Dynamics Unit- Contact Forces Sub-Unit Physics

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2.1.1 Newton’s Laws

Newton’s First Law An object at rest remains at rest and an object in motion will continue in motion with

constant velocity (that is, constant speed in a straight line) unless it experiences a net external force.

• Also known as the Law of _______________________

• _______________________ : tendency of an object to maintain its current state

of motion.

o more inertia = ____________________________

o more inertia = harder to _______________________________

Force

• A force is a _______________________________________ that may change an object’s state of motion.

o Contact force – requires touching

▪ ________________________________________________

o Field force – no contact required (“Action over a distance”)

▪ ________________________________________________

A block of wood is placed on a table and is motionless. What forces are acting on it?

Net Force

• No NET FORCE on an object = ___________________________... either

o _______________________________________________________

o _______________________________________________________ • A “NET” or “UNBALANCED” force changes an object’s ____________________

o This means _______________________________________ change

o Also called _________________________________ • How much acceleration a net force causes an object to have depends on...

o amount of FORCE ▪ greater force = ____________________________________

o amount of MASS

▪ greater mass = ____________________________________

Newton’s Second Law The acceleration of an object is directly proportional to the net external force acting on the

object and inversely proportional to the mass of the object.

Example • A 2.0 kilogram box is pushed with a net force of 10 newtons. What is the

acceleration experienced by the box?

Equation Unit of force is the

_______________________

a reaction force that any object exerts when it is

pushed on.

____________________ a force pulling any object

toward…

Weight

• The force with which gravity pulls on an object.

Example • What is the weight of an object with a mass of 30 kilograms?

Newton’s Third Law For every action there is an equal and opposite reaction.

Examples

• A firefighter directs a stream of water from a hose to the east. In what direction is the force on the hose?

• A man getting out of a rowboat jumps north onto a dock. What happens to the boat?

• A 60 kilogram astronaut pushes against a 120 kilogram satellite with a force of 15 newtons. How much force does the satellite exert on the astronaut?

PRACTICE

1) An object is pushed with an unbalanced force of 8.0 newtons and accelerates at a rate of 2.0 meters per second2. What is the mass of this object?

2) What is the mass of an object with a weight of 500 newtons?

3) A net force, F causes mass M to accelerate at a rate of 2.0 meter per second2. What acceleration would force F cause on an object with a mass of 2M?

4) An object with a weight of 30 newtons is placed on a flat, level surface. What is the normal force with which the surface pushes back on the object?

Equation

Dynamics Unit- Contact Forces Sub-Unit Physics

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2.1.1c – Explain the relationship between mass and weight.

- What is the weight of a 5.0 kilogram object when it is near the surface of the Earth?

[49.05 N]

- The acceleration due to gravity on Planet X is 6.0 N/kg. What is the weight of a

4.0 kilogram object on Planet X?

[24 N]

- A 2.5 kilogram object is transported from Earth to the Moon. When the object

arrives on the Moon its weight is _________________ compared to that on Earth while its mass is _________________ compared to that on Earth.

[less, the same]

- Sketch a graph to show the relationship between mass and weight on the axes below. What does the slope of this graph represent?

[accel due to gravity]

2.1.1d – Explain the relationship between action/reaction pairs.

- A boy pushes a cart across the floor with a force of 10 newtons. The box pushes on the boy with a force of…

[10 N]

- What is the normal force acting on a 2.0 kilogram object that is placed on a flat,

level table?

[19.62 N]

weight

mass

Review Questions

2.1.1a – Explain the relationship between mass and inertia.

- Which of the following has the greatest inertia?

(a) 10 kg object (c) 20 kg object (b) 15 kg object (d) 25 kg object

[d]

- Which of the following has the greatest inertia?

(a) a 3 kg object moving at 2 m/s (b) a 0.5 kg object moving at 200 m/s (c) an 8 kg object moving at 0.1 m/s (d) a 10 kg object moving at 6 m/s

[d]

2.1.1b – Explain the relationship between net force, mass, and acceleration.

- Which of the following statements MUST apply to an object with no net force acting on it?

(1) The object must be accelerating. (2) The object must not be accelerating. (3) The object may be accelerating. (4) The object may be moving with a constant speed. (5) The object must be moving with a constant speed. (6) The object must be motionless. (7) The object cannot be motionless. (8) The object may be motionless.

[2, 5, 8]

- A 20 newton net force acts on a 5.0 kilogram object. What rate of acceleration

will this object experience?

[4.0 m/s2]

- An object of mass M experiences a net force F causing it to accelerate at rate A. At what rate would an object of mass M/2 accelerate if pushed with net force F?

(a) 2A (b) A (c) A/2 (d) A/4 [a]

2.1.2A Free Body Diagrams and Net Force

Free Body Diagrams

• _______________ diagrams

• Show ____________________________ acting on an object.

• Must be properly labeled!

Determining Net Force

• equilibrium → net force = 0 → acceleration = 0

– _______________________ or ________________________

• net Force ≠ 0

– ______________________ or _________________________

Consider each dimension separately then combine using Pythagorean Theorem.

Top-View

Example #1

• A 30 newton force and a 20 newton force act concurrently on an object.

o What min/max net force can these two forces produce? At what angle between the forces does each happen?

o What net force is produced when the angle between the two forces is 90°?

Side-View

Example #2

• A 50 kilogram object is pushed along a flat, frictionless surface with a constant force of 100 newtons.

o Sketch this object. Include all forces with labels and quantities.

o What rate of acceleration will the crate experience?

Vertical

Example #3

• What is the net force acting on a 3000 newton rocket if its engine produces an upward thrust of 4500 newtons?

Hor. Vert.

+8.0 N -2.0 N

Fg

FN

2 kg object

X Y 2 kg object

+7.0 N

-5.0 N

+3.0 N

-3.0 N

Dynamics Unit- Contact Forces Sub-Unit Physics

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PRACTICE

1) A 5.0 kilogram object is pulled east with a force of 20 newtons while acted upon by a friction force of 15 newtons.

a. What is the net force acting on the object?

b. What is the object’s rate direction and rate of acceleration?

2) A force of 35 newtons pulling a 3.0 kilogram object north causes it to accelerate north at a rate of 4.0 meters per second2.

a. What is the net force acting on the object?

b. What is the direction and magnitude with which the friction force acts on the object?

3) Force A has a magnitude of 15 newtons and produces a maximum resultant of 35 newtons when added to force B. What is the magnitude of force B? What minimum force can be produced by adding forces A and B?

Review Questions

2.1.2a – Determine: net force and acceleration for objects subjected to one or more parallel/perpendicular force;. missing forces in systems where acceleration is known; and max/min resultant forces.

- Two forces of 10 newtons and 25 newtons act concurrently on an object. a. If the angle between the two vectors is 0°, what is the resultant force?

[35 N]

b. If the angle between the two vectors is 180°, what is the resultant force?

[15 N]

- What happens to the resultant produced by two forces if the angle between

them is changed from 20° to 80°?

[decreases]

- A 3.0 kilogram object is subjected to a friction force of 10 newtons while being

accelerated at a rate of 2.0 meters per second2. What force must the object be pulled with?

[16 N]

- Determine the net force in each case. [2.8N / 3N / 0N / 3N / 3.2N]

2 N

2 N

2 N

5 N

2 N

5 N 3 N

3 N 3 N 2 N

3 N

3 N

5 N

2 N

2.1.2B Forces on Angles

Forces with Angles – Top View

F1

F2

F1

F2

F1

F2

F1 F2

F1

F1

F2

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• Redraw force vectors head-to-tail then draw resultant from start to finish.

Determine the direction of the net force

• Equilibrant is the force that is added to a system to produce a net force of __________.

– Opposite of the __________________________.

Forces with Angles – Side View • Determine net horizontal force.

Pulling Upward

Pushing Downward

Example #1

A 40 kilogram box is pulled across a smooth, frictionless surface with a 20 newton force that is 30° above horizontal.

– What is the net force acting on the box?

– What is the acceleration of the box?

Example #2

A woman pushes a 30 kilogram lawnmower with a force of 15 newtons at an angle of 60° below horizontal.

– What is the net force acting on the mower?

– What is the acceleration of the mower?

frictionless

H

+Fx

V

-Fy

-Fg

+FN

frictionless

H

+Fx

V

+Fy

-Fg

+FN

frictionless

PRACTICE

1) Forces A and B are applied to the object below as shown. Sketch the direction of the resultant and equilibrant forces for this system. Label the resultant “R” and the equilibrant “E”.

2) A 20 kilogram sled is pulled with a force of 100 newtons at an angle of 20° above the horizontal. A friction force of 15 newtons acts on the sled as it slides horizontally along the surface.

a. Sketch the sled and all of the forces acting on it.

b. The weight and normal force are NOT equal – which is bigger in this case?

c. What is the horizontal component of the pulling force?

d. What is the net force acting on the sled?

Review Questions

2.1.2b – Determine the direction an d relative size of resultants and equilibrants in top-view problems and to calculate net force and acceleration in side view problems with angles. To understand how the conditions for equilibrium are met and to identify systems in which equilibrium is possible.

- Which of the following is an equilibrant to the system shown below? [4]

Which of the following could produce equilibrium when combined with a 10N and 15N force?

(a) 2N (d) 15N (b) 6N (e) 20N (c) 10N (f) 30N

[b,c,d,e]

Which of the following systems could produce equilibrium?

(a) 3N, 5N, 7N (b) 10N, 30N, 45N (c) 2N, 2N, 2N (d) 5N, 7N, 9N (e) 12N, 15N, 30N

[a,c,d]

(1) (2)

(3) (4)

Determine the net force and acceleration in each of the diagrams. (Assume that all objects have a mass of 2.0 kilograms and all surfaces are frictionless)

[10N; 5m/s2] [8.7N; 4.3m/s2]

[6N; 3m/s2] [9N; 4.5m/s2]

10 N 10 N 4 N

10 N

30°

15 N

30° 4 N

A B

Dynamics Unit- Contact Forces Sub-Unit Physics

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2.1.3 Friction

Definitions

• friction: a force that ______________________________________

• Friction force strength

– How “sticky” are the surfaces involved?

• coefficient of friction ___________________________

– How hard are the surfaces pushing together?

• ____________________________________________

– Are the surfaces sliding against each other?

• ___________________________________________

Equation

Which Coefficient?

• Kinetic

– Used ONLY for ______________________ objects

• _____________________________

• _____________________________

• Static

– Used for any _______________________ objects

• ____________________________

• ____________________________

Example #1

A 20 newton wooden box is sliding across a wooden surface.

– What is the friction force acting on the box?

Example #2

A 40 newton copper box is placed on a flat, steel table.

– What is the minimum force needed to make the box move?

PRACTICE

1) A 2000 kilogram car with rubber tires is rolling along a dry asphalt road. What is the friction force between the car’s tires and the road?

2) What is the coefficient of friction between a 50 newton box and a surface if the box is pulled along the surface at a constant speed with a force of 10 newtons?.

3) Does it take more force to make an object move from rest or to keep it moving at a constant velocity?

2.1.4 Inclined Planes

Principle Forces

• Gravitational force (Fg) – _________________________________________________

– Should be broken into components

• Perpendicular to incline - _________________________________

• Parallel to incline - ______________________________________

• Normal force (FN) – ______________________________________________________

– Always equal to ________________________________________________

• Friction force (Ff) – ______________________________________________________

– If Ff < Fg|| then _________________________________________________

– If Ff = Fg|| then _________________________________________________

Review Questions

2.1.3 – Calculate minimum force of static friction. Determine amount of static friction acting on a motionless object. Determine minimum coefficient of friction in a system. Determine net forc, force of kinetic friction and/or acceleration in a sliding system.

- A 2.0 kilogram wooden object is a on a wooden surface. What is the maximum force of friction that can be produced in this system?

[8.2 N]

- A motionless 30 newton steel object on a steel surface is pushed with a 2.0 newton force. What is the force of static friction?

[2.0 N]

- What is the minimum coefficient of static friction between a 25 newton object and a surface if it is pushed with a force of 10 newtons and does not move?

[0.4]

- A wooden 10 newton object is sliding along a wooden surface. What force of friction is acting on the object?

[3.0 N]

- A 20 newton object is pulled along a flat surface at a constant speed with a force of 4.0 newtons.

o What is the force of kinetic friction? o What is the kinetic coefficient of friction?

[4N; 0.2]

Dynamics Unit- Contact Forces Sub-Unit Physics

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• As the angle increases…

– NO CHANGE:

– INCREASES:

– DECREASES:

Example #1

A 50 newton box is sliding down a 30° incline at a constant speed.

– What is the normal force acting on the box?

– What is the friction force acting on the box?

– What is the kinetic coefficient of friction in this system?

Fg = 50N

30°

0°

15°

30° 45°

60° 90°

40°

F

What is the mass of a 60 newton object that is placed on a frictionless 40° incline?

[6.1kg]

A force F is used to keep a 60 newton object at rest on a frictionless 40° incline. What is the magnitude of force F?

[39N]

A 30 newton object is sliding down a 20° incline at a constant speed.

20°

Determine the component of the object’s weight that is parallel to the incline.

[10N]

Determine the component of the object’s weight that is perpendicular to the incline.

[28N]

What is the normal force acting on the block?

[28N]

What is the net force acting on the block?

[0N]

What is the force of friction acting on the block?

[10N]

Review Questions

2.1.4– Determine the components of an object’s weight when placed on an incline. Determine the effects of changing the angle of the incline on the components of weight. Determine behavior of objects on frictionless inclines and inclines with friction. Determine friction, net force and/or applied forces on inclines based on the situation.

- A 3.0 kilogram object is placed on a frictionless, 25° incline.

Determine the component of the object’s weight that is parallel to the incline.

[12N]

Determine the component of the object’s weight that is perpendicular to the incline.

[27N]

25°

What is the normal force acting on the block? [27N]

What is the net force acting on the block?

[12N]

If the angle were increased to 65°: - parallel component of weight will (INCREASE/DECREASE/NOT CHANGE) - perpendicular component of weight will (INCREASE/DECREASE/NOT CHANGE) - normal force will (INCREASE/DECREASE/NOT CHANGE) - net force will (INCREASE/DECREASE/NOT CHANGE)

[increase; decrease; decrease; increase]

Dynamics Unit- Contact Forces Sub-Unit Physics

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A 5.0 kilogram block accelerates down a 35° incline at a rate of 2.0 meters per second2. Sketch all of the forces acting on the block.

35°

A force F is used to accelerate a 3.0 kilogram block up an incline at a rate of 2.0 meters per second2.

15°

How big must force F be if the force of friction acting on the block is 4.0 newtons? (Hint: which way is friction acting in this system?)

[17.6N]

F

What is the net force acting on the block?

[10N]

What is the friction force acting on the block?

[18N]