A block of mass m 1 = 2.45 kg and a block of mass m 2 = 5.65 kg are connected by

Question

A block of mass m1 = 2.45 kg and a block of mass m2 = 5.65 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of ? = 30.0

A block of mass m1 = 2.45 kg and a block of mass m2 = 5.65 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of ? = 30.0degree as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) Determine the tensions in the string on both sides of the pulley.

Explanation / Answer

b)

force equation for both blocks and pulley

for m2

5.65 g sin theta - T1 - fr1 = 5.65 a -- 1

fr1 = 5.65 g cos theta *0.360

for m1

T2 - fr2 = 2.45 a -- 2

fr2 = 2.45 g *0.360

for pulley

(T1-T2 )*R = I alpha

alpha = a/r and I = 0.5 M R^2

T1-T2 = 0.5 *10a -- 3

adding 1,2 and 3

we get

5.65 g sin theta - fr1- fr2 = a(5.65+5+2.45)

a = 0.136 m/s^2

c)

left of the pulley = T2= fr2 + 2.45 a = 8.98 N

right of the pulley = T1 = T2 + 5a= 9.66 N

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