Newton’s Second Law of MotionForce & Acceleration

Introduction to Science

A. King

EHS

Acceleration

• Galileo define rate of change of velocity as acceleration.

• The term acceleration is typically used when the velocity increases.

• The term deceleration is typically used when the velocity decreases – another way of saying this is that “deceleration” is when negative acceleration is occurring.

• In both cases, “acceleration” is the process that’s actually occurring.

Calculating Acceleration

ΔV

Acceleration = ---------

t

Where ΔV is the change in velocity and t is the time it takes for the velocity to change.

ΔV

acc t: :x

Units for Acceleration

• Speed and velocity are easily measured in distance/time units, such as miles/hr, m/s, etc.

• Units of acceleration are more complicated, and have to take other stuff into account.

• Sample problem: What is the acceleration if we speed up from 10 km/h to 30 km/h in 10 seconds?

• Acceleration = Δv/t

• (30 km/h – 10 km/h)/ 10 sec =

• 2 km/h/s

Acceleration depends on the

net force.

Acceleration ~ net force.

Mass

• Mass is a measure of an object’s inertia and a measure of how much material an object contains. (It depends on the number and kind of atoms making the object up.)

• Mass is measured in grams: grams, kilograms, milligrams…

Weight

• Weight depends on gravity.

• Weight is the force due to gravity that acts on an object’s mass.

• Although weight and mass are different from each other, they are directly proportional to each other.

• 1 kilogram weighs 9.8 newtons.

Volume

• Volume is a measure of space.

Newton’s Second Law states:

• The acceleration produced by a net force on an object – is directly to the net force.– Is in the same direction as the net force.– Is inversely proportional to the mass of the

object.– In formula: F = m x a

By using consistent units, such as newtons (N) for force, kilograms

(kg) for mass, and meters per second squared (m/s2) for acceleration, we

get the exact equation: Δ v vf – vi

Acceleration = -------- = ----------

t t

Acceleration Problems

• While drag racing out of our school parking lot, I time myself at a speed of 40 meters per second seven seconds after starting. What was my acceleration during this time?

• A = vf – vi / t

• = (40 m/s – 0 m/s )/7s

• = (40 m/s)/7s

• = 5.7 m/s/s

Friction

• Occurs when one object rubs against something else.

• Occurs for solids, liquids and gases.

• Always acts in a direction opposite to motion.

• The amount of friction between two surfaces depends on the kinds of material and how much they are pressed together.

Free Fall

• When an object is dropped in a place with gravity (k.e. not deepspace), gravity causes the object to fall downward.

• When this occurs, the object is said to be in “free fall.”

• For problems like this, we’ll imagine that gravity is the only force that’s acting on the object – wind resistance and other stuff will be ignored.

How fast is an object moving in free fall?

• Let’s consider the following data table:

• The increase in speed per second is the acceleration which in this case is 10 m/s/s.

• The instantaneous speed of an object that is accelerating is equal to the acceleration multiplied by the amount of time the object is falling.

• In equation form: v = at

Elapsed time (sec)

Instantaneous speed (m/sec)

0 0

1 10

2 20

3 30

t 10t

Formulas

Wt

m g: :

x

d

½ g t2

: :

x

Δv

acc t: :

x

v

a t: :

x

vf - vi

acc t: :

x

F

m a: :

x