cylindrical röller of mass m and radius r, initially stationary, is pulled along on a rough horizontal plane by a force F, as shown in the figure. a m i) Sketch the forces and torques acting on the roller. ii) By resolving forces horizontally and vertically show that the acceleration of the roller, a, will be given by: 2F a = Зт where u, is the coefficient of static friction. iii) Recalling that the condition for the roller to roll is that a = ar, where a is the angular acceleration of the cylinder, show that the cylinder will slide if: F> 3µsmg.
cylindrical röller of mass m and radius r, initially stationary, is pulled along on a rough horizontal plane by a force F, as shown in the figure. a m i) Sketch the forces and torques acting on the roller. ii) By resolving forces horizontally and vertically show that the acceleration of the roller, a, will be given by: 2F a = Зт where u, is the coefficient of static friction. iii) Recalling that the condition for the roller to roll is that a = ar, where a is the angular acceleration of the cylinder, show that the cylinder will slide if: F> 3µsmg.
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![C7] :
a) A cylindrical roller of mass m and radius r, initially stationary, is pulled
along on a rough horizontal plane by a force F, as shown in the figure.
a
>>
F
m
i) Sketch the forces and torques acting on the roller.
ii) By resolving forces horizontally and vertically show that the acceleration of the
roller, a, will be given by:
2F
a =
Зт
where u, is the coefficient of static friction.
iii) Recalling that the condition for the roller to roll is that a = ar, where a is the
angular acceleration of the cylinder, show that the cylinder will slide if:
F > 3µsmg.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd382491f-da3f-4b93-81d5-2060893755a3%2F0f1aeb2f-49b1-466b-9640-ede69021cbe0%2F4ldsads_processed.jpeg&w=3840&q=75)
Transcribed Image Text:C7] :
a) A cylindrical roller of mass m and radius r, initially stationary, is pulled
along on a rough horizontal plane by a force F, as shown in the figure.
a
>>
F
m
i) Sketch the forces and torques acting on the roller.
ii) By resolving forces horizontally and vertically show that the acceleration of the
roller, a, will be given by:
2F
a =
Зт
where u, is the coefficient of static friction.
iii) Recalling that the condition for the roller to roll is that a = ar, where a is the
angular acceleration of the cylinder, show that the cylinder will slide if:
F > 3µsmg.
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