Newtons Second Law of Motion Force Acceleration ChinSung

Newton’s Second Law of Motion – Force & Acceleration Chin-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 F What will the unbalanced force result in?

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 ~ Net force (Direct Proportion) a a ~ Fnet F

Mass Resists Acceleration ~ 1/mass (Inverse Proportion) a a ~ 1/m m

Force Causes Acceleration ~ Net force a ~ Fnet Acceleration ~ 1/mass a ~ 1/m a = Fnet /m or Fnet = m a

F=ma

Example: How much Force? ?

Example: What’s the Acceleration?

Example: What’s the mass? m=? a = 100 m/s 2 F = 1000000 N

Weight is Gravitational Force Fnet = m a Fg = m g or W=mg

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 (m) 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 Ff Maximum Static Friction Kinetic Friction F Maximum Static Friction

Coefficient of Friction (m)

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 Maximum Static Friction F

Maximum Static Friction Force Maximum static friction force is directly proportional to the normal force and the coefficient of static friction ( s). F f = F N s Ff Maximum Static Friction F

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 Kinetic Friction F

Kinetic Friction Force Kinetic friction force is directly proportional to the normal force and the coefficient of static friction ( s). F f = F N k Ff Kinetic Friction F

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/s 2, (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 30 o 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? g k 40 o 0 3

Application – Anti-Lock Brake

Air Resistance R Fg

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/s 2 = g – R/m g = R/m R = mg

Reduce the Terminal Speed

Force vs. 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 Which one has larger pressure? 5 kg 200 kg 5 kg. 2 m x. 2 m 2 m x 2 m

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 (m) Static friction force and kinetic friction force

Summary Friction force Ff = m FN Air resistance and terminal speed Pressure vs. force