18 8. If you pull on a roll of toilet paper hard enough, the toilet paper...

Transcribed Image Text:

18 8. If you pull on a roll of toilet paper hard enough, the toilet paper will break. Therefore, there is a maximum tension force you can pull on the toilet paper and thus a maximum angular acceleration possible for the toilet paper roll. R R Consider the situation drawn above. A roll of toilet paper (outer radius R = 8.0 cm, inner radius R = 3.0 cm, width W = 12.0 cm, and mass mTp = 0.920 kg) is sitting on a solid core (radius R, width W, and mass mcore = 1.25 kg) which in turn sits on frictionless bearings. The toilet paper and core thus spin together without slipping with respect to each other. The toilet paper is just about to tear when we apply a tension force of F = 15 N, tangent to the outer surface of the toilet paper. a. Calculate the total moment of inertia of the toilet paper and core about an axis out of the page through their center and verify that is it equal to 3.92 10-3 kgm. b. What is the maximum angular acceleration of the toilet paper without the toilet paper breaking? c. If you pull for 0.15 s starting from rest, what length of toilet paper would you have pulled by the end of the 0.15 s? Assume the outer radius of the toilet paper does not change significantly during the pull. 18 8. If you pull on a roll of toilet paper hard enough, the toilet paper will break. Therefore, there is a maximum tension force you can pull on the toilet paper and thus a maximum angular acceleration possible for the toilet paper roll. R R Consider the situation drawn above. A roll of toilet paper (outer radius R = 8.0 cm, inner radius R = 3.0 cm, width W = 12.0 cm, and mass mTp = 0.920 kg) is sitting on a solid core (radius R, width W, and mass mcore = 1.25 kg) which in turn sits on frictionless bearings. The toilet paper and core thus spin together without slipping with respect to each other. The toilet paper is just about to tear when we apply a tension force of F = 15 N, tangent to the outer surface of the toilet paper. a. Calculate the total moment of inertia of the toilet paper and core about an axis out of the page through their center and verify that is it equal to 3.92 10-3 kgm. b. What is the maximum angular acceleration of the toilet paper without the toilet paper breaking? c. If you pull for 0.15 s starting from rest, what length of toilet paper would you have pulled by the end of the 0.15 s? Assume the outer radius of the toilet paper does not change significantly during the pull.