A 6 kg uniform cylinder with radius .1 m rolls down smoothly with an initial spe

Question

A 6 kg uniform cylinder with radius .1 m rolls down smoothly with an initial speed of 0 from the top of a slope of angle 30 degrees. Respect to horizontal. (The rotational inertia of a cylinder is I= MR^2/ 2.)

Part A: The magnitude of the friction force between the cylinder and the slope is:

a: 9.8 N b: 20 N c: 29 N d: 51 N e:it is varying because the cylinder is accelerating

Part B: the linear acceleration of the cylinder in m/s^2 is about

a: 3.3 b:4.9 c: 6.5 d: 9.8 e: none of the above

Part C: if the top of the slope is t a height of 1 meter, what is the linear speed of the cylinder when it reaches the bottom of the slope?

a: 1.8 m/s b: 2.2 m/s c: 3.6 m/s d: 4.4 m/s e. 5.4 m/s

Part d: when the cylinder reached the bottom, its kinetic energy is

A: 9.8 J b: 20 J c: 39J d: 59 J e: 78J

Explanation / Answer

Part A : answer is c =29 N

Part B: answer is e none of these as a=1.96 m/s^2

PartC: answer is d i.e 4.4m/s as mgh=1/2mv^2

Part d: K.E =1/2 mv2 =0.5 x6 x (4.4)^2 =58.08 i.e when we have taken g=9.81m/s^2 if you take g=10m/s^2 it is exactly 59J so option d is answer

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