Answer:
1309.1 Nm
Explanation:
Torque is given as a product of Moment of innertia and acceleration hence
T=Ia where T is torque and a is acceleration
To get acceleration, it is rate of change of speed per unit time hence where v and t represent velocity and time respectively while subscripts f and i represent final and initial respectively. Also, I is given by
where m js mass and r is radius hence the net torque can now be written as
By substituting the given figures then
To prevent cars from falling, the radius at the top of the circle should be
small such cars inverted at the top remain attached during motion.
Correct response;
The radius of the coaster can be <u>C) 20 m</u>
<h3>Method by which the above option is selected</h3>Mass of roller coaster car, m = 500 kg
Speed at the top of the circle, v = 20 m/s
Required:
The maximum radius of the circular path the roller coaster car.
Solution:
Where;
r = The radius of the circular path.
Weight of the roller coaster car = m·g = The centripetal force
Where;
g = Acceleration due to gravity = 9.81 m/s²
At equilibrium, we have;
Centrifugal force = Centripetal force
Therefore;
Which gives;
The maximum radius for safety of a roller coaster, r ≈ 40.77 meters
Which gives;
Range of the radius of the circle = 10.2 ≤ Radius of circle ≤ 40.77
The correct option for safety considerations is therefore;
<em>The possible question options are;</em>
<em>A) 5 m B) 10 m C) 20 m D) 40 m E) 80 m</em>
Learn more about centripetal force here:
Complete Question
For each of the following scenarios, describe the force providing the centripetal force for the motion:
a. a car making a turn
b. a child swinging around a pole
c. a person sitting on a bench facing the center of a carousel
d. a rock swinging on a string
e. the Earth orbiting the Sun.
Answer:
Considering a
The force providing the centripetal force is the frictional force on the tires \
i.e
where is the coefficient of static friction
Considering b
The force providing the centripetal force is the force experienced by the boys hand on the pole
Considering c
The force providing the centripetal force is the normal from the bench due to the boys weight
Considering d
The force providing the centripetal force is the tension on the string
Considering e
The force providing the centripetal force is the force of gravity between the earth and the sun
Explanation: