hi,need help please.thank.
A car is designed to get its energy from a rotating flywheel (solid disk) with a radius of 2.00 m and a mass of 525 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.
1 J
(b) If the flywheel is to supply energy to the car as would a 20.0-hp motor, find the length of time the car could run before the flywheel would have to be brought back up to speed.
2 h
Are those your answers? 1 J and 2 h? How dd you obtain them?
a) Use the formula E = (1/2) I w^2, where w is the angular speed in rad/s and I is the moment of inertia.
(b) Time = (Full speed energy)/Power
You will have to convert horsepower to Watts when using the formula.
(a) To find the kinetic energy stored in the flywheel, we can use the formula for the kinetic energy of a rotating object:
KE = 0.5 * I * ω^2
Where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
The moment of inertia of a solid disk can be calculated using the formula:
I = 0.5 * m * r^2
Where m is the mass of the flywheel and r is its radius.
Plugging in the given values, we have:
m = 525 kg
r = 2.00 m
I = 0.5 * 525 kg * (2.00 m)^2
= 1050 kg * m^2
Since the angular velocity is given in terms of revolutions per minute (rev/min), we need to convert it to radians per second (rad/s).
ω = (4000 rev/min) * (2π rad/rev) / (60 s/min)
= 418.879 rad/s
Now, we can substitute the values into the formula for kinetic energy:
KE = 0.5 * (1050 kg * m^2) * (418.879 rad/s)^2
= 0.5 * 1050 kg * m^2 * (175583.14 rad^2/s^2)
≈ 92,228,927.5 J
Therefore, the kinetic energy stored in the flywheel is approximately 92,228,927.5 Joules.
(b) To find the length of time the car could run before the flywheel would have to be brought back up to speed, we can use the formula for power:
Power = Energy / Time
Where Power is given as 20.0 hp (horsepower). We need to convert horsepower to watts, as the SI unit for power is watts:
1 hp = 746 W
So, 20.0 hp is equal to:
Power = (20.0 hp) * (746 W/hp)
= 14,920 W
Now, we can rearrange the formula to solve for time:
Time = Energy / Power
Plugging in the values we found earlier:
Energy = 92,228,927.5 J
Power = 14,920 W
Time = (92,228,927.5 J) / (14,920 W)
≈ 6185.56 s
Finally, we can convert the time from seconds to hours:
Time = 6185.56 s * (1 min / 60 s) * (1 h / 60 min)
≈ 2.04 h
Therefore, the car could run for approximately 2.04 hours before the flywheel would have to be brought back up to speed.