Part A Assuming that there is sufficient friction on the ramp so that thehoop wi

Question

Part A
Assuming that there is sufficient friction on the ramp so that thehoop will roll without slipping, how far (measured along theincline) does the hoop roll? Give your answer in meters asmeasured along the incline.










Part B Instead of the assumption made in Part A,assume that the ramp is very slick, so that the hoop can experienceno friction as soon as it starts up the ramp; how far (measuredalong the incline) does the hoop move in this case? Hint: the hoopwill no longer be rolling without slipping when on the ramp. Give your answer in meters asmeasured along the incline.










Part C Suppose the rolling object were a hollowsphere of the same mass and radius as the hoop, and with the samestarting speed; if the sphere is able to roll without slipping onthe ramp, how far along the incline would it roll? Give your answer in meters asmeasured along the incline.











Part D Suppose the rolling object were a hollowsphere of the same mass and radius as the hoop, and with the samestarting speed; if the ramp were frictionless, how far along theincline would the sphere move in this case? Give your answer in meters asmeasured along the incline.

Explanation / Answer

w = v/r A) a hoop has I = mr^2 1/2 mv^2 + 1/2 Iw^2 = mgh 1/2 mv^2 + 1/2 (mr^2)(v/r)^2 - solve for h -----> h = v^2/g ----> h = 5.36m then to find the distance up the ramp d = h/sin -----> d = 5.36/sin(15) ----->d = 20.7 m B) since there is slipping you will just use ----> 1/2 mv^2 =mgh - again solve for h -----> h = 1/2v^2/g -----> h = 2.68 m then to find the distance up the ramp d = h/sin -----> d = 2.68/sin(15) ----->d = 10.36 m C) a hollow sphere has I = 2/3mr^2 1/2 mv^2 + 1/2 Iw^2 = mgh 1/2 mv^2 + 1/2 (2/3mr^2)(v/r)^2 - solve for h -----> h = v^2/g ----> h = 4.47m then to find the distance up the ramp d = h/sin -----> d = 4.47/sin(15) ----->d = 17.3 m D) this will be the same as part B) because only translationalenergy is used. again since there is slipping you will just use ----> 1/2 mv^2 =mgh - again solve for h -----> h = 1/2v^2/g -----> h = 2.68 m then to find the distance up the ramp d = h/sin -----> d = 2.68/sin(15) ----->d = 10.36 m

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