A car is designed to get its energy from a rotating flywheel with a radius of 1.50 m and a mass of 600 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 4000 rev/min.
(a) Find the kinetic energy stored in the flywheel.
(b) If the flywheel is to supply energy to the car as would a 15.0 hp motor, find the length of time the car could run before the flywheel would have to be brought back up to speed.
I think for a i might have the wrong answer it seems really large. first i converted the revs/min to rad/s and got 418.88 rad/s. is this were i am wrong. also what is its moment of inertia.
To find the kinetic energy stored in the flywheel, we can use the formula:
Kinetic Energy = (1/2) * I * ω^2
where I is the moment of inertia of the flywheel and ω is the angular velocity of the flywheel.
(a) First, let's calculate the moment of inertia of the flywheel. The moment of inertia of a solid cylinder can be found using the formula:
I = (1/2) * m * r^2
where m is the mass of the flywheel and r is its radius.
Given:
Mass of the flywheel (m) = 600 kg
Radius of the flywheel (r) = 1.50 m
Substituting these values into the formula, we get:
I = (1/2) * 600 kg * (1.50 m)^2
I = 450 kg⋅m^2
Now, let's convert the angular velocity from rev/min to radians/second. Since 1 revolution = 2π radians, we can convert as follows:
Angular velocity (ω) = 4000 rev/min * (2π rad/1 rev) * (1 min/60 s)
ω = 418.88 rad/s (rounded to two decimal places)
Substituting the values into the kinetic energy formula, we get:
Kinetic Energy = (1/2) * 450 kg⋅m^2 * (418.88 rad/s)^2
Kinetic Energy = 18015197.5 J (rounded to one decimal place)
Therefore, the kinetic energy stored in the flywheel is approximately 18,015,197.5 J.
(b) To find the length of time the car could run before the flywheel needs to be brought back up to speed, we need to convert the power of the flywheel (given in horsepower) to watts, and then use the formula:
Time = Energy / Power
Given that the power is 15.0 hp, we can convert it to watts using the conversion factor:
1 hp = 745.7 W
So, the power in watts is:
Power = 15.0 hp * 745.7 W/hp
Power = 11185.5 W (rounded to one decimal place)
Using the formula, we can calculate the length of time:
Time = 18,015,197.5 J / 11185.5 W
Time ≈ 1610.6 s
Therefore, the car could run for approximately 1610.6 seconds (or about 26.8 minutes) before the flywheel needs to be brought back up to speed.