4 A 6.00-k .00-kg, 5.00-cm radius cylinders placed undA 6.00N magnitude force pu

Question

4 A 6.00-k .00-kg, 5.00-cm radius cylinders placed undA 6.00N magnitude force pulls the beam at its end, coplanar with its surface as depicted. As the beam moves forward, the cylinders roll without slipping 12. g beas supported by two 2 PHysIcs 281 General Physics I Problem Set 9 relative to the floor and bea a) At the instant the cylinders are equidistant from each end, what is the acceleration of the beam? (b) What is the acceleration of the cylinders? (c) Determine the frictional forces at this time

Explanation / Answer

12. given M = 6 kg

m = 2 kg

r = 5 cm = 0.05 m

F = 6 N

a. for the given instant let te acceleration of the beam be a

then

normal reaction on both the cylinders is the same form symmetry and hence frictionforces are the same

let friction between cylinder and the beam be f

F - 2f = M*a

let friction between cylinder and the ground be f'

f + f' = m*a' ( where a' is acceleration of the cylinders)

for every x meters travelled by the beam, the cylinders have angulr motion of x/r

so alpha' = a/r

hence a' = a

hence

F - 2f = Ma

f + f' = m*a

also,

(f - f')r = 0.5mr^2*a/r ( torque balance)

f - f' = 0.5ma

2f = 1.5ma

F - 1.5ma = Ma

a = F/(M + 1.5m) = 6/(6 + 1.5*2) = 0.6667 m/s/s

b. a' = a = 0.6667 m/s/s

c. 2f = 1.5ma

f = 1 N

f' = 0.333 N

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