Force and Motion - UofL Department of Physics & … 298 summer 18...Force and Motion You need a...

1Prof. Sergio B. MendesSummer 2018

Chapter 4 of Essential University Physics, Richard Wolfson, 3rd Edition

Force and Motion

2Prof. Sergio B. MendesSummer 2018

Mechanics

DynamicsKinematics• How something moves ?? • Why something moves ??

• Geometrical description

• Mathematics

• Physical cause

• Physics

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Net Force

Force is a vector quantity.

Add the individual forces as vectors.

The resulting vector from the summation of the individual forces gives the netforce.

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Force and Motion

You need a force to changethe motion (velocity) of an object.

A moving object will keep moving in the absence of a force applied to it.

It is the change in velocity that matters.

5Prof. Sergio B. MendesSummer 2018

Newton’s First LawA body will remain at constant velocity (constant magnitude and direction) unless acted by a non-zero net force. Inertial Frames of Reference:

those frames of reference where Newton’s First Law is valid.

𝒗𝒗 𝒕𝒕 = 𝒗𝒗𝑜𝑜

𝒗𝒗 𝒕𝒕 = 0

We must use inertial frames of reference to describe Newton’s laws.

𝒂𝒂

𝒂𝒂

6Prof. Sergio B. MendesSummer 2018

Newton’s Second Law

𝑭𝑭 ∝ ∆𝒗𝒗

𝑭𝑭 ∝∆𝒗𝒗∆𝑡𝑡

𝑭𝑭 = 𝒎𝒎𝒂𝒂

𝒎𝒎: mass is an intrinsic property of an object and it measures the resistance to change its motion.

SI unit of mass is the kg.

𝑭𝑭 ∝ 𝒂𝒂 𝐹𝐹 = 𝑚𝑚 𝑎𝑎

𝐹𝐹 = 𝑘𝑘𝑘𝑘𝑚𝑚𝑠𝑠2

≡ 𝑁𝑁

7Prof. Sergio B. MendesSummer 2018

𝑑𝑑𝑑𝑑 𝑡𝑡𝑑𝑑𝑡𝑡

= 𝑣𝑣 𝑡𝑡

𝑑𝑑 𝑡𝑡

𝑑𝑑𝑣𝑣 𝑡𝑡𝑑𝑑𝑡𝑡

= 𝑎𝑎 𝑡𝑡

�0

𝑡𝑡𝑣𝑣 𝑡𝑡 𝑑𝑑𝑡𝑡 = 𝑑𝑑 𝑡𝑡 − 𝑑𝑑𝑜𝑜

�0

𝑡𝑡𝑎𝑎 𝑡𝑡 𝑑𝑑𝑡𝑡 = 𝑣𝑣 𝑡𝑡 − 𝑣𝑣𝑜𝑜

Big Picture of Chapter 2:Kinematics in 1D

8Prof. Sergio B. MendesSummer 2018

Example 4.1

𝑚𝑚 = 1200 𝑘𝑘𝑘𝑘

𝑣𝑣 = 20 𝑚𝑚/𝑠𝑠𝑣𝑣0 = 0 𝑚𝑚/𝑠𝑠

𝑡𝑡0 = 0 𝑠𝑠 𝑡𝑡 = 7.8 𝑠𝑠

𝑣𝑣 = 20 𝑚𝑚/𝑠𝑠

𝑟𝑟 = 85 𝑚𝑚

𝑎𝑎 = ? ? 𝑎𝑎 = ? ?

𝐹𝐹 = 𝑚𝑚 𝑎𝑎 ? ? 𝐹𝐹 = 𝑚𝑚 𝑎𝑎 ? ?

9Prof. Sergio B. MendesSummer 2018

A few examples of forces we routinely encounter:

10Prof. Sergio B. MendesSummer 2018

Forces in Nature:

electric, magnetic, friction, tension, compression, pushing, pulling, air resistance, etc.

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Example 4.2

𝑤𝑤𝑒𝑒 = 8.82 𝑘𝑘𝑁𝑁 on Earth

𝑚𝑚 = ? ?

𝑤𝑤𝑚𝑚 = ? ?

𝑘𝑘𝑒𝑒 = 9.81 𝑚𝑚/𝑠𝑠2

𝑘𝑘𝑚𝑚 = 3.71 𝑚𝑚/𝑠𝑠2

on Mars

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Free-Body Diagram:

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14Prof. Sergio B. MendesSummer 2018

Example 4.3

𝑚𝑚 = 740 𝑘𝑘𝑘𝑘

𝑎𝑎 = 1.1 𝑚𝑚/𝑠𝑠2

𝑭𝑭 = 𝒎𝒎𝒂𝒂

𝑭𝑭 = 𝑻𝑻 + 𝑭𝑭𝒈𝒈

𝑻𝑻 + 𝑭𝑭𝒈𝒈 = 𝒎𝒎𝒂𝒂

𝑻𝑻 = 𝒎𝒎𝒂𝒂 −𝒎𝒎𝒈𝒈

15Prof. Sergio B. MendesSummer 2018

4.4Got It ?

What would the cable tension in Example 4.3 beif the elevator starts moving upward, acceleratingfrom rest?

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

© 2016 Pearson Education, Inc.

What would the cable tension in Example 4.3 beif the elevator starts moving upward, acceleratingfrom rest?

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

© 2016 Pearson Education, Inc.

What would the cable tension in Example 4.3 beif the elevator decelerates to a stop while movingupward?

© 2016 Pearson Education, Inc.

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

What would the cable tension in Example 4.3 beif the elevator decelerates to a stop while movingupward?

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

© 2016 Pearson Education, Inc.

What would the cable tension in Example 4.3 beif the elevator starts moving downward,accelerating from rest?

© 2016 Pearson Education, Inc.

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

What would the cable tension in Example 4.3 beif the elevator starts moving downward,accelerating from rest?

© 2016 Pearson Education, Inc.

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

What would the cable tension in Example 4.3 beif the elevator slows to a stop while movingdownward?

© 2016 Pearson Education, Inc.

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

What would the cable tension in Example 4.3 beif the elevator slows to a stop while movingdownward?

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

© 2016 Pearson Education, Inc.

What would the cable tension in Example 4.3 beif the elevator is moving upward with constantspeed?

© 2016 Pearson Education, Inc.

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

What would the cable tension in Example 4.3 beif the elevator is moving upward with constantspeed?

a) greater than the elevator's weightb) less than the elevator's weightc) equal to the elevator's weight

© 2016 Pearson Education, Inc.

26Prof. Sergio B. MendesSummer 2018

Newton’s Third Law

𝑭𝑭𝑨𝑨𝑩𝑩 = − 𝑭𝑭𝑩𝑩𝑨𝑨

𝑭𝑭𝑨𝑨 𝑩𝑩 = − 𝑭𝑭𝑩𝑩𝑨𝑨 𝑭𝑭𝟏𝟏 = − 𝑭𝑭𝟐𝟐

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Example 4.4

𝑭𝑭𝟐𝟐 𝟏𝟏 = ? ?

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4.5Got It ?

The figure shows two blocks with two forces acting on the pair. Is the net force on the larger block?

a) greater than 2 Nb) equal to 2 Nc) less than 2 N

© 2016 Pearson Education, Inc.

The figure shows two blocks with two forces acting on the pair. Is the net force on the larger block?

a) greater than 2 Nb) equal to 2 Nc) less than 2 N

© 2016 Pearson Education, Inc.

31Prof. Sergio B. MendesSummer 2018

How to Measure Forces ??

Hooke’s Law

𝑭𝑭𝒔𝒔 ≅ −𝑘𝑘 𝒙𝒙

Empirical results when a force is applied

to a spring

Force of the spring on an

object attached to it, which is valid for small values of x

32Prof. Sergio B. MendesSummer 2018

Example 4.5

𝑭𝑭 = 𝒎𝒎𝒂𝒂

𝑭𝑭 = 𝑭𝑭𝒔𝒔 + 𝑭𝑭𝒈𝒈

𝑭𝑭𝒔𝒔 + 𝑭𝑭𝒈𝒈 = 𝒎𝒎𝒂𝒂

𝑭𝑭𝒔𝒔 = 𝒎𝒎𝒂𝒂 −𝒎𝒎𝒈𝒈𝑎𝑎 = 0 𝑚𝑚/𝑠𝑠2 𝑎𝑎 = 1.9 𝑚𝑚/𝑠𝑠2

𝑚𝑚 = 35 𝑘𝑘𝑘𝑘

𝑘𝑘 = 3.4 N/m

33Prof. Sergio B. MendesSummer 2018

4.6Got It ?

Would the answer to (a) in Example 4.5 change if the helicopter were not at rest but moving upward at constant speed?

a) Yesb) No

© 2016 Pearson Education, Inc.

Would the answer to (a) in Example 4.5 change if the helicopter were not at rest but moving upward at constant speed?

a) Yesb) No

© 2016 Pearson Education, Inc.

because acceleration is still zero

Would the answer to (b) in Example 4.5 change if the helicopter were moving downward but still accelerating upward?

a) Yesb) No

© 2016 Pearson Education, Inc.

Would the answer to (b) in Example 4.5 change if the helicopter were moving downward but still accelerating upward?

a) Yesb) No

© 2016 Pearson Education, Inc.

because the direction of the velocity is irrelevant to the acceleration

38Prof. Sergio B. MendesSummer 2018

Problem 4.54, HW # 3

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Summary

𝑭𝑭𝑨𝑨𝑩𝑩 = − 𝑭𝑭𝑩𝑩𝑨𝑨Newton’s Third Law:

Newton’s Second Law: 𝑭𝑭 = 𝒎𝒎𝒂𝒂

Newton’s First Law: 𝑭𝑭 = 0 𝒂𝒂 = 0𝒂𝒂

𝒂𝒂