Question

1. A 4 kg mass is resting on a ramp inclined at an angle of 30 degrees with respect to the horizontal. A string is attached to the 4 kg mass and passes over a frictionless pulley and is connected to a 5 kg mass hanging over the side. If the coefficient of friction between the ramp and the 4 kg mass if 0.3 find; A) The acceleration of both masses B) The tension in the string C) Find the speed of both blocks after they move a distance of 2 meters.

Answer 1

tension T and forces are in equal magnitudes

after using Newtons 2nd law for m1 we get

Ta - W1 = m1a

for mass mw, itgives

W2 +Tb-Ta = m2a

for mass m3, W3 -Tb +Ta = m2a

so

at origin W = mg

Ta +m1g = m1a

m2g + Tb -ta = m2a

m3g -Tb = ma

so

solving for acleration a   = g*(m2+m3-m1)/(m1+m2+m3)

a = 9.81 *(4 +5-4) /(4+5+4)

a =6.79 m/s^2

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Ta = 2gm1cos theta *(m2+m3)/(m1+m2+m3)

Ta = 2*9.81 * 4 * cos 30 * (4+5)/13)

Ta =47.05 N

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as V^2 = 2aS

V^2 = 2* 6.79 * 2

V = 5.211 m/s