Galileo's Conclusion on Inclined Planes and Acceleration

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What was Galileo's main frustration with Aristotle's approach to physics?

Aristotle relied on philosophical hot air instead of measurable observations (correct)

Aristotle's principles of motion and stationariness were too complex

Aristotle's conclusions were based on human will rather than truth

Aristotle's book lacked authority compared to the great book of nature

According to Galileo, where does authority reside in the study of physics?

In the principles of motion and stationariness

In the renowned and influential works of Aristotle

In the philosophical conclusions of Aristotle

In the great book of nature, based on observation and measurement (correct)

How did Galileo simplify his task in teaching physics?

By relying on the renowned books of Aristotle

By focusing on philosophical concepts rather than measurable motions

By defending errors using philosophical hot air

By sticking to measurable motions and observations (correct)

What did Galileo emphasize as having the power to lock down a physical concept in his classes?

Observations of measurable quantities Signup and view all the answers

What force does the object experience to move along the horizontal plane?

0.02 metric units of force Signup and view all the answers

Which ratio is mentioned as the key in the example?

1:5 ratio of push force to weight force Signup and view all the answers

What is the weight of the spherical object?

0.10 metric units of force Signup and view all the answers

What does Professor Galileo ask the youngster to construct?

A right-angled triangle with a ratio of 1:5 between hypotenuse and height Signup and view all the answers

What does Professor Galileo hand over to the youngster to roll down the ramp?

A steel ball bearing of diameter 5 centimeters Signup and view all the answers

What is the size of the downhill force on the ball if the ramp is constructed with a ratio of 1:5?

0.02 units Signup and view all the answers

What is considered important according to Professor Galileo?

"Percent" terminology usage Signup and view all the answers

What does Aristotle advise the youngster to do?

"Apply some trigonometry" Signup and view all the answers

What does the youngster claim about keeping an object in motion at constant speed on a frictionless, horizontal plane?

"In general, a 1:5 ratio will do the job" Signup and view all the answers

"Do you recall how to calculate the size of that force down the ramp?" - Who says this?

"Professor Galileo" Signup and view all the answers

What are the dimensions of the inclined plane constructed by the youngster?

Height 1 unit of length and hypotenuse 5 units in length Signup and view all the answers

What was the focus of Aristotle's book Physics?

The motion of various objects in nature Signup and view all the answers

How did Aristotle differ from Galileo in their approach to studying motion?

Aristotle's approach was complicated, while Galileo simplified the study of motion. Signup and view all the answers

What did Galileo restrict his study of motion to?

Positions, distances, times, and intervals of time Signup and view all the answers

What concept did Galileo use as an exemplar of accelerated motion?

Free-fall acceleration Signup and view all the answers

According to Galileo, what happens to the downward speed during free fall on the surface of the Earth?

It increases continually at a rate of 9.8 m/sec Signup and view all the answers

What does Galileo customarily call the acceleration experienced by everyone on Earth?

G Signup and view all the answers

Where would astronauts in the International Space Station experience less acceleration?

In space above the surface of Earth Signup and view all the answers

"Is there a state in between accelerated states?" - This question refers to:

"event A in space and time" Signup and view all the answers

"This is what we mean about the acceleration of an object in free fall, that for every second of free fall in the gravitational field at the surface of Earth, the downward speed increases 9.8 m/sec" - This statement best exemplifies:

"the concept of free-fall acceleration" Signup and view all the answers

What is the main difference between Aristotle's and Galileo's approach to studying motion?

Aristotle considered non-measurable motions, while Galileo focused on measurable aspects. Signup and view all the answers

What was Galileo's first conclusion concerning free fall and vertical acceleration?

Inclined planes of equal heights but different tilt angles accelerate a ball to the same speed at the bottom of the ramp. Signup and view all the answers

How did Galileo explain the acceleration of an object on an inclined plane?

By showing that the fraction of g down the ramp accelerates the body, and the fraction into the ramp has no effect if the ramp is rigid. Signup and view all the answers

What did Galileo's analysis of a projectile's motion through its arc rest on?

The assumption that a projectile's path is a parabola and can be split into independently analyzable horizontal and vertical parts. Signup and view all the answers

What did Galileo teach his students about motion on an ideal, frictionless inclined plane compared to motion on an ideal, frictionless horizontal plane?

The object on the ramp gets a fraction of free fall force of gravity, but there is no force required for the object on the horizontal plane. Signup and view all the answers

What did Galileo envision about the motion of an object on a horizontal plane?

The object keeps moving out past the edge of the plane like a Ferrari driving off a cliff. Signup and view all the answers

What did Galileo assert about unperturbed motion horizontally at constant speed?

It is indifferent to being at rest or moving along a horizontal line at constant speed. Signup and view all the answers

How did Galileo explain motion using proportional triangles?

He used them to show that horizontal motion at constant speed is indifferent to being at rest. Signup and view all the answers

What was Galileo's conclusion concerning objects on frictionless inclined planes?

"An object on an inclined plane gets a small fraction of free fall force of gravity." Signup and view all the answers

What was Galileo's approach to teaching about motion on inclined planes compared to horizontal planes?

"He compared motions on both types of planes to highlight key differences in forces acting on objects." Signup and view all the answers

What did Galileo insist about motion horizontally at constant speed?

It allows for both rest and constant speed without any change in external forces. Signup and view all the answers

What was Galileo's conclusion regarding forces acting on objects on inclined planes compared to horizontal planes?

Objects experience different forces depending on whether they are on inclined or horizontal planes. Signup and view all the answers

What is the ratio of the downward push force on the ramp to the downward force on the horizontal, frictionless plane?

1:10 Signup and view all the answers

What is the significance of the number 10 in the context of the forces discussed?

It's a special number because it's the sum of the first four numbers. Signup and view all the answers

What did Galileo conclude about the force required to keep an object rolling at constant speed on a frictionless, horizontal plane?

It must be less than 0.01 units of force. Signup and view all the answers

What did the student realize about the value of the force required to keep the object at constant speed on a frictionless, horizontal plane?

It cannot be a positive number greater than 0. Signup and view all the answers

What did Professor Galileo conclude about the state of motion at constant speed and constant direction on a frictionless, horizontal surface?

It does not require any force to maintain. Signup and view all the answers

What was Aristotle's response after realizing his mistake regarding the force needed to keep an object rolling at constant speed on a frictionless, horizontal plane?

He insisted that a small positive force is still required. Signup and view all the answers

What did Galileo emphasize as crucial to the scientific enterprise?

Accurate computation modeling nature. Signup and view all the answers

What shape does the trajectory of a projectile take when launched from a frictionless, horizontal plane?

Parabola Signup and view all the answers

'We should therefore use _____ in the drop distance formula.' - What term fills in the blank?

$9.8m/s^2$ Signup and view all the answers

'How do you calculate the size of that force down the ramp?' - Who asks this question?

'You...' Signup and view all the answers

'Is there a state in between accelerated states?' - This question refers to:

'A state of motion at constant speed and constant direction.' Signup and view all the answers