The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation. Find a further general expression for the horizontal displacement of the rider from its initial position with respect to both time and angle of rotation and hence determine the speed of the rider when t= 180 sec. Using calculus, determine what the maximum horizontal and vertical speeds of the rider would be and at which points during the ride they occur. State expressions for the acceleration of the rider in both horizontal and vertical directions and show that the resultant acceleration experienced by the rider is independent of where on the ride he/she might be. In designing a new wheel with the same diameter and same ride duration as before it is proposed that the wheel’s angular speed should not be constant but instead should take the form of dθ/dt=0.00049365 t^0.5 in rad/sec during the first half of the ride when the rider is ascending and dθ/dt=0.017895 t^(-0.1882) in rad/sec during the second half, when the rider is descending. Determine the total angular displacement of the wheel between the time intervals of t=250 sec and t= 600 sec. Also calculate the total curved distance that the rider travels between the times of t=150 sec and t=720 sec.
The 100 meter diameter wheel needs to be designed so that it rotates at a constant rate and every complete revolution takes 15 minutes. The wheel has been installed in a vertical plane and the lowest seat is 2m above the ground surface. Each ride consists of only one full rotation.
Find a further general expression for the horizontal displacement of the rider from its initial position with respect to both time and angle of rotation and hence determine the speed of the rider when t= 180 sec.
Using calculus, determine what the maximum horizontal and vertical speeds of the rider would be and at which points during the ride they occur.
State expressions for the acceleration of the rider in both horizontal and vertical directions and show that the resultant acceleration experienced by the rider is independent of where on the ride he/she might be.
In designing a new wheel with the same diameter and same ride duration as before it is proposed that the wheel’s angular speed should not be constant but instead should take the form of
dθ/dt=0.00049365 t^0.5 in rad/sec during the first half of the ride when the rider is ascending and dθ/dt=0.017895 t^(-0.1882) in rad/sec during the second half, when the rider is descending.
Determine the total angular displacement of the wheel between the time intervals of t=250 sec and t= 600 sec. Also calculate the total curved distance that the rider travels between the times of t=150 sec and t=720 sec.
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