EXAMPLE 10.9Calculating Helicopter EnergiesA typical small rescue helicopter, similar to the one in Figure 10.18, has four blades, each is 4.00 m longand has a mass of 50.0 kg. The blades can be approximated as thin rods that rotate about one end of anaxis perpendicular to their length. The helicopter has a total loaded mass of 1000 kg. (a) Calculate therotational kinetic energy in the blades when they rotate at 300 rpm. (b) Calculate the translational kineticenergy of the helicopter when it flies at 20.0 m/s, and compare it with the rotational energy in the blades.(c) To what height could the helicopter be raised if all of the rotational kinetic energy could be used to liftit?Solution for (a)The rotational kinetic energy is1KErot = lu.10.73We must convert the angular velocity to radians per second and calculate the moment of inertia before wecan find KErot - The angular velocity w israd= 31.4300 rev 27 rad 1.00 minW =10.741.00 min1 rev60.0 sThe moment of inertia of one blade will be that of a thin rod rotated about its end, found in Figure 10.12.The total I is four times this moment of inertia, because there are four blades. Thus,(50.0 kg)(4.00 m)²I = 4-= 4 x3= 1067 kg · m?.10.753Entering w and I into the expression for rotational kinetic energy givesKErot = 0.5(1067 kg - m²)(31.4 rad/s)²10.76= 5.26 x 105 JSolution for (b)Translational kinetic energy was defined in Uniform Circular Motion and Gravitation. Entering the givenvalues of mass and velocity, we obtain1KEtrans =mv² =(0.5)(1000 kg)(20.0 m/s)² = 2.00 × 105 J.10.77To compare kinetic energies, we take the ratio of translational kinetic energy to rotational kinetic energy.This ratio is2.00 x 105 J= 0.380.10.785.26 x 105 JSolution for (c)At the maximum height, all rotational kinetic energy will have been converted to gravitational energy. Tofind this height, we equate those two energies:KErot = PEgrav10.79orlu = mgh.- Iw?10.80We now solve for h and substitute known values into the resulting equation5.26 x 105 Jh =mg= 53.7 m.10.81(1000 kg) (9.80 m/s²) 5. In Section 10.4 (Rotational Kinetic Energy) of the OpenStax College Physics textbook, go toExample 10.9 (Calculating Helicopter Energies) and change the mass of the helicopter bladesfrom 50.0 kg to Y kg. Also, change the rotation rate from 300 rpm to Z rpm. Then write theanswers (a), (b), and (c) to the question below.Y = 46:83Z = 294.83t boilgge

Part (5): Given:The mass of the helicopter is Y = 46.83 kg. The anguar speed is Z = 294.83 rpm. The…

5. In Section 10.4 (Rotational Kinetic Energy) of the OpenStax College Physics textbook, go to Example 10.9 (Calculating Helicopter Energies) and change the mass of the helicopter blades from 50.0 kg to Y kg. Also, change the rotation rate from 300 rpm to Z rpm. Then write the answers (a), (b), and (c) to the question below. Y = 46:83 Z = 294.83

5. In Section 10.4 (Rotational Kinetic Energy) of the OpenStax College Physics textbook, go to Example 10.9 (Calculating Helicopter Energies) and change the mass of the helicopter blades from 50.0 kg to Y kg. Also, change the rotation rate from 300 rpm to Z rpm. Then write the answers (a), (b), and (c) to the question below. Y = 46:83 Z = 294.83

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter12: Rotation I: Kinematics And Dynamics

Section: Chapter Questions

Problem 33PQ: Consider again the two wind turbines in Problem 32. a. At what point along the 40-m blade would the...

See similar textbooks

Similar questions

1. The velocity of a rotating disk is independent of a point's position on the disk.a. Trueb. False explain 2. The angular velocity of a rotating disk is independent of a point's position on the disk.a. Trueb. False explain
I Review I Constants You are designing a rotating metal flywheel that will be used to store energy. The flywheel is to be a uniform disk with radius 35.0 cm. Starting from rest at t = 0, the flywheel rotates with constant angular acceleration 3.00 rad/s? about an axis perpendicular to the flywheel at its center. Part A If the flywheel has a density (mass per unit volume) of 8600 kg/m³, what thickness must it have to store 800 J of kinetic energy at t = 8.00 s? Express your answer with the appropriate units. HA h = Value Units Submit Request Answer
Consider again the two wind turbines in Problem 32. a. At what point along the 40-m blade would the angular speed of thepoint be the same as the angular speed at the end of the 20-mblade? Explain your answer. b. At what point along the 40-mblade would the translational speed of the point be the same asthe speed at the end of the 20-m blade? Explain your answer.
Current Attempt in Progress M d M m The device shown above is made of low-mass rods and four point masses. The smaller masses (m = 0.20 kg) are a distance d = 0.35 m from the center, and the larger masses (M = 0.63 kg) are a distance D = 0.19 m from the center. The device is initially rotating about its center with a period of 0.67 s. You do 9.4 J of work to make the device rotate faster. What is its new period? New period = i
Two – pulleys belt drive-system is commonly used in washing machines as shown in Figure.1. Your role in a company that manufactures washing machine is to analyze the power transmission through the belt drive system which operates under uniform angular acceleration in such a manner that ensures the required torque and power output are optimum. The system under study includes two pulleys and one belt with the following design specifications: The driver pully rotates at angular velocity win = 1700 rpm. - The driver pully input torque is Tin = 20 N.m. - The driver pully has a diameter of 100 mm. - The driven pully has a diameter of 220 mm. The system operates for long period under uniform angular speed, - Power transmission operates under no slipping condition. 220 mm |Belt 100 mm W= 1700 rpm in out T= 20 N.m T in out P in Pat Driver pulley Driven pulley Figure.1(a) Belt drive system used in washing machine
A session.masteringphysics.com n Canvas Login - Santa Monica College MyLab and Mastering e https://session.masteringphysics.com
I Review I Constants A pulley on a frictionless axle has the shape of a uniform solid disk of mass 2.90 kg and radius 20.0 cm. A 1.50 kg stone is attached to a very light wire that is wrapped around the rim of the pulley (Figure 1), and the system is released from rest. Part A How far must the stone fall so that the pulley has 6.50 J of kinetic energy? For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of An unwinding Express your answer with the appropriate units. cable ii. µA h = Value Units Submit Previous Answers Request Answer Figure 1 of 1 X Incorrect; Try Again; 4 attempts remaining pulley Part B What percent of the total kinetic energy does the pulley have? Express your answer in percent. ΑΣφ ? stone Kp Ktot II
A. Similar bars as shown are translating and/or rotating with the given linear and angular speeds. Which bar has the greatest amount of kinetic energy? B. Similar bars as shown are translating and/or rotating with the given linear and angular speeds. Which bar has the least amount of kinetic energy?
3.6% Resources veUp? V Hint A spherical shell of radius 2.84 cm and a sphere of radius 6.97 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are have the same total kinetic energy, what should the ratio of the spherical shell's angular speed @shi to the sphere's angular speed wsph be? Wshl @sph about us privacy policy terms of use contact us help careers
OneNote for Windows 10 Insert Draw View Help BIU O Calibri 11 5. The two torques cancel...What must F be? 200 N 3 m 45° 5 m II !!!
Shown is the angular position of a potter’s wheel.a. What is the angular displacement of the wheel between t = 5 s and t = 15 s?b. What is the angular velocity of the wheel at t = 15 s?c. What is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
A solid uniform ball rolls without slipping up a hill, as shown in (Figure 1). At the top of the hill, it is moving horizontally, and then it goes over the vertical cliff. Neglect rolling friction and assume the system's total mechanical energy is conserved. Part A How far from the foot of the cliff does the ball land? Express your answer with the appropriate units. ? Value Units Submit Request Answer Figure 1 of 1 Part B How fast is it moving just before it lands? Express your answer with the appropriate units. 25.0 m/s 28.0 m μΑ Value Units V = Submit Request Answer