College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Textbook Question
Chapter 6, Problem 13PE
The propeller of a World War Il fighter plane is 2.30 m in diameter.
(a) What is its
(b) What is the linear speed of its tip at this angular velocity if the plane is stationary on the tarmac?
(c) What is the centripetal acceleration of the propeller tip under these conditions? Calculate it in meters per second squared and convert to multiples of g.
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SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
How does boiling point of water decreases as the altitude increases?
Chapter 6 Solutions
College Physics For Ap® Courses
Ch. 6 - There an analogy between rotational and physical...Ch. 6 - Can centripetal acceleration change the speed of...Ch. 6 - If you wish to reduce the stress (which related to...Ch. 6 - Define centripetal force. Can any type of force...Ch. 6 - If centripetal force is directed toward the...Ch. 6 - Pace car drivers routinely cut corners as shown in...Ch. 6 - A number of amusement parks have rides that make...Ch. 6 - What is the direction of the force exerted by the...Ch. 6 - As a skater forms a circle, what force is...Ch. 6 - Suppose a child is riding on a merry-go-round at a...
Ch. 6 - Do you feel yourself thrown to either side when...Ch. 6 - Suppose a mass is moving in a circular path on a...Ch. 6 - When a toilet is flushed or a sink is drained,...Ch. 6 - Is there a real force that throws water from...Ch. 6 - In one amusement park ride, riders enter a large...Ch. 6 - Actin at a distance, such as is the case for...Ch. 6 - Two friends are having a conversation. Anna says a...Ch. 6 - A frame of reference placed at the center of the...Ch. 6 - Action at a distance, such as is the case for...Ch. 6 - Two friends are having a conversation. Anna says a...Ch. 6 - Draw a free body diagram for a satellite in an...Ch. 6 - Newton's laws of motion and gravity were among the...Ch. 6 - In what frame(s) of reference are Kepler's laws...Ch. 6 - Semi-trailer trucks have an odometer on one hub of...Ch. 6 - Microwave ovens rotate at a rate of about 6...Ch. 6 - An automobile with 0.260 m radius tires travels...Ch. 6 - (a) What is the period of rotation of Earth in...Ch. 6 - A baseball pitcher brings his arm forward during a...Ch. 6 - In lacrosse, a ball is thrown from a net on the...Ch. 6 - A truck with 0.420-m-radius tires travels at 32.0...Ch. 6 - Integrated Concepts When kicking a football, the...Ch. 6 - Construct Your Own Problem Consider an amusement...Ch. 6 - A fairground ride spins its occupants inside a...Ch. 6 - A runner taking part in the 200 m dash must run...Ch. 6 - Taking the age of Earth to be about 4109 years and...Ch. 6 - The propeller of a World War Il fighter plane is...Ch. 6 - An ordinary workshop grindstone has a radius of...Ch. 6 - Helicopter blades withstand tremendous stresses....Ch. 6 - Olympic ice skaters are able to spin at about 5...Ch. 6 - What percentage of the acceleration at Earth's...Ch. 6 - Verify that the linear speed of an ultracentrifuge...Ch. 6 - A rotating space station is said to create...Ch. 6 - At takeoff, a commercial jet has a 60.0 m/s speed....Ch. 6 - Integrated Concepts Riders in an amusement park...Ch. 6 - Unreasonable Results A mother pushes her child on...Ch. 6 - (a) A 22.0 kg child is riding a playground...Ch. 6 - Calculate the centripetal force on the end of a...Ch. 6 - What is the ideal banking angle for a gentle turn...Ch. 6 - What is the ideal speed to take a 100 m radius...Ch. 6 - (a) What is the radius of a bobsled turn banked at...Ch. 6 - Part of riding a bicycle involves leaning at the...Ch. 6 - A large centrifuge, like the one shown in Figure...Ch. 6 - Integrated Concepts If a car takes a banked curve...Ch. 6 - Modern roller coasters have vertical loops like...Ch. 6 - Unreasonable Results (a) Calculate the minimum...Ch. 6 - (a) Calculate Earth's mass given the acceleration...Ch. 6 - (a) Calculate the magnitude of the acceleration...Ch. 6 - (a) What is the acceleration due to gravity on the...Ch. 6 - (a) Calculate the acceleration due to gravity on...Ch. 6 - The Moon and Earth rotate about their common...Ch. 6 - Solve part (b) of Example 6.6 using ac=v2/r.Ch. 6 - Astrology, that unlikely and vague pseudoscience,...Ch. 6 - The existence of the dwarf planet Pluto was...Ch. 6 - (a) The Sun orbits the Milky Way galaxy once each...Ch. 6 - Unreasonable Result A mountain 10.0 km from a...Ch. 6 - A geosynchronous Earth satellite is one that has...Ch. 6 - Calculate the mass of the Sun based on data for...Ch. 6 - Find the mass of Jupiter based on data for the...Ch. 6 - Find the ratio of the mass of Jupiter to that of...Ch. 6 - Astronomical observations of our Milky Way galaxy...Ch. 6 - Integrated Concepts Space debris left from old...Ch. 6 - Unreasonable Results (a) Based on Kepler's laws...Ch. 6 - Construct Your Own Problem On February 14, 2000,...
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