Answered

Get the most out of your questions with the extensive resources available on IDNLearn.com. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg.
(a) Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 20.0 m/s, assuming 90.0% of the rotational kinetic energy can be transformed into translational energy.
(b) How high a hill can the bus climb with this stored energy and still have a speed of 3.00 m/s at the top of the hill? Explicitly show how you follow the steps in the Problem-Solving Strategy for Rotational Energy.

Sagot :

Answer:

Explanation:

moment of inertia of flywheel = 1/2 m R²

= .5  x 1500 x .6²

= 270 kg m²

If required angular velocity be ω

rotational kinetic energy = 1/2 I ω²

= .5 x 270 x ω² = 135 ω²

kinetic energy of bus when its velocity is 20 m/s

= 1/2 x 10000 x 20²

= 2000000 J

Given 90 % of rotational kinetic energy is converted into bus's kinetic energy

135 ω² x 0.9 = 2000000 J

ω²=16461

ω = 128.3 radian /s

b )

Let the height required be h .

Total energy of bus at the top of hill = mgh + 1/2 m v²

m ( gh + .5 v²)

= 10000 ( 9.8h + .5 x 3²)

From conservation of mechanical energy theorem

10000 ( 9.8h + .5 x 3²) = 2000000

9.8h + .5 x 3² = 200

9.8h  = 195.5

h = 19.95 m .

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For trustworthy answers, rely on IDNLearn.com. Thanks for visiting, and we look forward to assisting you again.