-A roller coaster cart of mass (m1=127 kg) initially sits atrest on a track. Once the motor is activated, the cart isaccelerated forward (across level ground) until it reaches thebottom of a giant circular loop with a radius of (r1=17.5 m). Atthis point, the motor is turned off and the cart must \"coast\" forthe remainder of the ride. Assume the track is frictionless andignore air resistance. At the top of the loop, what is the minimumspeed the cart must have in order to stay in its circular motionaround the loop? (Give your answer to 3 sig figs.)
-Letting the base of the loop represent h=0, how much GPE doesthe cart have at the top? (Give your answer to 3 sig figs. and inunits of J)Â Â
-What is the total mechanical energy of the cart at the top ofthe loop? (Give your answer to 3 sig figs. and in units of J)
-What speed does the cart have at the base of the loop? (Giveyour answer to 3 sig figs.)
-What work must be done by the motor to accelerate the cart fromrest to its final velocity at the base of the loop? (Give youranswer to 3 sig figs. and in units of J. Indicate whether the workis positive or negative with the sign of your answer.)
-When the cart is at the 9 o'clock position of the loop (it hasa height above the base of the loop of exactly one loop radius),what is the speed of the cart? (Give your answer to 3 sigfigs.)
-When the cart is at the 9 o'clock position of the loop, what isthe magnitude of the force of the track exerted on the cart? (Giveyour answer to 3 sig figs. and in units of N)
-When the cart is at the 9 o'clock position of the loop, what isthe magnitude of the torque applied by the force of the track? Letthe center of the loop be the axis of rotation. (Give your answerto 3 sig figs. and in units of N*m [which is the SI unit fortorque])
-When the cart is at the 9 o'clock position of the loop, what isthe magnitude of the net torque exerted on the cart? Let the centerof the loop be the axis of rotation. (Give your answer to 3 sigfigs. and in units of N*m [which is the SI unit for torque])
