A rollercoaster car loaded with passengers has a mass of 2,000 kilograms. The track of the roller coaster has a semi-circular valley with a radius of 24 meters. If the vehicle has a speed of 18 m/sec at the very bottom of the valley, the force exerted on the vehicle by the track is about:
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To find the force exerted on the vehicle by the track, we need to consider the forces acting on the car at the bottom of the valley. At this point, there are two forces acting on the car: the gravitational force and the normal force.
1. Gravitational Force:
The gravitational force (weight) acting on the car is given by the formula F_gravity = m * g, where m is the mass of the car (2,000 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, F_gravity = 2,000 kg * 9.8 m/s^2 = 19,600 N.
2. Normal Force:
The normal force (N) is the force exerted by the track on the car, perpendicular to the surface. At the bottom of the valley, the normal force is equal in magnitude and opposite in direction to the gravitational force to balance it out. Therefore, the normal force is also 19,600 N.
So, the force exerted on the vehicle by the track at the bottom of the valley is approximately 19,600 N.
To find the force exerted on the roller coaster car by the track, we can make use of centripetal force.
Centripetal force is the force required to keep an object moving in a circular path. It always acts towards the center of the circular path and is given by the equation:
F = (mv²) / r
Where:
F is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius of the circular path
In this case, the roller coaster car has a mass of 2,000 kilograms and is traveling with a velocity of 18 m/s at the bottom of the valley, which has a radius of 24 meters.
Plugging in the values into the formula:
F = (2000 kg * (18 m/s)²) / 24 m
Simplifying:
F = (2000 kg * 324 m²/s²) / 24 m
F = 216000 N
Therefore, the force exerted on the roller coaster car by the track is approximately 216,000 Newtons.