Chapter 5 Newton’s Laws of Motion - nsmn1.uh.edunsmn1.uh.edu/hpeng5/Peng05_LectureOutline.pdf · A book is lying at rest on a table. The book will remain there at ... frictionless

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Chapter 5

Newton’s Laws of Motion


Units of Chapter 5• Force and Mass

• Newton’s First Law of Motion

• Newton’s Second Law of Motion

• Newton’s Third Law of Motion

• The Vector Nature of Forces: Forces in Two Dimensions

• Weight

• Normal Forces


5-1 Force and Mass

Force: push or pull

Force is a vector – it has magnitude and direction


5-1 Force and Mass

Mass is the measure of how hard it is to change an object’s velocity.

Mass can also be thought of as a measure of the quantity of matter in an object.


5-2 Newton’s First Law of Motion

If you stop pushing an object, does it stop moving? Only if there is friction!

In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest.

This is also known as the law of inertia.


In order to change the velocity of an object – magnitude or direction – a net force is required.

An inertial reference frame is one in which the first law is true. Accelerating reference frames are not inertial.

5-2 Newton’s First Law of Motion

Question 5.1a Newton’s First Law Ia) there is a net force but the book has too

much inertiab) there are no forces acting on it at allc) it does move, but too slowly to be seend) there is no net force on the booke) there is a net force, but the book is too

heavy to move

A book is lying at rest on a table. The book will remain there at rest because:

There are forces acting on the book, but the only

forces acting are in the y-direction. Gravity acts

downward, but the table exerts an upward force

that is equally strong, so the two forces cancel,

leaving no net force.

Question 5.1a Newton’s First Law Ia) there is a net force but the book has too

much inertiab) there are no forces acting on it at allc) it does move, but too slowly to be seend) there is no net force on the booke) there is a net force, but the book is too

heavy to move

A book is lying at rest on a table. The book will remain there at rest because:

Question 5.1b Newton’s First Law II

a) more than its weight

b) equal to its weight

c) less than its weight but more than zero

d) depends on the speed of the puck

e) zero

A hockey puck slides on ice at constant velocity. What is the netforce acting on the puck?

The puck is moving at a constant velocity, and

therefore it is not accelerating. Thus, there must

be no net force acting on the puck.

Question 5.1b Newton’s First Law II

a) more than its weight

b) equal to its weight

c) less than its weight but more than zero

d) depends on the speed of the puck

e) zero

A hockey puck slides on ice at constant velocity. What is the netforce acting on the puck?

Follow-up: Are there any forces acting on the puck? What are they?

a) a net force acted on it

b) no net force acted on it

c) it remained at rest

d) it did not move, but only seemed to

e) gravity briefly stopped acting on it

Question 5.1c Newton’s First Law III

You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why?

a) a net force acted on it

b) no net force acted on it

c) it remained at rest

d) it did not move, but only seemed to

e) gravity briefly stopped acting on it

The book was initially moving forward (because it was

on a moving bus). When the bus stopped, the book

continued moving forward, which was its initial state of

motion, and therefore it slid forward off the seat.

Question 5.1c Newton’s First Law III

You put your book on the bus seat next to you. When the bus stops suddenly, the book slides forward off the seat. Why?

Follow-up: What is the force that usually keeps the book on the seat?


5-3 Newton’s Second Law of MotionTwo equal weights exert twice the force of one; this can be used for calibration of a spring:


5-3 Newton’s Second Law of Motion

Now that we have a calibrated spring, we can do more experiments.

Acceleration is proportional to force:



Acceleration is inversely proportional to mass:



Combining these two observations gives

Or, more familiarly,



An object may have several forces acting on it; the acceleration is due to the net force:

(5-1)





Question 5.4a Off to the Races Ia) 16 s

b) 8 s

c) 4 s

d) 2 s

e) 1 s

From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only ½ F, how long would it have to be applied to reach the same final speed?

v

F

In the first case, the acceleration acts over time T = T = 4 s4 s to give velocity vv = = aTaT. In the second case, the force is halfhalf, therefore the acceleration is also halfhalf, so to achieve the same final speed, the time must be doubledtime must be doubled.

Question 5.4aQuestion 5.4a Off to the Races IOff to the Races Ia) 16 s

b) 8 s

c) 4 s

d) 2 s

e) 1 s

From rest, we step on the gas of our Ferrari, providing a force F for 4 secs, speeding it up to a final speed v. If the applied force were only ½ F, how long would it have to be applied to reach the same final speed?

v

F

From rest, we step on the gas of our Ferrari, providing a force F for 4 secs. During this time, the car moves 50 m. If the same force would be applied for 8 secs, how much would the car have traveled during this time?

a) 250 m

b) 200 m

c) 150 m

d) 100 m

e) 50 m

ConcepTestConcepTest 5.4b5.4b Off to the Races IIOff to the Races II

v

F

In the first case, the acceleration acts over time T = 4 s to give a distance of x = aT 2 (why is there no v0T term?). In the 2nd case, the time is doubled, so the distance is quadrupled because it goes as the square of the time.

From rest, we step on the gas of our Ferrari, providing a force F for 4 secs. During this time, the car moves 50 m. If the same force would be applied for 8 secs, how much would the car have traveled during this time?

a) 250 m

b) 200 m

c) 150 m

d) 100 m

e) 50 m

ConcepTest 5.4b Off to the Races II

v

F12



Free-body diagrams:

A free-body diagram shows every force acting on an object.

• Sketch the forces

• Isolate the object of interest

• Choose a convenient coordinate system

• Resolve the forces into components

• Apply Newton’s second law to each coordinate direction


5-3 Newton’s Second Law of MotionExample of a free-body diagram:


5-4 Newton’s Third Law of Motion

Forces always come in pairs, acting on different objects:

If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1.

These forces are called action-reaction pairs.

Fr

Fr



Some action-reaction pairs:



Although the forces are the same, the accelerations will not be unless the objects have the same mass.

Contact forces:

The force exerted by one box on the other is different depending on which one you push.

Question 5.9a Collision Course I

A small car collides with a large truck. Which experiences the greater impact force?

a) the car

b) the truck

c) both the same

d) it depends on the velocity of each

e) it depends on the mass of each

Question 5.9a Collision Course I

A small car collides with a large truck. Which experiences the greater impact force?

a) the car

b) the truck

c) both the same



According to Newton’s Third Law, both vehicles

experience the same magnitude of force.

a) the car

b) the truck

c) both the same



In the collision between the car and the truck, which has the greater acceleration?

Question 5.9b Collision Course II

a) the car

b) the truck

c) both the same



In the collision between the car and the truck, which has the greater acceleration?

Question 5.9b Collision Course II

We have seen that both vehicles experience the same magnitude of force. But the acceleration is given by F/m so the carhas the larger acceleration,because it has the smaller mass.

Question 5.10a Contact Force I

If you push with force F on either the heavy box (m1) or the light box (m2), in which of the two cases below is the contact force between the two boxes larger?

a) case A

b) case B

c) same in both cases

F m2

m1

A

F m2

m1

B

Question 5.10a Contact Force I

The acceleration of both masses together is the same in either case. But the contact force is the only force that accelerates m1

in case A (or m2 in case B). Because m1 is the larger mass, it requires the larger contact force to achieve the same acceleration.

If you push with force F on either the heavy box (m1) or the light box (m2), in which of the two cases below is the contact force between the two boxes larger?

a) case A

b) case B

c) same in both cases

Follow-up: What is the acceleration of each mass?

F m2

m1

A

F m2

m1

B

Question 5.10b Contact Force II

2m m

F

Two blocks of masses 2m and mare in contact on a horizontal frictionless surface. If a force Fis applied to mass 2m, what is the force on mass m ?

a) 2F

b) F

c) ½F

d) 1/3F

e) ¼F

The force F leads to a specific acceleration of the entire system. In order for mass m to accelerate at the same rate, the force on it must be smaller! How small?? Let’s see...

Question 5.10b Contact Force II

Two blocks of masses 2m and mare in contact on a horizontal frictionless surface. If a force Fis applied to mass 2m, what is the force on mass m ?

a) 2F

b) F

c) ½ F

d) 1/3 F

e) ¼ F

Follow-up: What is the acceleration of each mass?

2m m

F

Hint: draw free-body diagrams for both objects


5-5 The Vector Nature of Forces: Forces in Two Dimensions

The easiest way to handle forces in two dimensions is to treat each dimension separately, as we did for kinematics.


F ma F ma F max x y y z z∑ ∑ ∑= = =

Newton’s Second Law

rr

r ra

FF a= =∑ ∑m

mor

Newton’s laws can be applied to each component of the forces independently


Summary of Chapter 5• Force: a push or pull

• Mass: measures the difficulty in accelerating an object

• Newton’s first law: if the net force on an object is zero, its velocity is constant

• Inertial frame of reference: one in which the first law holds

• Newton’s second law:

• Free-body diagram: a sketch showing all the forces on an object


Summary of Chapter 5• Newton’s third law: If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1.

• Contact forces: an action-reaction pair of forces produced by two objects in physical contact

• Forces are vectors

• Newton’s laws can be applied to each component of the forces independently

Fr

Fr

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Chapter 5 Newton’s Laws of Motion - nsmn1.uh.edunsmn1.uh.edu/hpeng5/Peng05_LectureOutline.pdf · A book is lying at rest on a table. The book will remain there at ... frictionless