WebAssign Printed Access Card for Serway/Vuille's College Physics, 11th Edition, Multi-Term
WebAssign Printed Access Card for Serway/Vuille's College Physics, 11th Edition, Multi-Term
11th Edition
ISBN: 9781337763486
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 8, Problem 80AP

Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope?

Chapter 8, Problem 80AP, Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of

Figure P8.80 Problems 80 and 81

(a)

Expert Solution
Check Mark
To determine
The angular momentum of the astronauts.

Answer to Problem 80AP

The angular momentum of the astronauts is 3.75×103kgm2s1

Explanation of Solution

Given Info:

The mass of the astronauts is 75kg , the speed of the astronauts is 5.00ms1 , the distance between them is 10.0m .

The formula to calculate angular momentum is given by

Li=mviri

  • Li is the initial angular momentum,
  • m is the mass of astronauts
  • vi is initial the speed of the astronauts
  • ri is the initial distance between the astronaut from the centre of mass.

Substitute 75kg for m, 5.00ms1 for vi and 10.0m for ri in the above expression to calculate Li .

Li=(75kg)(5.00ms1)(10.0m)=3750kgm2s1=3.75×103kgm2s1

Conclusion:

Therefore the angular momentum of the astronauts is 3.75×103kgm2s1

(b)

Expert Solution
Check Mark
To determine
The rotational energy of the system.

Answer to Problem 80AP

The rotational energy of the system is 1.88kJ .

Explanation of Solution

The formula to calculate rotational energy of the system is given by

KEi=mvi2

  • KEi is the initial rotational energy of the system.

Substitute 75kg for m, and 5.00ms1 for vi in the above equation to calculate rotational kinetic energy of the system.

KEi=(75kg)(5.00ms1)2=1875J(1kJ103J)1.88kJ

Conclusion: The rotational energy of the system is 1.88kJ

(c)

Expert Solution
Check Mark
To determine
The angular momentum of the system for the shortened distance.

Explanation of Solution

In the absence of external torque, the angular momentum of the system remains conserved.

According to conservation of angular momentum angular momentum must be conserved.

Li=Lf

Therefore the initial angular momentum is same as final angular momentum

Conclusion:

Therefore the new angular momentum is 3.75×103kgm2s1 .

(d)

Expert Solution
Check Mark
To determine
speed of the astronauts

Answer to Problem 80AP

The speed of the astronauts is 10ms1 .

Explanation of Solution

Given Info:

The formula to calculate angular speed of the system is

vf=Lfmrf

  • rf is the new distance between astronauts

Substitute 3750kgm2s1 for Lf , 75kg for m and 5.0m for rf to calculate vf

vf=3750kgm2s1(75kg)(5.0m)=10ms1

Conclusion:

Therefore the new speed of the astronauts is 10ms1

(e)

Expert Solution
Check Mark
To determine
The new rotational energy of the system.

Answer to Problem 80AP

The new rotational energy of the system is 7.5kJ

Explanation of Solution

Given Info:

The formula to calculate rotational energy of the system is given by

KEf=mvf2

Substitute 75kg for m, and 10ms1 for vf in the above equation to calculate new rotational kinetic energy

KEf=(75kg)(10ms1)2=7500J(1kJ103J)=7.5kJ

Conclusion: The rotational energy of the system is 7.5kJ

(f)

Expert Solution
Check Mark
To determine
The work done by the astronauts.

Answer to Problem 80AP

The work done by the astronaut is 5.62kJ .

Explanation of Solution

Given Info:

According to work energy theorem work done is change in kinetic energy here kinetic energy is rotational energy.

The formula to calculate rotational energy of the system is given by

W=KEfKEi

Substitute 7.5kJ for KE and 1.88kJ for KE to calculate W.

W=7.5kJ1.88kJ=562J(1kJ103J)=5.62kJ

Thus the work done is 5.62kJ

Conclusion: The work done by the astronaut is 5.62kJ

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Chapter 8 Solutions

WebAssign Printed Access Card for Serway/Vuille's College Physics, 11th Edition, Multi-Term

Ch. 8 - Why does a long pole help a tightrope walker stay...Ch. 8 - A person stands a distance R from a doors hinges...Ch. 8 - Orbiting spacecraft contain internal gyroscopes...Ch. 8 - If you toss a textbook into the air, rotating it...Ch. 8 - Stars originate as large bodies of slowly rotating...Ch. 8 - An object is acted on by a single nonzero force of...Ch. 8 - In a tape recorder, the tape is pulled past the...Ch. 8 - (a) Give an example in which the net force acting...Ch. 8 - Gravity is an example of a central force that acts...Ch. 8 - A cat usually lands on its feet regardless of the...Ch. 8 - A solid disk and a hoop are simultaneously...Ch. 8 - A mouse is initially at rest on a horizontal...Ch. 8 - The cars in a soapbox derby have no engines; they...Ch. 8 - A man opens a 1.00-m wide door by pushing on it...Ch. 8 - A worker applies a torque to a nut with a wrench...Ch. 8 - The fishing pole in Figure P8.3 makes an angle of...Ch. 8 - Find the net torque on the wheel in Figure P8.4...Ch. 8 - Figure P8.4 Calculate the net torque (magnitude...Ch. 8 - A dental bracket exerts a horizontal force of 80.0...Ch. 8 - A simple pendulum consists of a small object of...Ch. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - The Xanthar mothership locks onto an enemy cruiser...Ch. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Torque and the Two Conditions for Equilibrium 17....Ch. 8 - Prob. 18PCh. 8 - A cook holds a 2.00-kg carton of milk at arm's...Ch. 8 - A meter stick is found to balance at the 49.7-cm...Ch. 8 - Prob. 21PCh. 8 - A beam resting on two pivots has a length of L =...Ch. 8 - Prob. 23PCh. 8 - When a person stands on tiptoe (a strenuous...Ch. 8 - A 500.-N uniform rectangular sign 4.00 m wide and...Ch. 8 - A window washer is standing on a scaffold...Ch. 8 - A uniform plank of length 2.00 m and mass 30.0 kg...Ch. 8 - A hungry bear weighing 700. N walks out on a beam...Ch. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Write the necessary equations of equilibrium of...Ch. 8 - Prob. 33PCh. 8 - Prob. 34PCh. 8 - Prob. 35PCh. 8 - Prob. 36PCh. 8 - Four objects are held in position at the corners...Ch. 8 - If the system shown in Figure P8.37 is set in...Ch. 8 - A large grinding wheel in the shape of a solid...Ch. 8 - An oversized yo-yo is made from two identical...Ch. 8 - An approximate model for a ceiling fan consists of...Ch. 8 - A potters wheel having a radius of 0.50 m and a...Ch. 8 - A model airplane with mass 0.750 kg is tethered by...Ch. 8 - A bicycle wheel has a diameter of 64.0 cm and a...Ch. 8 - A 150.-kg merry-go-round in the shape of a...Ch. 8 - An Atwoods machine consists of blocks of masses m1...Ch. 8 - The uniform thin rod in Figure P8.47 has mass M =...Ch. 8 - A 2.50-kg solid, uniform disk rolls without...Ch. 8 - A horizontal 800.-N merry-go-round of radius 1.50...Ch. 8 - Four objectsa hoop, a solid cylinder, a solid...Ch. 8 - A light rod of length = 1.00 m rotates about an...Ch. 8 - A 240-N sphere 0.20 m in radius rolls without...Ch. 8 - A solid, uniform disk of radius 0.250 m and mass...Ch. 8 - A car is designed to get its energy from a...Ch. 8 - The top in Figure P8.55 has a moment of inertia of...Ch. 8 - A constant torque of 25.0 N m is applied to a...Ch. 8 - A 10.0-kg cylinder rolls without slipping on a...Ch. 8 - Use conservation of energy to determine the...Ch. 8 - A 2.00-kg solid, uniform ball of radius 0.100 m is...Ch. 8 - Each of the following objects has a radius of...Ch. 8 - A metal hoop lies on a horizontal table, free to...Ch. 8 - A disk of mass m is spinning freely at 6.00 rad/s...Ch. 8 - (a) Calculate the angular momentum of Earth that...Ch. 8 - A 0.005 00-kg bullet traveling horizontally with a...Ch. 8 - A light, rigid rod of length = 1.00 m rotates...Ch. 8 - Haileys comet moves about the Sun in an elliptical...Ch. 8 - A student holds a spinning bicycle wheel while...Ch. 8 - A 60.0-kg woman stands at the rim of a horizontal...Ch. 8 - A solid, horizontal cylinder of mass 10.0 kg and...Ch. 8 - A student sits on a rotating stool holding two...Ch. 8 - The puck in Figure P8.71 has a mass of 0.120 kg....Ch. 8 - A space station shaped like a giant wheel has a...Ch. 8 - A cylinder with moment of inertia I1 rotates with...Ch. 8 - A particle of mass 0.400 kg is attached to the...Ch. 8 - Additional Problems A typical propeller of a...Ch. 8 - Prob. 76APCh. 8 - Prob. 77APCh. 8 - Prob. 78APCh. 8 - A uniform ladder of length L and weight w is...Ch. 8 - Two astronauts (Fig. P8.80), each haring a mass of...Ch. 8 - S This is a symbolic version of problem 80. Two...Ch. 8 - Two window washers. Bob and Joe, are on a...Ch. 8 - A 2.35-kg uniform bar of length = 1.30 m is held...Ch. 8 - A light rod of length 2L is free to rotate in a...Ch. 8 - Prob. 85APCh. 8 - A uniform thin rod of length L and mass M is free...Ch. 8 - Prob. 87APCh. 8 - Prob. 88APCh. 8 - A war-wolf, or trebuchet, is a device used during...Ch. 8 - A string is wrapped around a uniform cylinder of...Ch. 8 - The Iron Cross When a gymnast weighing 750 N...Ch. 8 - In an emergency situation, a person with a broken...Ch. 8 - An object of mass m1 = 4.00 kg is connected by a...Ch. 8 - Prob. 94APCh. 8 - A 3.2-kg sphere is suspended by a cord that passes...
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