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4 years ago

10

three masses are connected by a light string that passes over a frictionless pulley as shown. (a) what is there acceleration of

the system? (b) what are the tensions in the string?

1 answer:

Ket [755]4 years ago

3 0

The mass on the left has a downslope weight of

W1 = 3.5kg * 9.8m/s² * sin35º = 19.7 N

The mass on the right has a downslope weight of

W2 = 8kg * 9.8m/s² * sin35º = 45.0 N

The net is 25.3 N pulling downslope to the right.

(a) Therefore we need 25.3 N of friction force.

Ff = 25.3 N = µ(m1 + m2)gcosΘ = µ * 11.5kg * 9.8m/s² * cos35º

25.3N = µ * 92.3 N

µ = 0.274

(b) total mass is 11.5 kg, and the net force is 25.3 N, so

acceleration a = F / m = 25.3N / 11.5kg = 2.2 m/s²

tension T = 8kg * (9.8sin35 - 2.2)m/s² = 27 N

Check: T = 3.5kg * (9.8sin35 + 2.2)m/s² = 27 N √

hope this helps. :)

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