Final answer:
The force that the track exerts on a 4000 kg train traveling at 100 km/h on a circular track with an 800 meter radius is 3850 newtons.
Step-by-step explanation:
To calculate the force the track exerts on the 4000 kg train traveling at 100 km/h on a circular track with a radius of 800 meters, we first need to convert the train's speed to meters per second (m/s). Since 100 km/h is equal to approximately 27.78 m/s, we can then use the centripetal force formula:
F = (mv²)/r
Where:
- F is the centripetal force,
- m is the mass of the train (4000 kg),
- v is the velocity of the train (27.78 m/s),
- r is the radius of the circular track (800 m).
By substituting the known values into the formula, we calculate the force:
F = (4000 kg × (27.78 m/s)²) / 800 m = 3850 N (rounded to the nearest whole number)
Therefore, the centripetal force exerted by the track on the train, which is equal to the force the track exerts on the train, is 3850 newtons.