Newton’s Laws February 22, 2013 - p. 1/10

February 22, Week 6

Today: Chapter 5, Applying Newton’s Laws

Homework Assignment #5 - Due March 1.

Mastering Physics: 10 problems from chapters 4 and 5.

Written Questions: 5.74

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

(b) The 200N downwards force on the crate

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

(b) The 200N downwards force on the crate

(c) The 200N downwards force on the earth

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

(b) The 200N downwards force on the crate

(c) The 200N downwards force on the earth

(d) The 200N upwards force on the earth

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

(b) The 200N downwards force on the crate

(c) The 200N downwards force on the earth

(d) The 200N upwards force on the earth

(e) Intentionally left blank

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

(b) The 200N downwards force on the crate

(c) The 200N downwards force on the earth

(d) The 200N upwards force on the earth

(e) Intentionally left blank Weight =−→w =

−→FE on B =

downwards force that earthexerts on box

Newton’s Laws February 22, 2013 - p. 2/10

Third Law Exercise

A 200-N crate is placed on a horizontal surface. The reactionto the force of gravity on the crate is:

(a) The 200N upwards normal force on the crate

(b) The 200N downwards force on the crate

(c) The 200N downwards force on the earth

(d) The 200N upwards force on the earth

(e) Intentionally left blank Weight =−→w =

−→FE on B =

downwards force that earthexerts on box

Reaction =−→FB on E upwards

force that box exerts on earth

Newton’s Laws February 22, 2013 - p. 3/10

Applying Newton’s Laws

There are two main tasks for which we will apply Newton’sLaws

Newton’s Laws February 22, 2013 - p. 3/10

Applying Newton’s Laws

There are two main tasks for which we will apply Newton’sLaws

■ To find the magnitude and sometimes direction of unknownforces.

Newton’s Laws February 22, 2013 - p. 3/10

Applying Newton’s Laws

There are two main tasks for which we will apply Newton’sLaws

■ To find the magnitude and sometimes direction of unknownforces.

■ To find the acceleration of masses.

Newton’s Laws February 22, 2013 - p. 3/10

Applying Newton’s Laws

There are two main tasks for which we will apply Newton’sLaws

■ To find the magnitude and sometimes direction of unknownforces.

■ To find the acceleration of masses.

It is imperative that we always identify and use the forcesacting ON objects (and not the forces exerted by objects).

Newton’s Laws February 22, 2013 - p. 3/10

Applying Newton’s Laws

There are two main tasks for which we will apply Newton’sLaws

■ To find the magnitude and sometimes direction of unknownforces.

■ To find the acceleration of masses.

It is imperative that we always identify and use the forcesacting ON objects (and not the forces exerted by objects).

−→a = 0 are called equilibrium or statics problems

Newton’s Laws February 22, 2013 - p. 3/10

Applying Newton’s Laws

There are two main tasks for which we will apply Newton’sLaws

■ To find the magnitude and sometimes direction of unknownforces.

■ To find the acceleration of masses.

It is imperative that we always identify and use the forcesacting ON objects (and not the forces exerted by objects).

−→a = 0 are called equilibrium or statics problems−→a 6= 0 are called dynamic or kinetics problems

Newton’s Laws February 22, 2013 - p. 4/10

Steps

Steps for applying Newton’s Laws in problems:

Newton’s Laws February 22, 2013 - p. 4/10

Steps

Steps for applying Newton’s Laws in problems:

■ Draw a picture.

Newton’s Laws February 22, 2013 - p. 4/10

Steps

Steps for applying Newton’s Laws in problems:

■ Draw a picture.■ For any object with mass, identify the forces acting on that

object.

Newton’s Laws February 22, 2013 - p. 4/10

Steps

Steps for applying Newton’s Laws in problems:

■ Draw a picture.■ For any object with mass, identify the forces acting on that

object.■ For each object with mass, draw a free body diagram.

Newton’s Laws February 22, 2013 - p. 4/10

Steps

Steps for applying Newton’s Laws in problems:

■ Draw a picture.■ For any object with mass, identify the forces acting on that

object.■ For each object with mass, draw a free body diagram.■ Find the net force components from vector addition and set

them equal to M−→a .

Newton’s Laws February 22, 2013 - p. 4/10

Steps

Steps for applying Newton’s Laws in problems:

■ Draw a picture.■ For any object with mass, identify the forces acting on that

object.■ For each object with mass, draw a free body diagram.■ Find the net force components from vector addition and set

them equal to M−→a .

■ Solve for unknowns.

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

First think of the forcesexerted by the rope

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

First think of the forcesexerted by the rope−→TR on M = force on massdue to bottom of rope−→TR on C = force on ceilingdue to top of rope

−→TR on M

−→TR on C

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

First think of the forcesexerted by the rope−→TR on M = force on massdue to bottom of rope−→TR on C = force on ceilingdue to top of rope

−→TR on M

−→TR on C

Look at forces on the rope

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

First think of the forcesexerted by the rope−→TR on M = force on massdue to bottom of rope−→TR on C = force on ceilingdue to top of rope

−→TR on M

−→TR on C

Look at forces on the rope

−→TM on R

−→TC on R

−→TM on R = Tension at thebottom of rope−→TC on R = Tension at thetop of rope

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

First think of the forcesexerted by the rope−→TR on M = force on massdue to bottom of rope−→TR on C = force on ceilingdue to top of rope

−→TR on M

−→TR on C

Look at forces on the rope

−→TM on R

−→TC on R

−→TM on R = Tension at thebottom of rope−→TC on R = Tension at thetop of rope

∑−→F = M−→

a ⇒

∑−→Frope = Mrope

−→arope

Newton’s Laws February 22, 2013 - p. 5/10

Massless Ropes

Massless ropes have the very useful property that the tensioneverywhere must be equal

First think of the forcesexerted by the rope−→TR on M = force on massdue to bottom of rope−→TR on C = force on ceilingdue to top of rope

−→TR on M

−→TR on C

Look at forces on the rope

−→TM on R

−→TC on R

−→TM on R = Tension at thebottom of rope−→TC on R = Tension at thetop of rope

∑−→F = M−→

a ⇒

∑−→Frope = Mrope

−→arope

Mrope = 0 ⇒−→TM on R = −

−→TC on R

Newton’s Laws February 22, 2013 - p. 6/10

Pulleys

Using a pulley we can have tensions in completely differentdirections.

Newton’s Laws February 22, 2013 - p. 6/10

Pulleys

Using a pulley we can have tensions in completely differentdirections.

Pulley - Machine thatchanges the direction ofapplied forces

Newton’s Laws February 22, 2013 - p. 6/10

Pulleys

Using a pulley we can have tensions in completely differentdirections.

Pulley - Machine thatchanges the direction ofapplied forces

We use perfect pulleys ⇒

massless and frictionless.They change force direc-tion with no change inmagnitude.

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

(b) 25N

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

(b) 25N

(c) 50N

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

(b) 25N

(c) 50N

(d) 100N

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

(b) 25N

(c) 50N

(d) 100N

(e) 400N

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

(b) 25N

(c) 50N

(d) 100N

(e) 400N

Newton’s Laws February 22, 2013 - p. 7/10

Equilibrium Exercise

How much force must a person exert on the massless ropeshown in order to hold the 100-N block at rest?

(a) 0N

(b) 25N

(c) 50N

(d) 100N

(e) 400N

Newton’s Laws February 22, 2013 - p. 8/10

Equilibrium versus Dynamics

At equilibrium, the individual forces acting on an object add tozero.

Newton’s Laws February 22, 2013 - p. 8/10

Equilibrium versus Dynamics

At equilibrium, the individual forces acting on an object add tozero.

∑Fx = 0,

∑Fy = 0

Newton’s Laws February 22, 2013 - p. 8/10

Equilibrium versus Dynamics

At equilibrium, the individual forces acting on an object add tozero.

∑Fx = 0,

∑Fy = 0

When an object accelerates, the forces do not add to zero andNewton’s Second Law becomes

∑Fx = Max,

∑Fy = May

But there are no NEW forces acting on the object!

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

30m/s

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

(a)

−→froad

−→D

−→n

−→w

30m/s

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

30m/s

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

30m/s

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

(d)

−→froad

−→D

−→n

−→w

30m/s

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

(d)

−→froad

−→D

−→n

−→w

(e)

−→froad

−→D

−→n

−→w

30m/s

Newton’s Laws February 22, 2013 - p. 9/10

Dynamics Exercise I

A minivan is traveling with a constant speed of 30m/s. Whichof the following is the correct free-body diagram for theminivan? (

−→D=Drag)

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

(d)

−→froad

−→D

−→n

−→w

(e)

−→froad

−→D

−→n

−→w

30m/s

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

30m/s

1m/s2

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

(a)

−→froad

−→D

−→n

−→w

30m/s

1m/s2

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

30m/s

1m/s2

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

30m/s

1m/s2

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

(d)

−→froad

−→D

−→n

−→w

30m/s

1m/s2

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

(d)

−→froad

−→D

−→n

−→w

(e)

−→froad

−→D

−→n

−→w

30m/s

1m/s2

Newton’s Laws February 22, 2013 - p. 10/10

Dynamics Exercise II

A minivan is traveling with speed of 30m/s and accelerating at1m/s2. Which of the following is the correct free-body diagramfor the minivan?

(a)

−→froad

−→D

−→n

−→w

(b)

−→froad

−→D

−→n

−→w

(c)

−→froad

−→D

−→n

−→w

(d)

−→froad

−→D

−→n

−→w

(e)

−→froad

−→D

−→n

−→w

30m/s

1m/s2