a 57.0 kg person on a rollercoaster moving through the bottom of a curved track of radius 42.7 m feels a normal force of 995 N how fast is the car moving
To determine how fast the car is moving, we need to use the concept of centripetal force and relate it to the gravitational and normal forces acting on the person.
In this scenario, the normal force provides the centripetal force that keeps the person moving in a circular path. The formula for centripetal force is given by Fc = (m * v^2)/r, where Fc is the centripetal force, m is the mass of the person, v is the velocity, and r is the radius of the track.
We can rearrange the formula to solve for velocity (v):
v = sqrt((Fc * r) / m)
Substituting the given values:
m = 57.0 kg (mass of the person)
Fc = 995 N (normal force)
r = 42.7 m (radius of the track)
v = sqrt((995 N * 42.7 m) / 57.0 kg)
Now we can calculate the velocity.
v = sqrt((995 N * 42.7 m) / 57.0 kg)
v ≈ sqrt(67466.5 N*m / 57.0 kg)
v ≈ sqrt(1183.512 N*m/kg)
v ≈ 34.42 m/s
Therefore, the car is moving at approximately 34.42 m/s.
gravity + centripetal = normal ... (m * g) + (m * v^2 / r) = 995 N
solve for v