Question

A roller-coaster car has a mass of 1080 kg when fully loaded with passengers. As the car passes over the top of a circular hill of radius 16 m, its speed is not changing. (a) At the top of the hill, what is the normal force (using the negative sign for the downward direction) FN on the car from the track if the car's speed is v = 7.6 m/s? (b) What is FN if v = 17 m/s? Use g=9.81 m/s^2.

Answer 1

(a): The normal force on the car from the track when the car's speed is v= 7.6 m/s is FN= -6696 N.

(b): The normal force on the car from the track when the car's speed is v= 17 m/s is FN= 8912.7 N.

Step-by-step explanation:

m= 1080 kg

r= 16m

v1= 7.6 m/s

v2= 17 m/s

g= 9.81 m/s²

v1= w1*r

w1= v1/r

w1= 0.475 rad/s

ac1= w1² * r

ac1= 3.61 m/s²

FN= m * (ac1 - g)

FN= -6696 N (a)

-----------------------------------------------------

v2= w2*r

w2= v2/r

w2= 1.06 rad/s

ac2= w2² * r

ac2= 18.06 m/s²

FN= m * (ac2 - g)

FN= 8912.7 N (b)