College Physics For Ap® Courses
16th Edition
ISBN: 9781938168932
Author: Gregg Wolfe, Irina Lyublinskaya, Douglas Ingram
Publisher: OpenStax
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Chapter 9, Problem 20PE
Suppose you needed to raise a 250-kg mower a distance of 6.0 cm above the ground to change a tire. If you had a 2.0-m long lever, where would you place the fulcrum if your force was limited to 300 N?
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
seconds. If the radius of the wheel is 400mm. calculate
ii)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
Question 04
in 20
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]
Chapter 9 Solutions
College Physics For Ap® Courses
Ch. 9 - What can you say about the velocity of a moving...Ch. 9 - Under what conditions can a rotating body be in...Ch. 9 - What three factors affect the torque created by a...Ch. 9 - A wrecking ball is being used to knock down a...Ch. 9 - Mechanics put a length of Pipe over the handle of...Ch. 9 - A round pencil lying on its side as in Figure 9.13...Ch. 9 - Explain the need for tall towers on a suspension...Ch. 9 - When visiting some countries, you may see a person...Ch. 9 - Scissors are like a double-lever "Stem, Which of...Ch. 9 - Suppose you pull a nail at a constant rate using a...
Ch. 9 - Why are the forces exerted on the outside world by...Ch. 9 - Explain why the forces in our joints are several...Ch. 9 - Why are the forces exerted on the outside world by...Ch. 9 - Explain why the forces in our joints are several...Ch. 9 - Certain of dinosaurs were bipedal (walked on two...Ch. 9 - Swimmers and athletes during competition need to...Ch. 9 - If the maximum force the biceps muscle can exert...Ch. 9 - Suppose the biceps muscle was attached through...Ch. 9 - Explain one of the reasons why pregnant women...Ch. 9 - (a) When opening a door, you push on it...Ch. 9 - When tightening a bolt, you push perpendicularly...Ch. 9 - Two children push on opposite sides of a door...Ch. 9 - Use the second condition for equilibrium (net =0 )...Ch. 9 - Repeat the seesaw problem in Example 9.1 with the...Ch. 9 - Suppose a horse leans against a wall as in Figure...Ch. 9 - Two children of mass 20.0 kg and 30.0 kg sit...Ch. 9 - (a) Calculate the magnitude and direction of the...Ch. 9 - A person carries a plank of wood 2.00 m long with...Ch. 9 - A 17.0-m-high and 11.0-m-long wall under...Ch. 9 - (a) What force must be exerted by the wind to...Ch. 9 - Suppose the weight of the drawbridge in Figure...Ch. 9 - Suppose a 900-kg car is on the bridge in Figure...Ch. 9 - A sandwich board advertising sign is constructed...Ch. 9 - (a) What minimum coefficient of friction is needed...Ch. 9 - A gymnast is attempting to perform splits. From...Ch. 9 - To get up on the roof, a person (mass 70.0 kg)...Ch. 9 - In Figure 9.21, the cg of the pole held by the...Ch. 9 - What is the mechanical advantage of a nail puller...Ch. 9 - Suppose you needed to raise a 250-kg mower a...Ch. 9 - a) What is the mechanical advantage of a...Ch. 9 - A typical car has an axle with 1.10 cm radius...Ch. 9 - What force does the nail puller in Exercise 9.19...Ch. 9 - If you used an ideal pulley of the type shown in...Ch. 9 - Repeat Exercise 9.24 for the pulley shown in...Ch. 9 - Verity that the force in the elbow joint in...Ch. 9 - Two muscles in the back of the leg pull on the...Ch. 9 - The upper leg muscle (quadriceps) exerts a force...Ch. 9 - A device for exercising the upper leg muscle is...Ch. 9 - A person working at a drafting board may hold her...Ch. 9 - We analyzed the biceps muscle example with the...Ch. 9 - Even when the head is held erect, as in Figure...Ch. 9 - A 75-kg man stands on his toes by exerting an...Ch. 9 - A father lifts his child as shown in Figure 9.43....Ch. 9 - Unlike most of the other muscles in our bodies,...Ch. 9 - Integrated Concepts Suppose we replace the 4.0-kg...Ch. 9 - (a) What force should the woman in Figure 9.45...Ch. 9 - You have just planted a sturdy 2-m-tall palm tree...Ch. 9 - Unreasonable Results Suppose two children are...Ch. 9 - Construct Your Own Problem Consider a method for...
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