Answer:
a)radius of the arc of the teardrop at the top is 10.58m
b)T = mg
c) the centipetal acceleration at the top is 14.5m/s
Explanation:
Part A
Given that roller coaster is of tear drop shape
So the speed at the top is given as
v = 14.4 m/s
acceleration at the top is given as
a = 2 g
now we know the formula of centripetal acceleration as
Part B
now
the total mass of the car and the ride is M
Let the force exerted by the track be n
By Newton law
Part C
If the radius of the loop is 21.4 m
speed is given by same v = 14.4 m/s
now the acceleration is given as
Now for normal force at the top is given by force equation
The force exerted by the rail is less than zero because acceleration is less than 9.69m/s²
So the normal force would have to point away from the centre, For safe ride this normal force must be positive i.e