Answers for Part A 5 ms2 and 2ms2R Part B 5pieR Part C 204 I

Example & A solid 2-kg disk is pulled P12 N P=12 N MP-12 N to the jeft by a force of 12 N against a frictional force of 2N, as shown. a) Find a cm, and cm b) Find the distance disk travels in one rev. (Is it \"rolling\"?) fr-2 N 92 c) Find the minimum such that disk is \"pure rolling\".

Solution

Here ,

P = 12 N

fr = 2 N

M= 2 Kg

a) for the acm

acm = net force/mass

acm = (12 - 2)/2

acm = 5 m/s^2

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for alpha(cm) = net torque/moment of inertia

alpha(cm) = 2 * R/(0.5 * 2 * R^2)

alpha(cm) = 2/R rad/s^2

b)

time taken for one rev

2pi = 0.5 * 2/R * t^2

t = sqrt(2 *pi * R)

distance traelled by disk = 0.5 * a * t^2

distance traelled by disk = 0.5 * 5 * 2 * R *pi

distance traelled by disk = 5 *pi * R

No , this is not rolling

c)

for pure rolling

12 - u *m * g = m * a

12 - u * 2 * 9.8 = 2 * a ----(1)

also , u *m * g * R = 0.5 * m * R^2 * (a/R)

u * g = 0.5 * (a)

a = 2 * u * g

putting in 1

12 - u *2 * 9.8 = 2 * 2 * u * 9.8

u = 0.204

the coefficient of friction needed is 0.204