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Ch. 12 - Forces & Motion

Force --> a push or a pull that acts on an object

Forces can:1. Cause a resting object to move2. Accelerate a moving object (by changing speed or direction)

Force is measured in Newtons (N), which is the force that causes a 1 kg mass to accelerate at a rate of 1 m/s/s

1 N = 1 kg.m/s2

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Vectors can be used to represent force with the size of the arrow equaling magnitude and the direction of the arrow showing direction.

Forces can be added and subtracted with the net force being the overall force acting on an object.

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Balanced forces --> net force is zero and there is no change in the object‛s motion

EX: arm wrestlers of equal strength

Unbalanced forces --> results in acceleration of the object

EX: losers of a tug-a-war

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Friction --> a force that opposes the motion of objects that touch as they move past each other; without friction, all surfaces would be more slippery than ice!

Note that objects “in contact” with each other can mean objects that are directly touching as well as objects moving through a liquid or gas.

4 types of friction:

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1. Static friction --> friction force that acts on objects that are not moving; acts in the direction opposite to that of the applied force.

ex: when you walk, static friction between the ground and your shoe keeps your shoe from sliding

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2. Sliding friction --> the force that opposes the direction of motion of an object as it slides over a surface; is less than static friction so less force is needed to keep an object moving than to start it moving.

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3. Rolling friction --> acts on rolling objects; is about 100-1000 times less than static or sliding friction for given materials which is why we put things on wheels to move them!

EX: ball-bearings (a set of round balls located between 2 smooth surfaces) are used in cars, skates, skateboards and bikes to replace sliding friction with rolling friction.

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4. Fluid friction --> opposes the motion of an object through a fluid (gas or liquid); it increases as the speed of the object moving through the fluid increases

Air resistance = fluid friction acting on an object as it moves through air

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Gravity --> an attractive force that acts between any two masses; doesn‛t require that the objects are touching for it to act.

Ex: earth‛s gravity acts downward towardthe center of the earth (but an upwardforce usually exists to keep things fromending up in the center of the earth!)

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Falling objects --> 2 forces usually act on falling objects: gravity causes them to accelerate downward and air resistance acts in the direction opposite to the motion and reduces acceleration

The faster an object falls, the greaterthe air resistance.

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Terminal velocity --> constant velocity of a falling object when the force of air resistance equals the force of gravity

Read “Terminal Speed” on pp. 370-371.

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Watch the video “Air Forces” and answer the following questions:

1. What is the net force on the skydiver just before stepping out of the plane? Explain your answer.

2. How do the force of gravity and air resistance compare as the skydiver is falling and gaining speed? Explain your answer.

3. How does the force of air resistance change as the skydiver gains speed while falling?

4. What happens to the skydiver‛s speed when the force of air resistance becomes equal to the force of gravity? Explain your answer.

5. How does the force of air resistance change when the skydiver‛s parachute opens?

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Projective motion --> the motion of a falling object (projectile) after it is given an initial forward velocity; air resistance and gravity are the only forces acting on a projectile; the path of a projectile will always be curved.

Which will hit the ground first - a bullet dropped and or a bullet shot out of a gun?

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Sect. 12.2 - Newton‛s Laws

Aristotle ( 300 B.C.), Galileo (100 A.D.) and Isaac Newton (late 1600‛s) were leading scientists studying forces and motion.

Newton‛s 1st Law of Motion (also called the “Law of Inertia”) --> An object‛s motion does not change as long as the net force acting on the object is zero.

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“An object at rest stays at rest; an object in motion stays in motion, unless a force acts upon them.”

Inertia = the tendency of an object to resist a change in its motion

Its the reason for seatbelts & airbags!

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Newton‛s 2nd Law of Motion --> the acceleration of an object is equal to the net force on it divided by the object‛s mass.

Acceleration = Net force/Mass

A = F/m

Rearranging to get rid of the denominator:

F = ma

Correct units for this formula:

Force = Newtons (N) Mass = kilograms (kg) Acceleration = meters/second/second (m/s2)

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Weight vs. Mass

Mass --> a measure of the inertia of an object; depends on the amount of matter in the object

Weight --> force of gravity acting on an object; is the product of the object‛s mass (m) & acceleration due to gravity (g) which is 9.8 m/s2

Weight = mass x gravity acceleration

W = m.g

(compare this to Newton‛s 2nd law --> w = f, g = a)

Units should be: W = Newton‛sg = m/s2

m = kg

If an astronaut has a mass of 112 kg, what is his weight on earth where the acceleration due to gravity is 9.8 m/s2?

m = 112 kg w = m.ga = 9.8 m/s2

w = ??? w = (112 kg)(9.8 m/s2)w = 1100 kg.m/s2

= 1100 N

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Sect. 12.3 - Newton‛s 3rd Law

Newton‛s 3rd Law --> When one object exerts a force (action force) on a second object, the second object exerts an equal and opposite force (reaction force) on the first object.

These action-reaction forces may or may not produce motion.

ex: Pushing against a wall --> action force is your pushing against the wall, the reaction force is the wall exerting a force back, but the result is no movement.

ex: Swimming --> action force is your pushing against the water, the reaction force is the water exerting an equal but opposite force on the swimmer, the result is forward movement.

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Only when equal and opposite forces act on the same object do they result in a net force of zero.

In the case of the swimmer, the action force was on the water while the reaction force acted on the swimmer - which is why movement resulted!

Momentum = product of an object‛s mass and its velocity.

The greater an object‛s momentum, theharder it is to stop.

Momentum for objects at rest is always zero.

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Momentum = mass x velocity p = m.v

Units: p = kg.m/sm = kgv = m/s

Law of Conservation of Momentum --> the loss of momentum of one object equals the gain in momentum of another object - momentum is conserved.

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Sect. 12.4 - Universal Forces

The 4 universal forces are:1. Electromagnetic force2. Strong nuclear force3. Weak nuclear force4. Gravitational forces

All of these forces can act between particles whether the particles are in contact or not but all are affected by the particle distance.

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1. Electromagnetic forces --> associated with charged particles; are the only forces that can both attract and repel

A. Electric forces --> act between charged particles (electrons & protons); like charges repel each other, opposite charges attract each other; static cling is a result of materials that lose electrons easily (cotton) & material that gains electrons easily (polyester)

B. Magnetic forces --> Exist on certain metals, on poles of magnets & on moving charges - due to electron spin and movement; like poles repel, opposite poles attract

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2. Strong nuclear forces --> force acting within the nucleus to hold the similarly charged protons and neutrally charged neutrons together; is 100 times stronger than the electric force of repulsion that acts among these protons but only acts over a very short distance (about the diameter of a proton)

3. Weak nuclear forces --> an attractive force acting over an even shorter range than the strong nuclear force; believed to be involved in some beta decay radioactivity & allows subatomic particles to transform into energy

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4. Gravitational Force --> weakest universal force but is the most effective force over long distances; is an attractive force that acts between any 2 masses; keeps everything in orbit

Newton‛s Law of Universal Gravitation = every object in the universe attracts every other object (you don‛t usually notice it because the attraction is so small compared to the earth‛s gravitational force)

This gravitational force between 2 objects is proportional to their masses and decreases rapidly as the distance between the masses increases.

Gravitational force = m1.m2/d2

m1 = mass of 1st objectm2 = mass of 2nd objectd = distance between the objects

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Gravitational force is responsible for orbits.The moon circles the earth because of its inertia (Newton‛s 1st law) and the earth‛s gravitational pull.

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Earth‛s gravitational force is a type of centripetal force - a center directed force that continuously changes the direction of an object to make it move in a

circle.

The traditional force of the moon is what produces the tides (1 bulge being on the side facing the moon and the other being on the side opposite the moon).

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Satellites also stay in orbit because of inertia and earth‛s gravitational pull. If the satellite gets too close to earth‛s atmosphere, it will lose speed due to

friction with the upper atmosphere and be pulled into the thicker lower atmosphere where it will burn up due excessive heat due to friction with the air.

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1. A net force of 25 N is applied to a 10.0 kilogram mass. What is the accelerationgiven to the mass?

2. A 16 N. force is applied to a 2.00 kilogram mass. What is the acceleration of the mass?

3. An athlete exerts a force of 150.00 N. on a shot­put giving it an acceleration of 20.00 m/s/s. What is the mass of the shotput?

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4. A 1.5 kilogram mass accelerates across a smooth table at 15 m/s/s. What netforce is applied to it?

5. What acceleration does a net force of 20.0 N impart to a mass of:a. 5.0 kg b. 10.0 kg c. 20.0 kg d. 40.0 kg e. 100.0 kg

6. Determine the acceleration that a force of 25 N gives to a 4.0 kg mass. Thefrictional force to be overcome is 5.0 N.

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7. Determine the weights of these masses:a. 14 kg b. 0.43 kg c. 0.7 kg

8. An economy car has a mass of 800 kg. What is the weight of the car?

9. A small yacht weighs 14,700 N. What is the mass of the yacht in kilograms?

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10. A rubber ball weighs 4.9 N. What is its mass?

11. At what rate would be the ball in problem #10 be accelerated if it were thrown straight up with a force of 69 N ?

12. A force of 90.00 N is exerted straight up on a stone that weighs 7.35 N. Calculate:

a. the mass of the stone.

b. the net force acting on the stone.

c. the acceleration of the stone.