A rollPhyer coaster loaded with passengers has a mass of 2000kg; the radius of curvature of the track at the lowest point of the ride is 24m. If the vehicle has a tangental speed of 18m/s at this point, what force is exerted on the vehicle by the track?
FORCE=mg +mv^2/r
To find the force exerted on the vehicle by the track, we need to apply the principles of circular motion.
The force exerted on an object moving in a circle is called the centripetal force. It is directed towards the center of the circle and is responsible for keeping the object moving in the circular path.
The centripetal force can be calculated using the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the object
v is the tangential velocity
r is the radius of curvature of the track at the lowest point
Given:
m = 2000 kg (mass of the roller coaster)
v = 18 m/s (tangential velocity at the lowest point)
r = 24 m (radius of curvature at the lowest point)
Substituting the given values into the equation, we can calculate the centripetal force:
F = (2000 kg * (18 m/s)^2) / 24 m
First, let's square the velocity:
(18 m/s)^2 = 324 m^2/s^2
Now, substitute the values into the equation:
F = (2000 kg * 324 m^2/s^2) / 24 m
Simplify further:
F = 864000 kg m/s^2 / 24 m
F = 36000 kg m/s^2
The force exerted on the vehicle by the track is 36000 Newtons (N).