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**Goal: To learn about Forces**

Objectives: To explore the basics of force and Newton’s first law To learn about weight and compare to mass To learn about the Normal force To learn about frictional force To learn about Tension To learn about force vectors and net force

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Newton’s First Law An object in rest or in motion will stay in rest or in motion until acted upon by an outside force This is called the law of inertia In other words, to change an objects motion (and you can consider at rest a “motion”) you have to do something to it

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**Force There are many different forces in the universe. The main 4 are:**

A) Gravity B) Electromagnetic C) Strong D) Weak

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**Force is a VECTOR Force is a vector Force has DIRECTION!**

Force ALWAYS has direction So, the units of force are Newton direction Newton is N So, a force could be +3 N up, +2 N down, N forward, N north, ect

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**Something we will look at in this class:**

Gravity near the surface of the Earth. Near the surface of the Earth the force of gravity is fairly straightforward Gravity force = mg If there are no other vertical forces (other than a Normal force) then the gravity force is the Weight Note that Weight is a FORCE

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**Questions 1) What is the unit(s) of Weight?**

2) g = 9.8 m/s2 does it have a direction?

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Weight vs Mass On the Earth I have a mass of about 90 kg and a weight of about 205 lbs (880 Newtons). On the moon gravity is 1/6th what it is on the earth. What is my mass and weight on the moon?

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Normal Force Anytime you contact something there is a Normal Force (Newton’s 3rd law, equal and opposite force) The normal force is the force that pushes you away from a surface and is perpendicular to the plane of that surface. What would happen if you stood on a surface that had no normal force?

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**How to find the normal force**

Find the sum of all the non normal forces. If the object is not moving in the vertical direction (that means there is no total force – which we call a net force) then the normal force is the force needed to cancel out all the other forces. So, if there is just gravity, then the normal force is equal to the weight. If I pull up on something then the normal is less because the total downward force (and up force is effectively a negative down) is less. If I push down then the normal force increases.

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**Friction One force you are probably familiar with is friction.**

Friction is always a force that opposes motion – that is the direction is opposite the direction of motion. There are actually two type of frictional forces. The first is called Static Friction

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Static Friction Static Friction is caused because on a microscopic level nothing is perfectly smooth. The bumps and pits of the two objects touching makes things rub and rip off small pieces. This takes energy to do which causes the static friction.

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Kinetic Friction Once an object starts to slide across another object it now glides over the top of the bumps and pits. As a result the force of friction is cut in half. A tire is stationary on the ground normally. If a tire slides you loose friction and you loose control.

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**Friction Equation F = μ N**

I am 90 kg. I walk down a sidewalk which has a frictional coefficient of 0.2 A) Find my normal force B) What is the frictional force on me C) What force do my legs need to exert to keep myself walking at a constant velocity and how do you use Newton’s First Law to determine this?

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**Tension Forces provided by strings or wires are called Tensions.**

The Tension in a wire is similar to the normal force except that it pulls an object towards it instead of pushing away. To find tension either: A) compare the total force to all the forces exerted on the string. The difference will be the tension of the string. B) find the force the string is exerting on something else

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Tension example A 10 kg mass is tied to the end of a string and allowed to hang. A person pulls down on the string with a force of 150 N. A) What is the tension of the string if the mass does not move (Hint, Newton’s first law)?

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Force Vectors In reality forces will often times have components in more than 1 dimension. This creates a vector. In order to solve for problems where you have forces in more than 1 dimension you need to create 2 accounts, that is 2 problems that are separate from one another. This is similar to having a checking account and a savings account.

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Calculator note Everyone use their calculators to find the answer to the following problem (even if you can do this one in your head): (2 * 6) / (3 * 4)

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Vector Break down Since the 2 components will be 90 degrees from each other you can use the following to find each component. Lets call the total force Ft The opposite leg in our right triangle has a length of: Ft sin(theta) where theta is the angle Adjacent is: Ft cos(theta) Finally tan(theta) = Opposite / Adjacent

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**One way to remember which is which**

Sin(0 degrees) = 0 So, ask yourself would this value be 0 if the angle is 0? If the answer is yes then use sine Cos(0 degrees) = 1 Ask yourself, if the angle was 0 would the total force be just this force? If the answer is yes then use the cosine.

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Adding Force vectors Once you break a force into its components (for this class we will often use x and y) now you are ready to add them. The x’s add to the x’s because the x direction is a UNIT! Same for the y’s because the y’s are a UNIT If you need a magnitude at the end, which you may for the homework then once you have the total x and total y you can use the Pythagorean Theorem. However, as we get further along we will treat the x and y as separate problems and may have to solve for 1 to get the other.

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Net Force Once you add up all the vectors for all the forces you have what is called the Net Force The Net Force will determine how the objects motion is changed Note that the Net Force is a vector. It can have x and y components – and if any are non-zero, then its motion in that direction will change. Meanwhile in any direction that the net force is exactly zero the motion in that direction will be constant (even if the motion is zero).

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**Net Force Net Force = sum of all forces**

Net Force = mass * net acceleration For example, if you have vertical forces, and need to solve the net force, find the net force from mass * net acceleration Then, plug that answer into Net Force = sum of all forces so that you can solve for the Normal force

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Your turn! The 3 Stooges decide to open a moving company and someone is crazy enough to hire them. The 3 are moving a rather large box by pushing it across the floor. Luckily the floor is slippery due to all the banana peals that…. Well that is another show. Anyhow, no friction Larry pushes on the box from behind. He pushes at an angle 30 degrees below the vertical with a force of 200 N. Curly (who has a mass of 70 kg) sits on the box. Not much help there… Mo pulls on the box at a 45 degree angle with a force of 350 N. The box has a mass of 50 kg. A) What is the net force on the box in the vertical direction (call this the y direction)? Hint, will the box lift off the ground? B) What is the normal force on the box (and no it is not = mg)? C) What is the net force on the box?

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**Conclusion We have learned about force.**

We have learned how to compute gravitational force We have learned how to find a normal force. We have learned how to use that normal force to find the frictional force We have learned how to find tension We have learned how to turn Forces into vectors and add those vectors to create a net force.

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