Physics 207: Lecture 7, Pg 1 "Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum.

Physics 207: Lecture 7, Pg 1

"Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools."

New York Times editorial, 1921,

about Robert Goddard's revolutionary

rocket work.

"Correction: It is now definitely

established that a rocket can

function in a vacuum.

The 'Times' regrets the error." New York Times editorial, July 1969.

Lecture 7


Lecture 7

Goals:Goals: Solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1st and 2nd laws.

Distinguish static and kinetic coefficients of friction

Differentiate between Newton’s 1st, 2nd and 3rd Laws

Assignment: HW4, (Chapters 6 & 7, due 2/18, 9 am, Wednesday)

Read Chapter 7

1st Exam Wednesday, Feb. 18 from 7:15-8:45 PM Chapters 1-7


Exercise, Newton’s 2nd Law

A. P + C < W

B. P + C > W

C. P = C

D. P + C = W

A woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows: P is the upward force being exerted on the crate by the personC is the contact or normal force on the crate by the floor, and W is the weight (force of the earth on the crate). Which of following relationships between these forces is true, while the person is trying unsuccessfully to lift the crate? (Note: force up is positive & down is negative)


Mass We have an idea of what mass is from everyday life. In physics:

Mass (in Phys 207) is a quantity that specifies how much inertia an object has

(i.e. a scalar that relates force to acceleration)

(Newton’s Second Law) Mass is an inherent property of an object. Mass and weight are different quantities; weight is

usually the magnitude of a gravitational (non-contact) force.

“Pound” (lb) is a definition of weight (i.e., a force), not a mass!


Inertia and Mass The tendency of an object to resist any attempt to

change its velocity is called Inertia Mass is that property of an object that specifies how

much resistance an object exhibits to changes in its velocity (acceleration)

If mass is constant then

If force constant

Mass is an inherent property of an object Mass is independent of the object’s surroundings Mass is independent of the method used to measure it Mass is a scalar quantity The SI unit of mass is kg

netFa

ma 1||

|a|

m


ExerciseNewton’s 2nd Law

A. increasingB. decreasingC. constant in timeD. Not enough information to decide

An object is moving to the right, and experiencing a net force that is directed to the right. The magnitude of the force is decreasing with time (read this text carefully).

The speed of the object is


Exercise Newton’s 2nd Law

A. B

B. C

C. D

D. F

E. G

A 10 kg mass undergoes motion along a line with a velocities as given in the figure below. In regards to the stated letters for each region, in which is the magnitude of the force on the mass at its greatest?


Moving forces around

Massless strings: Translate forces and reverse their direction but do not change their magnitude

(we really need Newton’s 3rd of action/reaction to justify)

Massless, frictionless pulleys: Reorient force direction but do not change their magnitude

string

T1 -T1

T1 -T1

T2

-T2| T1 | = | -T1 | = | T2 | = | T2 |


Scale Problem

You are given a 1.0 kg mass and you hang it directly on a fish scale and it reads 10 N (g is 10 m/s2).

Now you use this mass in a second experiment in which the 1.0 kg mass hangs from a massless string passing over a massless, frictionless pulley and is anchored to the floor. The pulley is attached to the fish scale.

What force does the fish scale now read?

1.0 kg

10 N

?

1.0 kg


Scale Problem

Step 1: Identify the system(s).

In this case it is probably best to treat each object as a distinct element and draw three force body diagrams. One around the scale One around the massless pulley (even

though massless we can treat is as an “object”)

One around the hanging mass

Step 2: Draw the three FBGs. (Because this is a now a one-dimensional problem we need only consider forces in the y-direction.)

?

1.0 kg


Scale Problem

Fy = 0 in all cases

1: 0 = -2T + T ’

2: 0 = T – mg T = mg

3: 0 = T” – W – T ’ (not useful here) Substituting 2 into 1 yields T ’ = 2mg = 20 N

(We start with 10 N but end with 20 N)

?

1.0 kg

? 1.0 kg

-mg

T

-T -T

-T ’

T”

W

1:2:3:T ’


No Net Force, No acceleration…a demo exercise

In this demonstration we have a ball tied to a string undergoing horizontal UCM (i.e. the ball has only radial acceleration)

1 Assuming you are looking from above, draw the orbit with the tangential velocity and the radial acceleration vectors sketched out.

2 Suddenly the string brakes.

3 Now sketch the trajectory with the velocity and acceleration vectors drawn again.


Static and Kinetic Friction Friction exists between objects and its behavior has been

modeled.

At Static Equilibrium: A block, mass m, with a horizontal force F applied,

Direction: A force vector to the normal force vector N N and the vector is opposite to the direction of acceleration if were 0.

Magnitude: f is proportional to the applied forces such that

fs ≤ s N

s called the “coefficient of static friction”


Friction: Static frictionStatic equilibrium: A block with a horizontal force F applied,

As F increases so does fs

Fm

1

FBD

fs

N

mg

Fx = 0 = -F + fs fs = F

Fy = 0 = - N + mg N = mg


Static friction, at maximum (just before slipping)

Equilibrium: A block, mass m, with a horizontal force F applied,

Direction: A force vector to the normal force vector N N and the vector is opposite to the direction of acceleration if were 0.

Magnitude: fS is proportional to the magnitude of N

fs = s N

Fm fs

N

mg


Kinetic or Sliding friction (fk < fs)

Dynamic equilibrium, moving but acceleration is still zero

As F increases fk remains nearly constant

(but now there acceleration is acceleration)

Fm

1

FBD

fk

N

mg

Fx = 0 = -F + fk fk = F

Fy = 0 = - N + mg N = mg v

fk = k N


Sliding Friction: Quantitatively

Direction: A force vector to the normal force vector N N and the vector is opposite to the velocity.

Magnitude: ffk is proportional to the magnitude of N N

ffk = k N N ( = Kmg g in the previous example)

The constant k is called the “coefficient of kinetic friction”

Logic dictates that S > K for any system


Coefficients of Friction

Material on Material s = static friction k = kinetic friction

steel / steel 0.6 0.4

add grease to steel 0.1 0.05

metal / ice 0.022 0.02

brake lining / iron 0.4 0.3

tire / dry pavement 0.9 0.8

tire / wet pavement 0.8 0.7


An experiment

Two blocks are connected on the table as shown. The

table has unknown static and kinetic friction coefficients.

Design an experiment to find S

Static equilibrium: Set m2 and add mass to m1 to reach the breaking point.

Requires two FBDsm1

m2

m2g

N

m1g

T

T

Mass 2

Fx = 0 = -T + fs = -T + S N

Fy = 0 = N – m2g

fS

Mass 1

Fy = 0 = T – m1g

T = m1g = S m2g S = m1/m2


A 2nd experiment



Design an experiment to find K.

Dynamic equilibrium: Set m2 and adjust m1 to find place when

a = 0 and v ≠ 0

Requires two FBDs

m1

m2

m2g

N

m1g

T

T

Mass 2

Fx = 0 = -T + ff = -T + k N

Fy = 0 = N – m2g

fk

Mass 1

Fy = 0 = T – m1g

T = m1g = k m2g k = m1/m2


An experiment (with a ≠ 0)



Design an experiment to find K.

Non-equilibrium: Set m2 and adjust m1 to find regime where a ≠ 0

Requires two FBDs

T

Mass 2

Fx = m2a = -T + fk = -T + k N

Fy = 0 = N – m2g

m1

m2

m2g

N

m1g

T

fk

Mass 1

Fy = m1a = T – m1g

T = m1g + m1a = k m2g – m2a k = (m1(g+a)+m2a)/m2g


Inclined plane with “Normal” and Frictional Forces

Weight of block is mg

NormalForce

Friction ForceSliding Down

“Normal” meansperpendicular

Note: If frictional Force = Normal Force (coefficient of friction)Ffriction = Fnormal = mg sin then zero acceleration

1. At first the velocity is v up along the slide

2. Can we draw a velocity time plot?

3. What the acceleration versus time?

v

mg sin

fk Sliding

Up


Recap

Assignment: HW4, (Chapters 6 & 7, due 2/18, 9 am, Wednesday)

Read Chapter 7 1st Exam Wednesday, Feb. 18 from 7:15-8:45 PM Chapters

1-7

Physics 207: Lecture 7, Pg 1 "Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum.

Documents

weight force

force constant

si unit of mass

normal force

upward force

net force

p c w

exercise newtons