Forces Outcome: SCI10-FM4 Explore the relationship between force and motion for objects moving in one and two dimensions. [SI, TPS]

Study of Forces Begins.. May the force be with you. 325 AD – Greek philosopher Aristotle developed a theory that heavier objects must fall faster than lighter ones. In 1589 that someone dared to question Aristotle. This someone was not just anyone…

Who was it? It was Galileo Galilei. He threw two balls of very different weights from the top of the Pisa tower. The heavy one arrived only shortly before, but he explained this short delay by a difference of air resistance. If it weren’t for air, all objects would fall equally fast. Galileo derived his conclusion from a thought experiment that proved Aristotle’s theory wrong.

What was the thought experiment?

According to Aristotle’s theory… On one hand, the weight of the basketball is less and so it should pull the weight of the other ball, making it fall slower. On the other hand, the weights are heavier so they should fall faster than the bowling ball alone. Therefore, Aristotle’s theory predicts both one thing and its opposite. The theory contradicts itself! Free Falling Objects: https://www.youtube.com/watch?v=aRhkQTQxm4w Free falling objects in a vacuum (no air resistance) https://www.youtube.com/watch?v=E43-CfukEgs

Aristotle thought that objects were falling at different speeds according to their weights. But, cleverly, Galileo noticed that gravity didn’t determine the speed of falling objects. Instead, it determined their accelerations. What does that mean? And how did he figure that out? Throw a ball upwards. It is evidently not falling down at a constant speed, since it is not even falling down. Yet, for Galileo, it was already in free fall, and there wasn’t much difference between a ball going upwards and a ball going downwards.

Imagine that you threw the object upwards at a speed of 20 meters per second. After 1 second: it would slow down its upwards motion, and be going upwards at 10 meters per second. After 2 seconds: it would no longer be going upwards. After 3 seconds: it would start falling down at 10 meters per second. What happens at 4 seconds?

After 4 seconds: it would fall down at 20 meters per second. Galileo noticed that the downwards speed would increase by 10 meters per second every second. In more rigorous terms, Galileo figured out that gravity caused a downwards acceleration of 10 meters per second square – 9.8 m/s/s to be exact. Therefore all objects have an acceleration due to gravity (g) of  9.8 m/s2 downward towards the earth.

If acceleration due to gravity (g) is 9 If acceleration due to gravity (g) is  9.8 m/s2 downward towards the earth… How fast would something fall if you dropped it off a cliff?

If acceleration due to gravity (g) is 9 If acceleration due to gravity (g) is  9.8 m/s2 downward towards the earth… How fast would something fall if you dropped it off a cliff? Recall that acceleration is the rate at which an object changes its velocity. “g” ag= Δv= 9.8m/s t 1s

If acceleration due to gravity (g) is 9 If acceleration due to gravity (g) is  9.8 m/s2 downward towards the earth… How fast would something fall if you dropped it off a cliff? Recall that acceleration is the rate at which an object changes its velocity. “g” ag= Δv= -9.8m/s t 1s

If acceleration due to gravity (g) is 9 If acceleration due to gravity (g) is  9.8 m/s2 downward towards the earth… How fast would something fall if you dropped it off a cliff? Recall that acceleration is the rate at which an object changes its velocity. “g” ag= Δv= -9.8m/s t 1s

If acceleration due to gravity (g) is 9 If acceleration due to gravity (g) is  9.8 m/s2 downward towards the earth… If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 9.8 2 19.6 3 29.4 4 39.2 5 49.0

How do we calculate acceleration due to gravity if something goes up in the air? Since acceleration due to gravity is 9.8 m/s2 downwards towards the earth, the acceleration of something up and away from the earth would make it a negative value (-9.8 m/s2). Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed.

Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed. In the question the velocity upwards is positive. The acceleration due to gravity as a negative number, since gravity always acts down.

Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed. In the question the velocity upwards is positive. The acceleration due to gravity as a negative number, since gravity always acts down. vf = vi + at

Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed. In the question the velocity upwards is positive. The acceleration due to gravity as a negative number, since gravity always acts down. vf = vi + at = 56.3m/s + (-9.81m/s2)(4.52s)

Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed. In the question the velocity upwards is positive. The acceleration due to gravity as a negative number, since gravity always acts down. vf = vi + at = 56.3m/s + (-9.81m/s2)(4.52s) vf = 12.0 m/s

Example 1: A ball is thrown up into the air at an initial velocity of 56.3m/s. Determine its velocity after 4.52s have passed. In the question the velocity upwards is positive. The acceleration due to gravity as a negative number, since gravity always acts down. vf = vi + at = 56.3m/s + (-9.81m/s2)(4.52s) vf = 12.0 m/s This value is still positive, but smaller. The ball is slowing down as it rises into the air.

Example 2: I throw a ball down off the top of a cliff so that it leaves my hand at 12m/s. Determine how fast is it going 3.47 seconds later.

Example 2: I throw a ball down off the top of a cliff so that it leaves my hand at 12m/s. Determine how fast is it going 3.47 seconds later.   vf = vi + at

Example 2: I throw a ball down off the top of a cliff so that it leaves my hand at 12m/s. Determine how fast is it going 3.47 seconds later.   vf = vi + at = 12m/s + (9.81m/s2)(3.47s)

Example 2: I throw a ball down off the top of a cliff so that it leaves my hand at 12m/s. Determine how fast is it going 3.47 seconds later.   vf = vi + at = 12m/s + (9.81m/s2)(3.47s) vf = 46 m/s

Example 2: I throw a ball down off the top of a cliff so that it leaves my hand at 12m/s. Determine how fast is it going 3.47 seconds later.   vf = vi + at = 12m/s + (9.81m/s2)(3.47s) vf = 46 m/s Here the number is getting bigger. It’s speeding up in the positive direction.

Gee’s All this means is that they are comparing the acceleration they are feeling to regular gravity. So, right now, you are experiencing 1g… regular gravity. During lift-off the astronauts in the space shuttle experience about 4g’s. That works out to about 39m/s2. Gravity on the moon is about 1.7m/s2 = 0.17g

Acceleration due to Gravity Solving for distance… Consider up and down direction as on the y-axis Then y = height Y = .5 gt2

Acceleration due to Gravity Y = .5 gt2 Example: A stone tumbles into a mine shaft and strikes bottom after falling for 4.2 seconds. How deep is the mine shaft?

Acceleration due to Gravity Y = .5 gt2 Example: A stone tumbles into a mine shaft and strikes bottom after falling for 4.2 seconds. How deep is the mine shaft? Y= .5 (9.8m/s2)(4.2 s)(4.2s)

Acceleration due to Gravity Y = .5 gt2 Example: A stone tumbles into a mine shaft and strikes bottom after falling for 4.2 seconds. How deep is the mine shaft? Y= .5 (9.8m/s2)(4.2 s)(4.2s)

Acceleration due to Gravity Y = .5 gt2 Example: A stone tumbles into a mine shaft and strikes bottom after falling for 4.2 seconds. How deep is the mine shaft? Y= .5 (9.8m/s2)(4.2 s)(4.2s) = 86 meters

From Galileo to Newton http://www.biography.com/people/isaac-newton-9422656 So what are Newton’s three laws? Law of Inertia An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. https://www.youtube.com/watch?v=TQxeutcYP6I

Newton’s second law 2. The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. Expressed as… Force (in Newtons or N)= Mass x acceleration OR F = MA https://www.youtube.com/watch?v=M6iI5T3Yzbo https://www.youtube.com/watch?v=IRuSxTjLlSU

Newton’s Third Law 3. For every action, there is an equal and opposite reaction. https://www.youtube.com/watch?v=8bTdMmNZm2M&index=31&list=PL772556F1EFC4D01C https://www.youtube.com/watch?v=cP0Bb3WXJ_k&list=PLlwib77IOrGGqlNBnl7Fs-tlxnF7QUkYO