Newton's Gravitational Conjecture
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Questions and Answers

What is the formula for the centripetal acceleration in uniform circular motion?

  • $a = v \times r$
  • $a = \frac{{v^2}}{{r}}$ (correct)
  • $a = \frac{{r}}{{v^2}}$
  • $a = r - v$

    • What is the centripetal force formula?

  • $F_c = \frac{{m}}{{r}}$
  • $F_c = m \times r$
  • $F_c = m \times a$
  • $F_c = \frac{{m \times v^2}}{{r}}$ (correct)

    • What is Newton's Third Law of Motion?

  • The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
  • An object that exerts a force on another object also experiences an equal force from that other object but in the opposite direction. (correct)
  • An object in motion stays in motion unless acted upon by an external force.
  • The force acting on an object is equal to the mass of the object multiplied by its acceleration.

    • In the context of Newton's third law, what forces are equal but opposite?

    <p>Action and reaction forces</p> Signup and view all the answers

    According to Newton’s third law, what is the magnitude of the pull that the moon exerts on Earth?

    <p>$2 x 10^26$ Newtons</p> Signup and view all the answers

    What did Sir Isaac Newton use as leverage to figure out his law of universal gravitation?

    <p>The geometry of the path</p> Signup and view all the answers

    What forms the small blue base of the velocity triangle?

    <p>$\Delta v$</p> Signup and view all the answers

    In the proportionality ratios for the isosceles triangles, what does $r$ represent?

    <p>Radius of the Nardo Ring</p> Signup and view all the answers

    What happens to your left hip when the bus turns right?

    <p>It collides with the seat to the left</p> Signup and view all the answers

    What happens to your right hip when the bus turns left?

    <p>It gets bumped unless stabilized with a grab bar</p> Signup and view all the answers

    What does locking onto a grab bar do?

    <p>Fixes your position in the bus</p> Signup and view all the answers

    What happens if a person fails to brace when the bus slows down?

    <p>They get thrown forward</p> Signup and view all the answers

    What can be a good way to meet people, according to the text?

    <p>Following the law of inertia</p> Signup and view all the answers

    What is a more serious example of the law of inertia mentioned in the text?

    <p>The effects of whiplash in a car accident</p> Signup and view all the answers

    What is the reason for automobiles to have head restraints and airbags?

    <p>To protect against whiplash in a car accident</p> Signup and view all the answers

    What does Newton's second law of motion state?

    <p>Acceleration is directly proportional to net force and inversely proportional to mass</p> Signup and view all the answers

    According to Newton's second law, how does acceleration change in relation to mass and net force?

    <p>Acceleration is directly proportional to mass but inversely proportional to net force.</p> Signup and view all the answers

    In one dimension, how are forces added up?

    <p>Addition of forces like positive and negative numbers.</p> Signup and view all the answers

    What does a negative number represent when working in one dimension?

    <p>Leftward quantity.</p> Signup and view all the answers

    What does force Fnet represent when two opposing forces are different sizes?

    <p>The larger force exceeds the smaller force.</p> Signup and view all the answers

    What does G control in the context of general relativity?

    <p>The size of the event horizon of a black hole</p> Signup and view all the answers

    If our star, the Sun, could be squeezed to a sphere of about 3 kilometer radius, what would it become?

    <p>A black hole</p> Signup and view all the answers

    What did Halley predict would return in the year 1758?

    <p>A comet</p> Signup and view all the answers

    What was Halley's interest in comets according to Newton's theory of universal gravitation?

    <p>Their precise orbits in the gravitational field of the Sun</p> Signup and view all the answers

    What is the event horizon of a black hole?

    <p>The point beyond which nothing can escape the black hole</p> Signup and view all the answers

    What did Halley and Newton successfully verify with their predictions and observations?

    <p>Newton's theory of universal gravitation</p> Signup and view all the answers

    What is the upward force that balances the weight force experienced by the objects?

    <p>Normal force</p> Signup and view all the answers

    At what point does the upward drag force balance the downward weight force, resulting in the skydiver reaching a constant speed?

    <p>When the drag force equals the weight force</p> Signup and view all the answers

    What is the direction of the acceleration on a circular path at constant speed?

    <p>Perpendicular to the path</p> Signup and view all the answers

    What does the term 'centripetal' refer to in the context of circular motion?

    <p>Acceleration pointing toward the center</p> Signup and view all the answers

    What is the name of the large circular test track in Nardo where European automakers test their vehicles at high speed?

    <p>Nardo Ring</p> Signup and view all the answers

    What is responsible for increasing resistance as a skydiver's speed increases?

    <p>Drag force</p> Signup and view all the answers

    In what direction is the acceleration on a circular path at constant speed?

    <p>'Fleeing' from the circle's center</p> Signup and view all the answers

    What do we call the arrow points away from the center in dynamic terms?

    <p>Centrifugal arrow</p> Signup and view all the answers

    Which force opposes his fall as his speed increases?

    <p>Drag force</p> Signup and view all the answers

    The Nardo Ring has lanes banked sufficiently for vehicles to travel at a constant speed of __________ m/s.

    <p>66.7</p> Signup and view all the answers

    The change in velocity's direction as a vehicle goes around the track is due to __________.

    <p>Radial acceleration</p> Signup and view all the answers

    What did the ancient Greeks believe was circling around Earth, carrying the stars on their paths?

    <p>A clear crystalline sphere</p> Signup and view all the answers

    What held the Jovian moons in predictable orbits around Jupiter?

    <p>Gravity</p> Signup and view all the answers

    What did Newton describe in his book Principia as having a total period of repetitive motion of 2 seconds?

    <p>A pendulum oscillating in Paris</p> Signup and view all the answers

    What did Newton use to make a very nice calculation of the moon’s centripetal acceleration?

    <p>Force that keeps the moon on orbit</p> Signup and view all the answers

    What did Sir Isaac Newton know about the force of gravity on Earth?

    <p>It controls the pendulum's tick tock</p> Signup and view all the answers

    What did the length of the pendulum set up in Paris equal to, according to Newton?

    <p>The drop distance for 1 second of free fall</p> Signup and view all the answers

    What did Newton assume when discussing gravity?

    <p>Mean distance of 60 Earth radii for Earth-moon distance</p> Signup and view all the answers

    What did Sir Isaac Newton use to measure Earth's circumference?

    <p>'Ticking' and 'tocking' pendulum</p> Signup and view all the answers

    Why did Newton decide to work with a round figure when discussing gravity?

    <p>To simplify calculations</p> Signup and view all the answers

    How precise was French mathematician Jean Picard's measurement of Earth’s circumference?

    <p>~0.2% above NASA’s modern value</p> Signup and view all the answers

    What did Newton use to make a very nice calculation of the moon’s centripetal acceleration?

    <p>Force that keeps the moon on orbit</p> Signup and view all the answers

    What was necessary for Galileo, Newton, and Halley to understand about stars and planets?

    <p>What orders the stars and planets in their courses.</p> Signup and view all the answers

    What did Newton estimate in terms of the moon's fall?

    <p>The distance the moon would fall if held at 60 Earth radii away and dropped</p> Signup and view all the answers

    In which unit did Newton estimate the distance the moon would fall?

    <p>Paris feet and inches</p> Signup and view all the answers

    What pattern from astronomical observations did Newton build his conjecture on?

    <p>Patterns in the behavior of satellites of Jupiter</p> Signup and view all the answers

    In what book did Sir Isaac Newton write his first statement of the law of gravitation?

    <p>Book III of Principia</p> Signup and view all the answers

    What is the formula for the gravitational force according to the text?

    <p>$F = G\frac{m_1m_2}{r^2}$</p> Signup and view all the answers

    How does one convert square meters in the denominator into Newtons of force?

    <p>Using a conversion factor</p> Signup and view all the answers

    What physically measurable quantity might go into the numerator of the formula for gravitational force?

    <p>Mass and distance</p> Signup and view all the answers

    What is the metric unit of force mentioned in the text?

    <p>$kg m/s^2$</p> Signup and view all the answers

    What is the multiplicative constant known as in the text?

    <p>&quot;Newton's Constant&quot;</p> Signup and view all the answers

    Who set out to measure the gravitational force of a mountain named Schiehallion?

    <p>Nevil Maskelyne</p> Signup and view all the answers

    How did Henry Cavendish make a more precise measurement of gravitational force?

    <p>Using large lead spheres and a very precise balance</p> Signup and view all the answers

    What could be calculated using Henry Cavendish's measurements?

    <p>The value for Newton's constant, G</p> Signup and view all the answers

    What is the weight force of the 5.0 kg box of hammers?

    <p>5.0 N</p> Signup and view all the answers

    When two forces act on an object in two different directions, what determines the direction of the resulting acceleration?

    <p>The diagonal of a parallelogram formed by the two forces</p> Signup and view all the answers

    How can the size of the net force be computed when two forces act together but in different directions?

    <p>By using the Pythagorean Theorem</p> Signup and view all the answers

    In the dragster example, what balances the weight force acting upon it?

    <p>Rigidity force from concrete and asphalt</p> Signup and view all the answers

    Why does the dragster not trench itself into the track even though it has a downward weight force and a forward force?

    <p>Because the track provides an upward rigidity force</p> Signup and view all the answers

    What would happen if a dragster were to race on a pool of liquid water?

    <p>The dragster would sink into the water</p> Signup and view all the answers

    What is responsible for providing an upward rigidity force that balances the weight force on a drag strip?

    <p>Rigidity force from concrete and asphalt</p> Signup and view all the answers

    Why use liquid water as an example of what a race track is not?

    <p>To highlight that a dragster cannot race on liquid water</p> Signup and view all the answers

    What does the 'normal' force refer to in this context?

    <p>The perpendicular force to a surface due to molecular bonds holding together</p> Signup and view all the answers

    What did Sir Isaac Newton describe as a resistance to changes in the state of motion unless some unbalanced force acts on the object?

    <p>The law of inertia</p> Signup and view all the answers

    What is an interesting way to understand Newton’s First Law of Motion, according to the text?

    <p>Taking a trip on the UCF shuttle bus</p> Signup and view all the answers

    What happens if a person fails to brace when the bus slows down, according to the text?

    <p>They bump into the seat next to them</p> Signup and view all the answers

    According to Sir Isaac Newton's First Law of Motion, what does every object persevere in unless compelled to change by forces acting upon it?

    <p>Its state of rest or constant velocity</p> Signup and view all the answers

    What is the main focus of Newton’s first law of motion?

    <p>The resistance to changes in the state of motion</p> Signup and view all the answers

    How does Newton describe inertia in his first law of motion?

    <p>As indifference to being at rest or in constant velocity</p> Signup and view all the answers

    What does the example of the UCF shuttle bus illustrate about Newton's first law of motion?

    <p>The resistance to changes in the state of motion</p> Signup and view all the answers

    Why do passengers need to stabilize themselves on the UCF shuttle bus?

    <p>To counteract the forces changing the bus's state of motion</p> Signup and view all the answers

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