An experimental flywheel, used to store energy and replace an automobile engine, is a solid disk of mass 202.0 kg and radius 0.35 m.
(a) What is its rotational inertia?
(b) When driving at 22.4 m/s (50 mph), the fully energized flywheel is rotating at an angular speed of 3160 rad/s. What is the initial rotational kinetic energy of the flywheel?
(c) If the total mass of the car is 1120.0 kg, find the ratio of the initial rotational kinetic energy of the flywheel to the translational kinetic energy of the car.
(d) If the force of air resistance on the car is 700.0 N, how far can the car travel at a speed of 22.4 m/s (50 mph) with the initial stored energy? Ignore losses of mechanical energy due to means other than air resistance.
a. Look this up, flat disk, moment of inertia table.
b. KE= 1/2 I w^2
To answer these questions, we need to understand the concept of rotational inertia and rotational kinetic energy.
(a) The rotational inertia, also known as the moment of inertia, is a measure of an object's resistance to changes in its rotational motion. For a solid disk rotating about its axis, the formula for rotational inertia is given by:
I = (1/2) * mass * radius^2
Plugging in the values from the problem, we get:
I = (1/2) * 202.0 kg * (0.35 m)^2 = 24.183 kg·m²
So the rotational inertia of the flywheel is 24.183 kg·m².
(b) The formula for rotational kinetic energy is:
K_rot = (1/2) * I * ω^2
where K_rot is the rotational kinetic energy, I is the rotational inertia, and ω is the angular speed.
Plugging in the given values, we can calculate the rotational kinetic energy:
K_rot = (1/2) * 24.183 kg·m² * (3160 rad/s)^2 = 1.5205 x 10^8 J
Therefore, the initial rotational kinetic energy of the flywheel is 1.5205 x 10^8 Joules.
(c) To find the ratio of the initial rotational kinetic energy of the flywheel to the translational kinetic energy of the car, we need to calculate the translational kinetic energy of the car first.
The translational kinetic energy is given by the formula:
K_trans = (1/2) * mass * velocity^2
Plugging in the values for the car, we have:
K_trans = (1/2) * 1120.0 kg * (22.4 m/s)^2 = 281548.8 J
The ratio of the initial rotational kinetic energy of the flywheel to the translational kinetic energy of the car is:
Ratio = K_rot / K_trans = (1.5205 x 10^8 J) / (281548.8 J) = 539.81
So the ratio is approximately 539.81.
(d) To calculate the distance the car can travel with the initial stored energy, we need to take into account the work done by the force of air resistance.
The work done by the force of air resistance is given by:
Work = Force * Distance
Since we want to find the distance, we rearrange the equation:
Distance = Work / Force
Substituting the given values, we have:
Distance = (1.5205 x 10^8 J) / 700.0 N = 217228.57 m
Therefore, the car can travel approximately 217228.57 meters or 217.23 kilometers with the initial stored energy, neglecting other energy losses.