Lecture 8: Forces &

The Laws of Motion

Questions of Yesterday1) 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 acceleratingb) when both objects are acceleratingc) never

Newton’s Second Law

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

inversely proportional to its mass

a = F/m

F = maSI Unit of force =

Newton

1 N = 1 kg*m/s2

F and a arevectors!

Vector equation!

Fx = max Fy = may Fz = maz

Free Body Diagrams

F

g

N

N’

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

Fg’

Free Body DiagramsTennis ball undergoing projectile motion

F

g

Free Body DiagramsTennis 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 an angle 30o with the horizontal.

F

g

What is the magnitude and direction of the net

force on the ball?

What is the resultant acceleration?

FA30o

Free Body DiagramsA block sliding down a frictionless inclined plane.

F

g

In what direction?

N

Is the block accelerating?

Free Body DiagramsA block sliding down a frictionless inclined plane.

F

g

N

+ y

+ x

- x

- y

Choose coordinate system to be in direction of incline plane!

Fgy

Fgx

Fgx = Fgsin

Fgy = Fgcos

Free Body DiagramsWhat is the acceleration of the block?

F

g

N

30o

+ y

+ x

- x

- y

Fgy

Fgx

Fgx = Fgsin

Fgy = Fgcos

3 kg

Fx = max Fy = mayFy = may = 0

N - Fgy = 0

Fx = max

max = Fgx

FBDs and using Newton’s LawsHow 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:

a) 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?

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.

a) What is the final speed of the train?

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

TensionFree 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

Tension

Tension at one end of the rope is equal to the otherTension is CONSTANT all along the rope

Tension = force exerted along a rope

FA

N

Fg

TT’

2nd law: ma = T’ + FA =

0

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

3rd law: T = -T’

Tension: Practice Problem

Find the acceleration of each object and the tension in the rope

5 kg

10 kg

Objects in Equilibrium

When is ∑F = 0?

Conditions for equilibrium:∑Fx = 0∑Fy = 0

When is a = 0?

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

Objects in Equilibrium

Conditions for

equilibrium:∑Fx = 0∑Fy = 0

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

40o 40o

Questions of the DayYou 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 Fd) 0

1b) Are other forces acting on the book in the horizontal direction?a) YESb) NOc) 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 accelerationb) opposite the direction of the truck’s accelerationc) the net force is zero