PH-211 Andres La Rosa

CHAPTER 5: Force and The Newton's Laws of Motion ____________________________________________________________________

DYNAMICS

The HORIZONTAL motion is independent of the VERTICAL motion

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SIDE VIEW

TOP VIEW

Review: Uniform circular motion

TOP VIEW

NEWTON's FIRST LAW

NEWTON's SECOND LAW

-

-

NEWTON's SECOND LAW

Total external force acting on the mass m

F1

F2

F3

=

1 Newton

Unit of force:

All these experimental observations lead to:

Optional reading

EXAMPLE: Problem 3 from the textbook

Example

3 Kg

Cos(62o) Cos(62o)

= [ 9 - 8Cos(62o) ] N + 8NSin(62o)

Newton's second law implies

[ 9 - 8Cos(62o) ] N + 8NSin(62o) = m ( ax + ay )

Solution

Two forces act on the block shown in the figure

Question :

m

m

m

90 92

F2 = 5N F1 = 3N

Example:

NEWTON's THIRD LAW

NEWTON's THIRD LAW

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EXAMPLE

35Let's establish all the action and reaction forces first (see arrows)

T2'

T2' Force due to the ceiling acting on rope-2

Force on B due to rope-2

T2

T2

T1 =T1'

T1 =T1'

T1

T1

Equilibrium of block-B implies: T2 = mBg + T1'

Equilibrium of block A implies: T1 = mAg

Roof

T1 is the force on A due to rope-1

Weight force = mA g

Force on rope-1 due to A

Force on rope-1 due to B

Force on B due to rope-1

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Approximation: No friction force

Approximation: Cord is massless

(Or its mass is very small compared to M and m)

Since the cord is massless: T = T'

If the cord does not elongate, then:

aM

am

Let's call it a

Example

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