it can static friction.

A graph of friction:

As you can see, the maximum static friction is greater than kinetic friction, and static friction increases as more force is applied then drops to a constant kinetic friction as the object settles into motion.

 General form of the Friction equation ffriction = µN Static Friction fstatic = µsN Kinetic Friction fkinetic = µfN

What is µ? It is the coefficient of friction (µs for the coefficient of static friction in static friction situations and µf for the coefficient of kinetic friction in kinetic friction situations)

What is N? N is the normal force.

Apparent Weight

Sometimes scale readings can be distorted if it is put in an accelerating frame of reference. Simply put, the actual weight of a object is its gravitational force. The object's apparent weight is the force the body exerts on whatever it is resting on. The most common example of this is the person who is standing in the elevator

Tension

This is the force exerted on string, rope, wire, etc. due to an external force (pull). And like the normal force, acts in the direction opposite to the force being exerted on it.

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Key Themes
• Newton's 3 Laws of Motion
• Concurrent Forces
• Weight
• Normal Force
• Frictional Force
• Apparent Weight
• Tension
• Practice Questions

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