Questions and Answers
Match the following laws and terms with their definitions:
Kepler's Second Law of Motion = A line from planet to sun sweeps out equal areas in equal times Newton's Second Law of Motion = Acceleration is directly proportional to the force and inversely proportional to the mass Newton's Third Law of Motion = Every action produces an equal and opposite reaction Impulse = FΔt Gravitational mass = F/g Acceleration due to gravity = 32 ft/s²
How many years ago was evidence for a round earth first available?
The contribution of Tycho Brahe was primarily his:
The astronomer who was imprisoned by the church for announcing his scientific discoveries was:
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An impulse always produces a change in:
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If, in the above diagram, no gravitational force retarded the ball's movement, how far would the ball travel?
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If a cart of 2 kg mass has a force of 8 newtons exerted on it, what is its acceleration?
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If a cart of 4 kg mass has a force of 8 newtons exerted on it, what is its acceleration?
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The impulse given to a ball with a mass of 2 kg is 16 N*s. If the ball starts from rest, what is its final velocity?
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The impulse given to a ball with a mass of 2.0 kg is 16 N*s. If the ball were already moving at 3.0 m/s, what would the final velocity be?
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If a boy (m = 50kg) at rest on skates is pushed by another boy who exerts a force of 200 N on him, and if the first boy's final velocity is 8 m/s, what was the contact time?
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Calculate the force at sea level that a boy of mass 50 kg exerts on a chair in which he is sitting.
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If the 50 kg boy were in a spacecraft 5.0R from the center of the earth, what would his weight be?
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Objects on the moon's surface have an acceleration due to gravity one-sixth that on the earth's. What would the 50.0 kg boy weigh on the moon?
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If an object moves in uniform circular motion in a circle of radius R = 1.00 meter, and the object takes 4.00 seconds to complete ten revolutions, calculate the centripetal acceleration.
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An object moves in uniform circular motion at 25 m/s and takes 1.0 second to go a quarter circle. What is the radius of the circle?
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Calculate the centripetal acceleration for an object moving in uniform circular motion at 25 m/s and takes 1.0 second to go a quarter circle.
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Planet Geos in orbit a distance of 1 A.U. from the star Astra has an orbital period of 1 year. If planet Logos is 4 A.U. from Astra, how long does Logos require for a complete orbit?
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Our moon is 240,000 miles away and takes about 28 days to orbit the earth. How high up (in miles) would a satellite have to be placed if it were to orbit the earth in 24 hours?
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If an object is thrown in an upward direction from the top of a building 160 ft high at an initial speed of 21.82 mi/h, what is its final speed when it hits the ground?
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At a distance of 1 A.U., the earth takes one year to travel around the sun. How far away is a planet that takes eight years to go around the sun?
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A 20.0 kg cart travels at 10.0 m/s in a circle with a radius of 15.0 m. What is the centripetal force?
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A 2,000-kg car traveling at 40 m/s hits a wall with a force of 40,000 N and comes to a stop. What was the impact time?
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A 10,000-kg railroad car travels down the track at 30 m/s and hits a second stationary railroad car of 20,000 kg. The cars become coupled and continue traveling. Calculate the final velocity of the cars.
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Study Notes
Laws of Motion and Definitions
- Kepler's Second Law of Motion: A line from a planet to the sun sweeps out equal areas in equal times.
- Newton's Second Law of Motion: Acceleration is directly proportional to the force and inversely proportional to the mass (F = ma).
- Newton's Third Law of Motion: For every action, there is an equal and opposite reaction.
- Impulse: Impulse (FΔt) results in a change in momentum.
- Gravitational Mass: The measure of the amount of matter in an object, contributing to its weight.
- Acceleration due to Gravity: On Earth, it is approximately 9.8 m/s² or 32 ft/s².
Historical Contributions
- Evidence for a round Earth has been available for approximately 2200 years.
- Tycho Brahe significantly contributed to astronomy through his observations.
Key Figures in Astronomy
- Galileo: Astronomer known for his conflict with the church over his scientific discoveries.
- Mass and Acceleration: Acceleration can be calculated using Newton's Second Law, with examples producing results of 4 m/s² and 2 m/s² for different forces and masses.
Calculations Involving Impulse and Momentum
- An impulse of 16 N*s on a 2 kg ball results in a final velocity of 8 m/s.
- If the ball is initially moving at 3.0 m/s, the final velocity after the impulse is applied is 11 m/s.
Gravitational Forces and Weight
- A 50 kg boy exerts a gravitational force of 490 N when at sea level.
- Weight on the Moon: A 50 kg boy weighs approximately 81.7 N due to the Moon's lower gravity.
Circular Motion
- Centripetal acceleration can be calculated for objects in circular motion; for example, an object moving at a radius of 1 meter takes 4 seconds to complete ten revolutions results in an acceleration of 247 m/s².
- Objects moving in uniform circular motion at 25 m/s for one second over a quarter circle have a radius of 16 m and a centripetal acceleration of 39 m/s².
Orbital Mechanics
- The orbital period of planet Logos at 4 A.U. from a star taking 8 years to orbit implies distance and time relationships governed by Kepler’s laws.
- A satellite must be 26,000 miles high to orbit Earth synchronously with Earth’s rotation, taking 24 hours.
Motion and Impact
- An object thrown upward from a height of 160 ft with an initial speed of 21.82 mi/h has a final speed of 110 ft/s upon hitting the ground.
- Using the conservation of momentum, if a 10,000 kg railroad car traveling at 30 m/s collides with a stationary car, the final velocity of both is 10 m/s after coupling.
Net Forces
- When two forces act on an object (e.g., 8 N right and 6 N down), the resultant net force can be illustrated with vector diagrams for clarity.
Impact Time Calculation
- A 2,000 kg car impacting a wall with a force of 40,000 N comes to a stop in 2 seconds.
Important Distances in Astronomy
- The distance of 1 A.U. (astronomical unit) corresponds to the distance from the Earth to the Sun, where the Earth's orbital period is 1 year, establishing a framework to find distances of other celestial bodies.
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Test your knowledge on key concepts in dynamics with these flashcards. Match important laws of motion and definitions to solidify your understanding of physics principles. Perfect for students looking to review and prepare for exams.
