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Lecture 8: Forces & The Laws of Motion. Questions of Yesterday. You must apply a force F 1 to begin pushing a crate from rest across the floor, you must apply a force F 2 to keep the crate moving at a constant velocity once its in motion. Which statement is true? a) F 1 = F 2

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slide2

Questions of Yesterday

You must apply a force F1 to begin pushing a crate from rest across the floor, you must apply a force F2 to keep the crate moving at a constant velocity once its in motion. Which statement is true?

a) F1 = F2

b) F1 > F2

c) F1 < F2

2) When do action and reaction pairs of forces not cancel one another out?

a) when one of the objects is accelerating

b) when both objects are accelerating

c) never

slide3

SI Unit of force =

Newton

1 N = 1 kg*m/s2

F and a are

vectors!

Vector equation!

F = ma

The acceleration a of an object is directly proportional to the net force acting on it and inversely proportional to its mass

Fx = max

Fy = may

Fz = maz

Newton’s Second Law

a = F/m

slide4

N

Fg

Fg’

N’

Free Body Diagrams

Diagram of a single object with all the forces acting ON it

DO NOT INCLUDE:

-Forces that the object exerts on other objects or the Earth

-Other objects that the object is in contact with

slide5

Fg

Free Body Diagrams

Tennis ball undergoing projectile motion

slide6

FA

30o

Fg

Free Body Diagrams

Tennis ball while a tennis player is serving it.

The player swings his racket, hitting the 60 g tennis ball with a force 60 N at anangle 30o with the horizontal.

What is the magnitude and direction of the net force on the ball?

What is the resultant acceleration?

slide7

N

q

Fg

Free Body Diagrams

A block sliding down a frictionless inclined plane.

q

Is the block accelerating?

In what direction?

slide8

+ y

- x

Fgy

+ x

- y

Fgx

Fg

Fgx = Fgsinq

Fgy = Fgcosq

Free Body Diagrams

A block sliding down a frictionless inclined plane.

N

q

q

Choose coordinate system to be in direction of incline plane!

slide9

+ y

- x

Fgy

+ x

- y

Fgx

Fg

Fgx = Fgsinq

Fgy = Fgcosq

Free Body Diagrams

What is the acceleration of the block?

N

3 kg

30o

q

Fx = max

Fy = may

Fy = may = 0

N - Fgy = 0

Fx = max

max = Fgx

slide10

FBDs and using Newton’s Laws

How much do you weigh in a moving elevator?

A 60-kg person stands on a scale in an elevator

Draw a free body diagram for the person

What does the scale read when

the elevator is:

at rest?

b) Ascending with a speed of 2.0 m/s?

c) Descending with a speed of 2.0 m/s?

d) Ascending with an acceleration of 2.0 m/s2?

e) Ascending with an acceleration of 2.0 m/s2?

slide11

Practice Problem

A train has a mass of 5.0*106 kg and is moving at 90 km/h. The engineer applies the brakes, resulting in a net backward force of 2.0*106 N on the train. The brakes are held on for 30.0 s.

What is the final speed of the train?

b) How far does the train travel in this period?

slide12

Tension

Free Body Diagrams and Newton’s 2nd law only use forces acting directly on an object

Draw a free body diagram for the block

What about the rope?

FA

a

slide13

N

T’

FA

T

Fg

Tension

Tension = force exerted along a rope

2nd law: ma = T’ + FA = 0

3rd law: T = -T’

Tension at one end of the rope is equal to the other

Tension is CONSTANT all along the rope

Applied force is acts “directly” on block through the rope

slide14

Tension: Practice Problem

5 kg

10 kg

Find the acceleration of each object and

the tension in the rope

slide15

Objects in Equilibrium

When is ∑F= 0?

When is a= 0?

An object at rest or moving with a constant velocity is in EQUILIBRIUM

Conditions for equilibrium:

∑Fx= 0

∑Fy= 0

slide16

40o

40o

Objects in Equilibrium

Find the tension in the two wires that support the light fixture

Conditions

for

equilibrium:

∑Fx= 0

∑Fy= 0

slide17

Questions of the Day

You must apply a force F to push your physics book across your desk at a constant velocity.

1a) The net force acting on the book is…

a) F

b) between 0 and F

c) greater than F

d) 0

1b) Are other forces acting on the book in the horizontal direction?

a) YES

b) NO

c) not enough information to know

3) A large crate is at rest in the bed of a truck. As the truck accelerates the crate remains at rest relative to the truck. In what direction is the net force on the crate?

a) the same direction as the truck’s acceleration

b) opposite the direction of the truck’s acceleration

c) the net force is zero