Newton’s Second Law of Motion – Force &

AccelerationChin-Sung Lin

Newton & His Second Law

Review – Newton’s First Law

Usually called the law of inertia

Every object continues in a state of rest, or of motion in a straight line at constant speed, unless it is compelled to change that state by an unbalanced force exerted upon it

Implies the second law of motion

Unbalanced Force

Unbalanced force means the net force ≠ 0

What will the unbalanced force result in?

F

Newton’s Second Law

Newton’s second law – Force & Acceleration

The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object

Net Force = 0

Zero net force means zero acceleration

No acceleration is the evidence of zero net force

Zero acceleration means

state of rest or

state of constant velocity

Force Causes Acceleration

Acceleration ~ Net force

(Direct Proportion)

a ~ Fnet

F

a

Mass Resists Acceleration

Acceleration ~ 1/mass

(Inverse Proportion)

a ~ 1/m

m

a

Force Causes Acceleration

Acceleration ~ Net force

a ~ Fnet

Acceleration ~ 1/mass

a ~ 1/m

a = Fnet /m or Fnet = m a

F = m a

Example: How much Force?

?

Example: What’s the Acceleration?

Example: What’s the mass?

m = ?

a = 100 m/s2

F = 1000000 N

Weight is Gravitational Force

Fnet = m a

Fg = m g

or

W = m g

Weight, mass and Acceleration

Weight, mass and Acceleration

Weight on Earth & Moon?

Same Mass

Mass on Earth & Moon?

Same Weight

Friction Force

Friction acts on materials that are in contact with each other, and is always acts in direction to oppose motion

When There is No Friction

Coefficient of Friction ()

Friction mainly due to the irregularities in the two surfaces

The irregularities between surfaces of different materials are described by the coefficients of friction ()

Friction mainly determined by the surface and the weight of the object

Friction Force (Ff)

Friction force (Ff) can be categorized into two different types: Static and Kinetic

Maximum Static Friction

Kinetic Friction

Maximum Static Friction

Ff

F

Coefficient of Friction ()

Static Friction Force

As long as an object does not move, the friction force (Ff) must be equal in size and opposite in direction to the applied force (F)

Ff = F

The static frictional force can have any value from zero up to a max. value (maximum static friction force)

Ff

F

Maximum Static Friction

Maximum Static Friction Force

Maximum static friction force is directly proportional to the normal force and the coefficient of static friction (s).

Ff = FN s

Ff

F

Maximum Static Friction

Example: Static Friction Force

If a block is not moving, what’s the friction force?

50 kg

20 N

Example: Static Friction Force

If the coefficient of static friction between a block and the ground is 0.2, (a) what’s the maximum static friction force? (b) Will the block move? (c) What’s the friction force?

50 kg

80 N

Example: Static Friction Force

If a wooden block is resting on a wooden floor, (a) How much force is required to make the block move? (b) Will the block move? (c) What’s the friction force while moving?

50 kg

100 N

Kinetic Friction Force

If the applied force exceeds the maximum static friction force, the object will slide in the direction of the applied force, and the friction force reduces to a constant value called kinetic friction force

The value of the kinetic friction is independent of the speed of the object Ff

F

Kinetic Friction

Kinetic Friction Force

Kinetic friction force is directly proportional to the normal force and the coefficient of static friction (s).

Ff = FN k

Ff

F

Kinetic Friction

Example: Kinetic Friction Force

If a block is moving at constant velocity, what’s the friction force?

50 kg

20 N

Example: Kinetic Friction Force

If a block is moving and coefficient of kinetic friction between the block and the ground is 0.1, (a) what’s the friction force? (b) What’s the acceleration of the block?

50 kg

80 N

Example: Kinetic Friction Force

If a wooden block is sliding on a wooden floor, (a) what’s the friction force? (b) What’s the acceleration of the block?

20 kg

100 N

Example: Kinetic Friction Force

If a 40-kg block is pushed by a force of 100 N and accelerates at 2 m/s2, (a) what’s the friction force? (b) What’s the coefficient of kinetic friction between the block and the ground?

40 kg

100 N

Example: Kinetic Friction Force

If a 40-kg block is sliding down an incline plane of 30o at constant speed, (a) what’s the friction force while sliding? (b) What’s the coefficient of kinetic friction between the block and the ground?

40 kg

30o

Application – Anti-Lock Brake

Air Resistance

Fg

R

Free Falling & Air Resistance

When there is air resistance (R), the acceleration of a free falling object reduced. The acceleration of a falling object is:

a = Fnet/m = (Fg – R)/m = (mg – R)/m = g – R/m

Air Resistance & Terminal Speed

When the air resistance on an object equals the weight of the object, the net force is zero and no further acceleration occurs. Acceleration terminates: the object has reached its terminal speed or terminal velocity.

a = 0 m/s2 = g – R/m g = R/m R = mg

Reduce the Terminal Speed

Force vs. Pressure

Pressure

Pressure (P):

The amount of force per unit of area

Pressure = Force / Area of application

or P = F/A

Unit:

Newtons per square meter, or pascals (Pa).

Example: Pressure 200 kg

200 kg

5 kg

5 kg

2m x 2m x 2m.2m x .2m x .2m

Which one has larger pressure?

Summary

Newton’s second law - Fnet = m a

Force causes acceleration & mass resists acceleration

Weight is gravitational force - Fg = m g

Acceleration of different masses on Earth

Mass and weight on Earth and moon

Friction force and coefficient of friction ()

Static friction force and kinetic friction force

Summary

Friction force Ff = FN

Air resistance and terminal speed

Pressure vs. force