Consider the waves in Figure 17.8 to be waves on a stretched string. Define the velocity of elements of the string as positive if they are moving upward in the figure. (i) At the moment the string has the shape shown by the red-brown curve in Figure 17.8a, what is the instantaneous velocity of elements along the string? (a) zero for all elements (b) positive for all elements (c) negative for all elements (d) varies with the position of the element (ii) From the same choices, at the moment the string has the shape shown by the red-brown curve in Figure 17.8b, what is the instantaneous velocity of elements along the string?
Consider the waves in Figure 17.8 to be waves on a stretched string. Define the velocity of elements of the string as positive if they are moving upward in the figure. (i) At the moment the string has the shape shown by the red-brown curve in Figure 17.8a, what is the instantaneous velocity of elements along the string? (a) zero for all elements (b) positive for all elements (c) negative for all elements (d) varies with the position of the element (ii) From the same choices, at the moment the string has the shape shown by the red-brown curve in Figure 17.8b, what is the instantaneous velocity of elements along the string?
Consider the waves in Figure 17.8 to be waves on a stretched string. Define the velocity of elements of the string as positive if they are moving upward in the figure. (i) At the moment the string has the shape shown by the red-brown curve in Figure 17.8a, what is the instantaneous velocity of elements along the string? (a) zero for all elements (b) positive for all elements (c) negative for all elements (d) varies with the position of the element (ii) From the same choices, at the moment the string has the shape shown by the red-brown curve in Figure 17.8b, what is the instantaneous velocity of elements along the string?
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 18 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Wave Speed on a String - Tension Force, Intensity, Power, Amplitude, Frequency - Inverse Square Law; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=vEzftaDL7fM;License: Standard YouTube License, CC-BY