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Forces and Motion Observations: 1. A force is not necessary for Two natural states of motion: 2. A force is necessary for

Definitions: 1) 2) 3)

a) Which object has more of a tendency to remain at rest? b) Which object has more of a resistance to changing its state? c) Which object has more inertia? d) Which object has more mass?

A B

3. Why do you feel thrown backwards when a car starts up quickly from rest? Are you really thrown backward? What is actually going on?

4. Why do you feel thrown forward when a speeding car stops abruptly? Are you really

thrown forward? What is actually going on?

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Above is the title page of Isaac Newton’s greatest work and one of the most influential books in all of science.

Isaac Newton

1. What is the title in English? 2. By what title is it commonly known? 3. When was it published? 4. What did it contain?

a) b)

Newton’s First Law of Motion (Law of Inertia)

An object at rest remains at rest and an object in motion remains in motion at a constant speed in a straight line (constant velocity) unless acted on by unbalanced forces.

Newton’s Three Laws of Motion (original version translated from Latin) “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.” “The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.” “To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Newton’s Second Law of Motion (Force Law)

When unbalanced forces act on an object, the object will accelerate in the direction of the resultant force. The acceleration is directly proportional to the resultant force

and inversely proportional to the mass of the object.

Newton’s Third Law of Motion (Action-Reaction Law)

When two objects (A and B) interact, the force that A exerts on B is equal and opposite to the force that B exerts on A.

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On the chart above, rank the fundamental forces from strongest to weakest.

Identifying Forces: Free-Body Diagrams

1.

What is a “free-body diagram?”

3. 2.

Fg: FA:

FN: Ff:

4. What is the cause of the normal force? 5. What is the cause of the frictional force?

4.

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Types of Forces

Holds nucleus together

Balanced and Unbalanced Forces

1. What will happen to the cart? Why? 2. What will change if a heavier weight is used? 3. What will change if a heavier cart is used?

A weight is hung over a pulley by a string that is attached to a cart. The weight is dropped.

A second weight is now hung over a pulley by a string pulling on the cart in the opposite direction.

4. What will happen to the cart if weight #1 is heavier than weight #2? 5. What will happen to the cart if weight #2 is heavier than weight #1? 6. What will happen to the cart if both weights are the same?

Net force (Fnet):

In each case below, determine the net force acting on the cart (magnitude and direction).

10 N 6 N 7.

5 N 16 N 8.

8 N 8 N 9.

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Balanced Forces If all the forces acting on an object are balanced,

Unbalanced Forces If all the forces acting on an object are not balanced,

Conclusions:

1) 2)

3)

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Newton’s Second Law of Motion:

Variable: Fnet m a

Quantity:

Units:

Type:

Write the unit for force in terms of fundamental units:

1) A net force of 100. N acts west on a 5.0 kg mass. Determine the magnitude and direction of the acceleration of the mass.

2) A 1.6 -kg box is accelerated at 2.0 m/s2. Determine the magnitude of the net force.

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3) An 80. kg student is pulled on roller blades by a friend who exerts a force of 20.0 N. Friction between the wheels and the ground exert a force of 5.0 N. What is the student’s acceleration?

4) A 1000. kg car accelerates from rest to 20. m/s in 5.0 seconds. What net force acts on the car?

5) A 15.0 kg crate is dragged across the floor with an acceleration of 0.80 m/s2 by an applied force of 22 N.

How much friction is acting on the crate?

Mass and Weight

Mass:

Property:

Weight:

Property:

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Relationship between mass and weight:

Estimation Skills - some common masses and weights: Penny = 3 grams (0.003 kg) 1 kilogram mass = 2.2 pounds 1 apple = 1 newton

1. What is the weight of a 1.0 kilogram mass: a) here on Earth? b) In deep space?

Variable: Fg g

Quantity:

Units:

Type:

2. What is the mass of a 1.0 N apple: a) here on Earth? b) In deep space?

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3. What is your mass in the MKS (metric) system of measurement? 4. Complete the chart below for your mass and weight (using the metric system) in various places.

Earth Moon (g = 1.6 m/s2) Deep Space

Mass

Weight

5. A 5.0 kg bowling ball is hanging from a rope.

a) Calculate the tension in the rope when the bowling ball is at rest.

b) What is the tension in the rope when the bowling ball is moving upwards at a constant speed?

c) Calculate the tension in the rope when the bowling ball is accelerating upwards at 0.50 m/s2.

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6. When does the scale read the normal weight of the person? 7. When does the scale read higher than the normal weight of the person? 8. When does the scale read less than the normal weight of the person? 9. What does a scale reading actually measure?

10. Determine the acceleration of the elevator in cases (b) and (c). 11. The elevator descends, accelerating at -2.7 m/s2. What does the scale read? 12. Suppose the cable snapped and the elevator fell freely. What would the scale read?

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Friction

Cause of friction:

a) no movement

d) while moving c) movement begins

b) no movement

Applied force (N)

Fric

tion

forc

e (N

)

Static Friction (Ffs) 1) 2) 3)

Kinetic Friction (Ffk) (dynamic friction, sliding friction) 1) 2) 3)

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Variable: Ff µ FN

Quantity:

Units:

Type:

1. What does the coefficient of friction measure?

Relationships:

2. Why are there two types of coefficients of friction? Compare them. 3. What materials on top of one another are the:

a) easiest to start moving?

b) hardest to start moving? c) easiest to slide over one another?

d) hardest to keep moving?

4. What coefficient of friction applies while dragging a wooden crate across a hardwood floor? 5. What coefficient of friction applies when a car skids across a dry asphalt roadway?

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6. A 4.0 kg block is being dragged across the floor by a student who finds that he must exert a force of 14.0 newtons to keep the block moving at a constant velocity.

a) Draw and label a free-body diagram for this situation.

i) Weight

iii) Force of friction

iv) Coefficient of friction

ii) Normal force

d) If that brick is replaced with one that has a mass of 8.0 kg, which of the following will change? If so, how much?

c) Calculate the coefficient of friction (µ) for the block and the floor in this case.

b) Determine each force acting on the block.

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7. A 45 newton sled rests on a frozen pond. A child pulls the sled with a horizontal force of 15.0 newtons and causes it to accelerate at a rate of 1.50 m/s2.

8. A driver slams on the brakes and her 2.0 x 103 kg car skids to a stop on a dry asphalt highway.

a) What is the force of friction stopping the car?

b) What is the acceleration of the car while it is stopping?

a) Determine the force of friction.

b) Determine the coefficient of friction.

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The Inclined Plane

Draw a free-body diagram for this box at rest on an inclined plane. Resolving Fg into components that are parallel and

perpendicular to the surface of the inclined plane:

Fg║ =

If the box is in equilibrium, then . . .

Fg┴ =

1. Draw and calculate the magnitude of all the forces acting on this box sliding down a hill at a constant speed of 12 m/s.

2. Calculate the force of tension in the rope holding this 50. N box held at rest on a frictionless hill.

300

3. Calculate the tension in the rope holding this 50. N box held at rest on a hill if there is a 10. N force of friction.

300

Tension Assumptions

a. b. c.

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200

4.5 kg

6. Calculate the force of friction acting on the box if it now accelerates down the incline at a rate of 0.67 m/s2.

5. Calculate how fast this box will accelerate down the hill if the hill is frictionless.

200

4.5 kg

7. As the angle θ increases, what happens to the . . . weight? normal force? force of friction? coefficient of friction?

300

4. a. Calculate the tension in the rope when this 50. N box is being dragged up the hill at a constant speed of 5.0 m/s if there is a 10. N frictional force acting on it.

b. what is the coefficient of kinetic friction between these surfaces?

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Newton’s Third Law

Newton's Third Law of Motion:

If a heavier student pushes a lighter student, who exerts more force? Explain.

Action-Reaction pairs:

Give some examples of “action-reaction pairs” of forces: 1) The force exerted

by _______________________________ on ______________________________ is equal and opposite to the force exerted by ______________________________ on ______________________________.

Newton’s Second Law deals with . . . Newton’s Third Law deals with . . ..

2) The force exerted

by _______________________________ on ______________________________ is equal and opposite to the force exerted by ______________________________ on ______________________________.

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Net force on ball: Action-Reaction pairs:

Fg

Net force on block: Action-Reaction pairs:

Equilibrium

What are some properties of an object in equilibrium?

Sketch a free-body diagram for this box at rest on a hill.

Then, find the resultant of the vectors you drew.

Based on your drawings above, what is another property of an object in equilibrium?

Is the system below in equilibrium?

Now, draw a single vector that will put the system into equilibrium.

Draw the resultant.

Equilibrant:

What is the relationship between the resultant and the equilibrant?

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October 11, 2014

4.00 kg

4.00 kg

October 11, 2014

4.00 kg

4.00 kg

Two body problems

1. Two buckets are hanging motionless from ropes as shown.. What is the tension in the top rope? The middle rope? What would change, if anything, if they moved upwards at a constant speed?

2. The two buckets are now accelerated upwards at a rate of 5 m/s2. What is the tension in each rope?

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3. Determine the tension in the string and the acceleration of each of the two objects connected by a light string over a light, frictionless pulley, as shown in each diagram.

a)

b)

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8 kg 8 kg 24 N

4 kg 12 kg 24 N

24 N 4 kg 8 kg

24 N

1 kg 2 kg 3 kg

a)

d) ++++++++++++++++++++++

c)

b)

4. In each case below, two boxes connected by ropes are pulled across a frictionless floor by a horizontal force of 24 newtons. Find the tension in each inner rope and the acceleration of each box.

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5. Find the acceleration of these two objects and the tension in the string as the block slides across a frictionless table.

6. Determine the acceleration of each system.

b) a)

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7. Find the acceleration of each object and the tension in each rope.

a)

b)

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Skydiving

1. What are some factors that affect the amount of air resistance a falling object experiences?

2. Compare the force of gravity to the force of air resistance for this 100. kg skydiver as well as his acceleration.

5. What is the force of air resistance acting on a 60 kg skydiver at terminal velocity?

4. What happens when the force of air resistance equals the force of gravity? Terminal velocity:

6. Which experiences a greater force of air resistance: an elephant or a feather? Explain.

velo

city

time

acce

lera

tion

time

3. Sketch how the magnitude of the skydiver’s velocity and acceleration vary with time as he falls.