University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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Textbook Question
Chapter 7, Problem 12CQ
Work done on a system puts energy into it. Work done by a system removes energy from it. Give an example for each statement.
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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 7 Solutions
University Physics Volume 1
Ch. 7 - Check Your Understanding Can kinetic friction ever...Ch. 7 - Check Your Understanding Can Earth’s gravity ever...Ch. 7 - Check Your Understanding Find the work done by the...Ch. 7 - Check Your Understanding The spring Example 7.5 is...Ch. 7 - Check Your Understanding (a) A car and a truck...Ch. 7 - Check Your Understanding You are rowing a boat...Ch. 7 - Check Your Understanding suppose the radius of the...Ch. 7 - Check Your Understanding Estimate the power...Ch. 7 - Give an example of something we think of as work...Ch. 7 - Give an example of a situation in which there is a...
Ch. 7 - Describe a situation in 4iich a force is exerted...Ch. 7 - A body moves in a circle at constant speed. Does...Ch. 7 - Suppose you throw a ball upward and catch it when...Ch. 7 - Why is it more difficult to do sit-ups while on a...Ch. 7 - As a young man, Tarzan climbed up a vine to reach...Ch. 7 - A particle of m has a velocity of . Is its kinetic...Ch. 7 - One particle has mass mand a second particle has...Ch. 7 - A person drops a pebble of mass m1from a height h,...Ch. 7 - The person shown below does work on the lawn...Ch. 7 - Work done on a system puts energy into it. Work...Ch. 7 - Two marbles of masses mand 2mare dropped from a...Ch. 7 - Compare the work required to accelerate a car of...Ch. 7 - Suppose you are jogging at constant velocity. Are...Ch. 7 - Two forces act to double the speed of a particle,...Ch. 7 - Most electrical appliances are rated in watts....Ch. 7 - Explain, in terms of the definition of power, why...Ch. 7 - A spark of static electricity, such as that you...Ch. 7 - Does the work done in lifting an object depend on...Ch. 7 - Can the power expended by a force be negative?Ch. 7 - How can a 50-W light bulb use more energy than a...Ch. 7 - Work How much work does a supermarket checkout...Ch. 7 - A 75.0-kg person climbs stairs, gaining 2.50 m in...Ch. 7 - (a) Calculate the work done on a 1500-kg elevator...Ch. 7 - Suppose a car travels 108 km at a speed of 30.0...Ch. 7 - Calculate the work done by an 85.0-kg man who...Ch. 7 - How much work is done by the boy pulling his...Ch. 7 - A shopper pushes a grocery cart 20.0 m at constant...Ch. 7 - Suppose the ski patrol lowers a rescue sled and...Ch. 7 - A constant 20-N force pushes a small ball in the...Ch. 7 - A toy cart is pulled a distance of 6.0 m in a...Ch. 7 - A 5.0-kg box rests on a horizontal surface. The...Ch. 7 - A sled plus passenger with total mass 50 kg is...Ch. 7 - Suppose that the sled plus passenger of the...Ch. 7 - How much work does the force do on a particle as...Ch. 7 - How much work is done against the gravitationaI...Ch. 7 - It takes 500 J of work to compress a spring 10 cm....Ch. 7 - A bungee cord is essentially a very long rubber...Ch. 7 - A bungee cord exerts a nonlinear elastic force of...Ch. 7 - Engineers desire to model the magnitude of the...Ch. 7 - A particle moving in the xy -plane is subject to a...Ch. 7 - A particle moves along a curved path...Ch. 7 - Kinetic Energy Compare the kinetic energy of a...Ch. 7 - (a) How fast must a 3000-kg elephant move to have...Ch. 7 - Estimate the kinetic energy of a 90,000-ton...Ch. 7 - Calculate the kinetic energies of (a) a 2000.0-kg...Ch. 7 - A 5.0-kg body has three times the kinetic energy...Ch. 7 - An 8.0-g bullet has a speed of 800 m/s. (a) What...Ch. 7 - (a) Calculate the force needed to bring a 950-kg...Ch. 7 - A car’s bumper is designed to withstand a 4.0-km/...Ch. 7 - Boxing gloves are padded to lessen the force of a...Ch. 7 - Using energy considerations, calculate the average...Ch. 7 - A 5.0-kg box has an acceleration of 2.0m/s2 when...Ch. 7 - A constant 10-N horizontal force is applied to a...Ch. 7 - In the preceding problem, the 10-N force is...Ch. 7 - Compare the work required to stop a 100-kg crate...Ch. 7 - A wagon with its passenger sits at the top of a...Ch. 7 - An 8.0-g bullet with a speed of 800 m/s is shot in...Ch. 7 - A 2.0-kg block starts with a speed of 10 m/s at...Ch. 7 - When a 3.0-kg block is pushed against a massless...Ch. 7 - A small block of mass 200 g starts at rest at A,...Ch. 7 - A small object is placed at the top of an incline...Ch. 7 - When released, a 100-g block slides down the path...Ch. 7 - A 0.22LR-caliber bullet like that mentioned in...Ch. 7 - A sled stalls from rest at the top of a...Ch. 7 - A person in good physical condition can put out...Ch. 7 - What is the cost of operating a 3.00-W electric...Ch. 7 - A large household air conditioner may consume 15.0...Ch. 7 - (a) What is the average power consumption in watts...Ch. 7 - (a) What is the average useful power output of a...Ch. 7 - A 500-kg dragster accelerates from rest to a final...Ch. 7 - (a) How long will it take an 850-kg car with a...Ch. 7 - (a) Fir the useful power output of an elevator...Ch. 7 - (a) How long would it take a 1.50105kg airplane...Ch. 7 - Calculate the power output needed for a 950-kg car...Ch. 7 - A man of mass 80 kg runs up a flight of stairs 20...Ch. 7 - The man of the preceding problem consumes...Ch. 7 - An electron in a television tube is accelerated...Ch. 7 - Coal is lifted out of a mine a vertical distance...Ch. 7 - A girl pulls her 15-kg wagon along a flat sidewalk...Ch. 7 - A typical automobile engine has an efficiency of...Ch. 7 - When jogging at 13 km/h on a level surface, a...Ch. 7 - A cart is pulled a distance D on a flat,...Ch. 7 - Consider a particle on which several forces act,...Ch. 7 - Consider a particle on which several forces act,...Ch. 7 - Consider a particle on which several forces act,...Ch. 7 - Consider a particle on which a force acts that...Ch. 7 - A boy pulls a 5-kg cart with a 20-N force at an...Ch. 7 - A crate of mass 200 kg is to be bright from a site...Ch. 7 - At hokey puck of mass 0.17 kg is shot across a...Ch. 7 - A horizontal force of 20 N is required to keep a...Ch. 7 - A 7.0-kg box slides along a horizontal...Ch. 7 - You are driving your car on a straight road with a...Ch. 7 - A crate is being pushed across a rough floor...Ch. 7 - Suppose a horizontal force of 20 N is required to...Ch. 7 - Grains from a hopper falls at a rate of 10 kg/s...Ch. 7 - A cyclist in a race must climb a 5 hill at a speed...Ch. 7 - Shown below is a 40-kg crate that is pushed at...Ch. 7 - The surface of the preceding problem is modified...Ch. 7 - The force F(x) varies with position, as shown...Ch. 7 - Find the work done by the same force in Example...Ch. 7 - Answer the preceding problem using polar...Ch. 7 - Find the work done by the same force in Example...Ch. 7 - Answer the preceding problem using polar...Ch. 7 - Constant power P is delivered to a car of mass m...Ch. 7 - Suppose that the air resistance a car encounters...Ch. 7 - Consider a linear spring, as in Figure 7.7(a),...
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