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Chapter 4

Forces and Mass

does not apply for

very tiny objects (< atomic sizes)

objects moving near the speed of light

Classical MechanicsIf the net force SF exerted on an object is zero the object continues in its original state of motion. That is, if SF = 0, an object at rest remains at rest and an object moving with some velocity continues with the same velocity.

Contrast with Aristotle!

Newton’s First LawQCD (Quantum chromodynamics) confines quarksby exchaning gluons

Nuclear force: binds protons and neutronsby exchanging pions

Strong Nuclear ForceElectromagnetic Forces

- Opposites attract, like-signs repel
- Electric forces bind electrons in atoms
- Magnetic forces arise from moving charges

Attractive force between any two bodies

Proportional to both masses

Inversely proportional to square of distance

GravityA measure of the resistance of an object to changes in its motion due to a force

Scalar

SI units are kg

MassAcceleration is proportional to net force and inversely proportional to mass.Newton’s Second Law

Single isolated force cannot exist

For every action there is an equal and opposite reaction

Force on “1” due to “2”

Newton’s Third LawNewton’s Third Law cont.

- F12 is action force F21 is reaction force
- You can switch action <-> reaction
- Action & reaction forces act on different objects

Define the OBJECT (free body)

- Newton’s Law uses the forces acting ON object
- n and Fg act on object
- n’ and Fg’ act on other objects

Objects behave as particles

ignore rotational motion (for now)

Consider only forces acting ON object

neglect reaction forces

Assumptions for F=maExample 4.1a

A Ford Pinto is parked in a parking lot

There is no net force on the Pinto

A) True

B) False

Example 4.1b

A Ford Pinto is parked in a parking lot

The contact force acting on the Pinto from the parking lot surface ______________ .

A) Points upwards

B) Is zero

C) Points downward

Example 4.1c

A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance)

The Pinto’s acceleration is __________

A) Less than zero

B) Equal to zero

C) Greater than zero

Example 4.1d

A Ford Pinto drives down a highway on the moon at constant velocity (where there is no air resistance)

The force acting on the Pinto from the contact with the highway is vertical.

A) True

B) False

Force from rope points AWAY from object

Magnitude of the force is tension

Tension does not change when going over frictionless pulley

Some Rules for Ropes and PulleysExample 4.2

a) Find acceleration

b) Find T, the tension above the bowling ball

c) Find T3, the tension in the rope between the pails

d) Find force ceiling must exert on pulley

a) a = g/6 = 1.635 m/s2b) T= 57.2 Nc) T3=24.5 Nd) Fpulley=2T = 114.5 N

Example 4.3a

2) Which statements are correct?Assume the objects are static.

T1 is _____ T2

A) Less than

B) Equal to

C) Greater than

cos(10o)=0.985 sin(10o)=0.173

Example 4.3b

2) Which statements are correct?Assume the objects are static.

T2 is ______ T3

A) Less than

B) Equal to

C) Greater than

cos(10o)=0.985 sin(10o)=0.173

Example 4.3c

2) Which statements are correct?Assume the objects are static.

T1 is _____ Mg

A) Less than

B) Equal to

C) Greater than

cos(10o)=0.985 sin(10o)=0.173

Example 4.3d

2) Which statements are correct?Assume the objects are static.

T1+T2 is ______ Mg

A) Less than

B) Equal to

C) Greater than

cos(10o)=0.985 sin(10o)=0.173

Example 4.4

Given that Mlight = 25 kg, find all three tensions

T3 = 245.3 N, T1 = 147.4 N, T2 = 195.7 N

Inclined Planes

- Choose x along the incline and y perpendicular to incline
- Replace force of gravity with its components

RESISTIVE force between object and neighbors or the medium

Examples:

Sliding a box

Air resistance

Rolling resistance

Forces of FrictionParallel to surface, opposite toother forces

~ independent of the area of contact

Depends on the surfaces in contact

Sliding FrictionKinetic Friction, ƒk

- mk is coefficient of kinetic friction
- Friction force opposes F
- n is the normal force

f

F

Example 4.7

The man pushes/pulls with a force of 200 N. Thechild and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0.15. For each case:What is the frictional force opposing his efforts?

What is the acceleration of the child?

f=59 N, a=3.80 m/s2 / f=29.1 N, a=4.8 m/s2

Example 4.8

Given m1 = 10 kg and m2 = 5 kg:

a) What value of ms would stop the block from sliding?

b) If the box is sliding and mk = 0.2, what is the acceleration?

c) What is the tension of the rope?

a) ms = 0.5 b) a=1.96 m/s2 c) 39.25 N

Example 4.9

What is the minimum ms required to prevent a sled from slipping down a hill of slope 30 degrees?

ms = 0.577

Example 4.9

An elevator falls with acceleration a = 8.0 m/s2. If a 200-lb person stood on a bathroom scale during the fall, what would the scale read?

36.9 lbs

F-maf looks like force in new frame, maf acts like fake gravitational force!

Fictitious Force: DerivationEq. of motion in fixed frame

Example 4.10

You are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards.

If M = 2.5 kg and the acceleration, a = 3.0 m/s2:a) At what angle does the ball swing backwards?

b) What is the tension in the string?

q =17 degT= 25.6 N

q

Example 4.11a

A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale.

In the instant just after the elevator begins to move upward, the reading on the scale will be ______________ 20 lbs.

Greater than

Less than

Equal to

Example 4.11b

A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale.

On the way back down, while descending at constant velocity, the reading on the scale will be ________________ 20 lbs.

Greater than

Less than

Equal to

Example 4.11c

A fisherman catches a 20 lb trout (mass=9.072 kg), and takes the trout in an elevator to the 78th floor to impress his girl friend, who is the CEO of a large accounting firm. The fish is hanging on a scale, which reads 20 lb.s while the fisherman is stationary. Later, he returns via the elevator to the ground floor with the fish still hanging from the scale.

In the instant just before the elevator comes to a stop on the 78th floor, the mass of the fish will be ______________ 9.072 kg.

Greater than

Less than

Equal to

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