Problem 5.4 Two weights are hanging as shown in the figure(Figure 1) (Figure 1)

Question

Problem 5.4 Two weights are hanging as shown in the figure(Figure 1) (Figure 1) Two Masses, a Pulley, and an Inclined Plane (Figure 1) Block 1, of mass m1 = 0.550kg , is connected over an ideal (massless and frictionless) pulley to block 2, of mass m2, as shown. For an angle of B = 30.0 and a coefficient of kinetic friction between block 2 and the plane of Mu = 0.400, an acceleration of magnitude a = 0.250m/s^2 is observed for block 2 Part A Find the tension in cable A. Part B Find the tension in cables B and C. Part A Find the mass of block 2, m2. Express your answer numerically in kilograms.

Explanation / Answer

part A:
tension in cable A supports 150 N

so Ta=150 N

part B:

angle made by each wire with vertical=30 degrees
then let tension in each wire be T. (as there is no horizontal external force, the horizontal component of each tension will cancel each other and as angle amde with vertical is same, tension in each string will be equal)

then balancing vertical force:

2*T*cos(30)=150+72=222

Tb=Tc=128.17 N

part C:

let tension in the string be T.

then for m1:

m1*g-T=m1*a

T=5.2525 N

for m2, the friction force=friction coefficeint*normal force=0.4*m2*9.8*cos(30)=3.4*m2

then T-m2*g*sin(30)-3.4*m2=m2*a

so m2=0.51 kg

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