As a gasoline engine operates, a flywheel turning with the crankshaft stores energy after each fuel explosion, providing the energy required to compress the next charge of fuel and air. For the engine of a certain lawn tractor, suppose a flywheel must be no more than 18.0 cm in diameter. Its thickness, measured along its axis of rotation, must be no larger than 8.00 cm. The flywheel must release energy 60.0 J when its angular speed drops from 800 rev/min to 600 rev/min. Design a sturdy steel (density 7.85 × 103 kg/m3) flywheel to meet these requirements with the smallest mass you can reasonably attain. Specify the shape and mass of the flywheel.
The design of sturdy steel flywheel with the small mass and specify it shape.
Answer to Problem 10.88CP
The shape of the flywheel is hollow cylinder of inner radius
Explanation of Solution
The diameter of the flywheel must be no more than
From the law of energy conservation,
Here,
Write the expression for the initial rotational energy of the flywheel is,
Here,
Write the expression for the final rotational energy of the flywheel is,
Here,
Substitute
Substitute
Formula to calculate the outer radius of the hollow cylinder is,
Here,
Substitute
For large energy storage by the moment of inertia of flywheel must be large but the mass should be small as much as possible for design to fulfill this requirement the mass should place as far away from the axis as possible to increase the moment of inertia.
Let choose a hollow cylinder to make the flywheel of
Formula to calculate the moment of inertia of the flywheel is,
Here,
Write the expression for the moment of inertia of the disk is,
Here,
Assume the radius of the disk is equal to the outer radius of the hollow cylinder.
Write the expression for the moment of inertia of the hollow cylinder is,
Here,
Substitute
Write the expression for the mass of the hollow cylinder wall is,
Here,
Write the expression for the mass of the disk is,
Here,
Substitute
Substitute
Solve the equation further,
Formula to calculate the mass of the flywheel is,
Substitute
Conclusion:
Substitute
Therefore, shape of the flywheel is hollow cylinder of inner radius
Want to see more full solutions like this?
Chapter 10 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- No chatgpt pls will upvotearrow_forward13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…arrow_forwardNo chatgpt pls will upvotearrow_forward
- a cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?arrow_forwardCalculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were: 222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33 Give in the answer window the calculated repeated experiment variance in m/s2.arrow_forwardNo chatgpt pls will upvotearrow_forward
- 2. Consider the situation described in problem 1 where light emerges horizontally from ground level. Take k = 0.0020 m' and no = 1.0001 and find at which horizontal distance, x, the ray reaches a height of y = 1.5 m.arrow_forward2-3. Consider the situation of the reflection of a pulse at the interface of two string described in the previous problem. In addition to the net disturbances being equal at the junction, the slope of the net disturbances must also be equal at the junction at all times. Given that p1 = 4.0 g/m, H2 = 9.0 g/m and Aj = 0.50 cm find 2. A, (Answer: -0.10 cm) and 3. Ay. (Answer: 0.40 cm)please I need to show all work step by step problems 2 and 3arrow_forwardFrom number 2 and 3 I just want to show all problems step by step please do not short cut look for formulaarrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegeGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill