cm [010] galileo's acceleration & newton's laws

© ABCC Australia 2015 new-physics.com

ACCELERATIONCM [010] Galileo’s


. . . it will change its state of motion only and only when it is compelled to do so by forces impressed on it.

Part 3 of Newton’s First Law

Part 3 of Newton’s First Law spells the relation between state of motion and force:

The right place for this part should be a part of the second law where it would probably read:

Force changes the state of motion [of a particle].

However, this is enough for us to start to discuss on a new state of motion.


The States of Motion

Rest = Motionless = Constant rest In constant Motion of velocity v.

The states of motion of an object can be summarized as rest and being in motion at any speed as described by Part 1 and 2 of Newton’s First Law.


The States of Motion

Velocity start from 0 to any speed 𝑣𝑣.Object accelerated.

In raising the object at rest to a state of motion, we have acceleration.

Time

Velo

city


AccelerationActually, when an object picks up speed, it accelerates. If it slows down it is said to decelerate. However, for convenience in general discussion, any motional change is said to be in acceleration.

Acceleration Deceleration


Acceleration due to Gravity

The most familiar event of acceleration is in free falling caused by gravity. The earth pulls the object and it falls straight to the ground. It can be seen that the rate of falling varies. It increase steadily with height. The object will fall faster and faster until it hits the ground. That is, the rate of acceleration increases on time, the longer an objects falls, the greater acceleration it will reach. The final velocity will be tremendous.


Rate of Free Fall

We know that things fall down because of the force of gravity. But Galileo did not yet have the concept of gravity at the time. He took falling for granted and concentrated on measuring how fast things can fall.


Galileo Measured Acceleration

Galileo used many devices to study constant motion and acceleration. One of the major gadgets he used was a ramp. The ramp would slow down the rate of fall to make measurement manageable. He could vary the slope of the ramp so that the speed of a ball rolling down the ramp can be adjusted. The less incline was the ramp, the slower would be the speed of the ball, making it easier for timing purpose.


Galileo Demonstrated his Ramp Experiment


Equation for Acceleration

Over a period of 20 years, Galileo observed the motions of objects rolling down in various inclination. By measuring the distance a ball rolled down the ramp in each unit of time with water clocks or other timing devices. Galileo concluded from his experiments that if an object is released from rest and gains speed at a steady rate, then the total distance, 𝑑𝑑, travelled by the object is proportional to the square of the time that it took in motion with g as the acceleration constant:

𝑑𝑑 ∝12𝑔𝑔𝑔𝑔2

Thus the first correct concept of accelerated motion was born.


Geometric Representation of Acceleration

Since in acceleration, the velocity changes from time to time. The graph of acceleration is different from that of velocity. The distance 𝑑𝑑 travelled by a particle at constant velocity 𝑣𝑣 is:

𝑑𝑑 = 𝑣𝑣Δ𝑔𝑔 =Δ𝑥𝑥Δ𝑔𝑔

× Δ𝑔𝑔 = Δ𝑥𝑥

The distance 𝑑𝑑 travelled by a particle at constant acceleration 𝑎𝑎 is:

𝑑𝑑 =12ΔvΔ𝑔𝑔

× (Δ𝑔𝑔)2

Obviously the distance is greater than constant motion due to increasing speed.

Dist

ance

(spa

ce)

Time

Δ𝑥𝑥

Δ𝑔𝑔𝑣𝑣 =

Δ𝑥𝑥Δ𝑔𝑔

𝑎𝑎


NEWTON’S 2ND LAWTo be continued on CM [011]:

ABCC

cm [010] galileo's acceleration & newton's laws

Science