Question

In: Physics

A bus contains a 1500 kg flywheel (a disk that has a 0.55 m radius) and...

A bus contains a 1500 kg flywheel (a disk that has a 0.55 m radius) and has a total mass of 11000 kg.

m = 1500 kg
r = 0.55 m
mt = 11000 kg
v1 = 19 m/s
v2 = 2.75 m/s

A. Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 19 m/s in rad/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 2.75 m/s at the top of the hill in m?

Solutions

Expert Solution

given :

M = total mass = 11000 kg

m = mass of flywheel = 1500 kg

Radius of flywheel = R = 0.55 m

Rotational KInetic Energy =

Translational Kinetic energy =

A) The translational kinetic energy attained by the bus is from the rotational kinetic energy of the flywheel.

Let I be the moment of inertia of the flywheel and it's value is = .

let be the angular velocity when the kinetic energy of the bus is zero.

In the question given, the 90% of rotational kinetic energy of flywheel is converted into tenslational kinetic energy of the bus and the bus attained linear velocity v = 19m/s.

therefore,

[answer]

B) after climbing a hill of height say h, the speed of bus is still v2 = 2.75 m/s.

Applying conservation of mechanical energy between ground where speed is 19 m/s and the height where speed is 2.75 m/s. :

total final energy = total initial energy

.

The height reachd is 18.01 m when it has speed 2.75m/s. [answer]


Related Solutions

A flywheel comprises a uniform circular disk with a mass of 97.0 kg and a radius...
A flywheel comprises a uniform circular disk with a mass of 97.0 kg and a radius of 1.1 m. It rotates with an angular velocity of 1420 rev/min. A constant tangential force is applied at a radial distance of 0.5 m. What is the initial kinetic energy of the wheel? (b) If the wheel is brought to rest in 133.0 s, what is the tangential force?
A disk with mass m = 11.8 kg and radius R = 0.31 m begins at...
A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ω = 31 rad/s. 1.What is the angular acceleration of the disk? 2. What is the angular displacement over the 17.2 s? 3. What is the moment of inertia of the disk? 4. What is the change in rotational energy of the disk?
A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies...
A uniform disk with mass m = 9.07 kg and radius R = 1.36 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 313 N at the edge of the disk on the +x-axis, 2) a force 313 N at the edge of the disk on the –y-axis, and 3) a force 313 N acts at the edge of the disk at an angle θ =...
A uniform disk with mass m = 9.28 kg and radius R = 1.42 m lies...
A uniform disk with mass m = 9.28 kg and radius R = 1.42 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 345 N at the edge of the disk on the +x-axis, 2) a force 345 N at the edge of the disk on the –y-axis, and 3) a force 345 N acts at the edge of the disk at an angle θ =...
A uniform disk with mass m = 9.44 kg and radius R = 1.32 m lies...
A uniform disk with mass m = 9.44 kg and radius R = 1.32 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk: 1) a force 318 N at the edge of the disk on the +x-axis, 2) a force 318 N at the edge of the disk on the –y-axis, and 3) a force 318 N acts at the edge of the disk at an angle θ =...
A solid disk of mass m1 = 9.3 kg and radius R = 0.22 m is...
A solid disk of mass m1 = 9.3 kg and radius R = 0.22 m is rotating with a constant angular velocity of ω = 31 rad/s. A thin rectangular rod with mass m2 = 3.9 kg and length L = 2R = 0.44 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? 2) What...
A solid disk of mass m1 = 9.9 kg and radius R = 0.2 m is...
A solid disk of mass m1 = 9.9 kg and radius R = 0.2 m is rotating with a constant angular velocity of ω = 35 rad/s. A thin rectangular rod with mass m2 = 3.1 kg and length L = 2R = 0.4 m begins at rest above the disk and is dropped on the disk where it begins to spin with the disk. 1) What is the initial angular momentum of the rod and disk system? 2) What...
A torsion pendulum is made from a disk of mass m = 6.6 kg and radius...
A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium 1)What is the torsion constant of this pendulum? 2)What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? 3)What is the angular frequency of oscillation of this torsion pendulum? 4)Which of the...
A disk with m=4.4 kg and radius 14.1 cm rolls a distance 4.3 m down a...
A disk with m=4.4 kg and radius 14.1 cm rolls a distance 4.3 m down a ramp that is inclined by an angle 26.9° with respect to the horizontal. At the bottom of the ramp, what is its translational kinetic energy?
A space station in the shape of a uniform disk (mass 4.45x105 kg, radius 262 m)...
A space station in the shape of a uniform disk (mass 4.45x105 kg, radius 262 m) rotates with period 86.1 seconds. There are also 734 astronauts (whom you can treat as point particles) working inside the space station, each of mass 155 kg, and all standing on the outside rim and rotating with the station. Now, all the astronauts move to a conference room at the very center of the space station. Find the new period of the rotation of...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT