College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Chapter 4, Problem 26PE
When landing after a spectacular somersault, a 40.0-kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion.
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Students have asked these similar questions
Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
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)…
Chapter 4 Solutions
College Physics
Ch. 4 - Propose a force standard different from the...Ch. 4 - What properties do forces have that allow us to...Ch. 4 - How are inertia and mass related?Ch. 4 - What is the relationship between weight and mass?...Ch. 4 - Which statement is correct? (a) Net force causes...Ch. 4 - Why can we neglect forces such as those holding a...Ch. 4 - Explain how the choice of the “Stem of interest”...Ch. 4 - Describe a situation in which the net external...Ch. 4 - A system can have a nonzero velocity while the net...Ch. 4 - A rock is thrown straight up. What is the net...
Ch. 4 - (a) Give an example of different net external...Ch. 4 - If the acceleration of a system is zero, are no...Ch. 4 - If a constant, nonzero force is applied to an...Ch. 4 - The gravitational force on the basketball in...Ch. 4 - When you take off in a jet aircraft, there is a...Ch. 4 - A device used since the 1940s to measure the kick...Ch. 4 - Describe a Situation in which one a force on and,...Ch. 4 - Why does an ordinary rifle recoil (kick backward)...Ch. 4 - An American football lineman reasons that it is...Ch. 4 - Newton's third law of motion tells us that forces...Ch. 4 - If a leg is suspended by a traction setup as shown...Ch. 4 - Ina traction setup a broken bone, with pulleys and...Ch. 4 - To simulate the apparent weightlessness of space...Ch. 4 - A cartoon shows the toupee coming off the head of...Ch. 4 - Explain, in terms of the properties of the four...Ch. 4 - What is the dominant force between astronomical...Ch. 4 - Give a detailed example of the exchange of a...Ch. 4 - A 63.0-kg sprinter starts a race with an...Ch. 4 - If the sprinter from the previous problem...Ch. 4 - A cleaner pushes a 4.50-kg laundry cart in such a...Ch. 4 - Since astronauts in orbit are apparently...Ch. 4 - In Figure 4.7, the net external force on the 24-kg...Ch. 4 - The same rocket sled drawn in Figure 4.31 is...Ch. 4 - (a) If the rocket sled shown in Figure 4.32 starts...Ch. 4 - What is the deceleration of the rocket sled if it...Ch. 4 - Suppose two children push horizontally, but in...Ch. 4 - A powerful motorcycle can produce an acceleration...Ch. 4 - The rocket sled shown in Figure 4.33 accelerates...Ch. 4 - Repeat the previous problem for the situation in...Ch. 4 - The weight of an astronaut plus his space suit on...Ch. 4 - Suppose the mass of a fully loaded module in which...Ch. 4 - What net external force is exerted on a 1100-kg...Ch. 4 - A brave but inadequate rugby player is being...Ch. 4 - Two teams of nine members each engage in a tug of...Ch. 4 - What force does a trampoline have to apply to a...Ch. 4 - (a) Calculate the tension in a vertical strand of...Ch. 4 - Suppose a 60.0-kg gymnast climbs a rope. (a) What...Ch. 4 - Show that, as stated in the text, a force F...Ch. 4 - Consider the baby being weighed in Figure 4.34....Ch. 4 - A 5.00105 -kg rocket is accelerating straight up....Ch. 4 - The wheels of a midsize car exert a force of 2100...Ch. 4 - Calculate the force a 70.0-kg high jumper must...Ch. 4 - When landing after a spectacular somersault, a...Ch. 4 - A freight train consists of two 8.00104 -kg...Ch. 4 - Commercial airplanes are sometimes pushed out of...Ch. 4 - A 1100-kg car pulls a boat on a trailer. (a) What...Ch. 4 - (a) Find the magnitudes of the forces F1 and F2...Ch. 4 - Two children pull a third child on a snow saucer...Ch. 4 - Suppose your car was mired deeply in the mud and...Ch. 4 - What force is exerted on the tooth in Figure 4.38...Ch. 4 - Figure 4.39 shows Superhero and Trusty Sidekick...Ch. 4 - A nurse pushes a cart by exerting a force on the...Ch. 4 - Construct Your Own Problem Consider the tension in...Ch. 4 - Construct Your Own Problem Consider people pushing...Ch. 4 - Unreasonable Results (a) Repeat Exercise 4.29, but...Ch. 4 -
Ch. 4 - A flea jumps by exerting a force of 1.20105 N...Ch. 4 - Two muscles in the back of the leg pull upward on...Ch. 4 - A 76.0-kg person is being pulled away from a...Ch. 4 - Integrated Concepts A 35.0-kg dolphin decelerates...Ch. 4 - Integrated Concepts When starting a foot race, a...Ch. 4 - Integrated Concepts A large rocket has a mass of...Ch. 4 - Integrated Concepts A basketball player jumps...Ch. 4 - Integrated Concepts A 2.50-kg fireworks shell is...Ch. 4 - Integrated Concepts Repeat Exercise 4.47 for a...Ch. 4 - Integrated Concepts An elevator filled with...Ch. 4 - Unreasonable Results (a) What is the final...Ch. 4 - Unreasonable Results A 75.0-kg man stands on a...Ch. 4 - (a) What is the strength of the weak nuclear force...Ch. 4 - (a) What is the ratio of the strength of the...Ch. 4 - What is the ratio of the strength of the strong...
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