Passage:
A ride consists of a carriage with a mass 300 kg and with a maximum occupancy of 300 kg. The carriage is attached to a mechanical arm of length = 5 m that is capable of rotation. The arm is able to provide the torque necessary to swing the riders back and forth on a circular path. Initially, the trips back and forth are very small, but with each trip the swings become larger. Eventually, the riders have enough momentum to swing 360 degrees around, performing a complete circle.
Please see link for associated image:
https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash3/580200_489717037780304_978342818_n.jpg
Question asks:
With a full carriage, the second ride suffers a power outage with the mechanical arm perpendicular to the horizontal. How much torque must the mechanical arm provide in order to prevent the passengers from swinging down? (Assume the mechanical arm itself does not require any torque to support)
A. 6 x 10^4 N*m
B. 12 x 10^4 N*m
C. 18 x 10^4 N*m
My rationale:
I knew that the torque needed has to oppose the torque produced by the force of gravity
so
Torque needed = mg * lever arm
= 6000 * 5????
I wound up taking the lever arm as 5 meters, and I'm confused as hell why the lever arm wouldn't be 5 meters. The solution in the book says the lever arm is 20 meters for solving the torque produced by the force of gravity. Why is the lever arm taken as 20 meters instead of 5 meters???
Answer is B
A ride consists of a carriage with a mass 300 kg and with a maximum occupancy of 300 kg. The carriage is attached to a mechanical arm of length = 5 m that is capable of rotation. The arm is able to provide the torque necessary to swing the riders back and forth on a circular path. Initially, the trips back and forth are very small, but with each trip the swings become larger. Eventually, the riders have enough momentum to swing 360 degrees around, performing a complete circle.
Please see link for associated image:
https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash3/580200_489717037780304_978342818_n.jpg
Question asks:
With a full carriage, the second ride suffers a power outage with the mechanical arm perpendicular to the horizontal. How much torque must the mechanical arm provide in order to prevent the passengers from swinging down? (Assume the mechanical arm itself does not require any torque to support)
A. 6 x 10^4 N*m
B. 12 x 10^4 N*m
C. 18 x 10^4 N*m
My rationale:
I knew that the torque needed has to oppose the torque produced by the force of gravity
so
Torque needed = mg * lever arm
= 6000 * 5????
I wound up taking the lever arm as 5 meters, and I'm confused as hell why the lever arm wouldn't be 5 meters. The solution in the book says the lever arm is 20 meters for solving the torque produced by the force of gravity. Why is the lever arm taken as 20 meters instead of 5 meters???
Answer is B
