Please show all steps to recieve rating! A block of mass m1 = 2.45 kg and a bloc

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Please show all steps to recieve rating!

A block of mass m1 = 2.45 kg and a block of mass m2 = 5.95 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 theta = 30.0 degree 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. left of the pulley right of the pulley

Explanation / Answer

for m2

m2*g*sin30 - u*m2*g*cos30 -T2 = m2*a

T2 = m2*g*sin30 - u*m2*g*cos30 - m2*a ...........(1)

for m1

T1 - u*m1*g = m1*a

T1 = = u*m1*g - m1*a........(2)

for M

(T2-T1)*R = I*alfa

(T2-T1)*R =(1/2)*M*R^2*a/R

T2 - T1 = (1/2)*M*a .........(3)

using 1 &2 in 3

m2*g*sin30 - u*m2*g*cos30 - m2*a - u*m1*g _ m1*a = 0.5*M*a

(m2*sin30 - u*m2*cos30 - u*m1)*g = a*(0.5M + m1 + m2)

a = (m2*sin30 - u*m2*cos30 - u*m1)*g/(0.5M + m1 + m2)

a = (9.8*((5.95*0.5)-(0.36*5.95*0.866)-(0.36*2.45)))/((0.5*10)+2.45+5.95)

a = 0.175 m/s^2 <----answer

+++++++++++++++

c) T1 = u*m1*g - m1*a = (0.36*2.45*9.8)-(2.45*0.175) = 8.21485 N

T2 = m2*g*sin30 - u*m2*g*cos30 - m2*a

T2 = (5.95*9.8*0.5)-(0.36*5.95*9.8*0.866)-(5.95*0.175)

T2 = 9.94 N

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