Find out tension in the rop:
Two blocks A and B are associated as shown in Figure (a). Mass of block A is 15 kg and this is resting on a surface having a coefficient of friction μ = 0.30. The mass of block B is equal to7 kg. The pulley is frictionless. Find out the acceleration of the mass B and tension in the rope.
Solution
As the pulley is frictionless, the tension in the string shall be same and acceleration of A and B also shall be same. Let a be the acceleration and T the tension in the string.
Consider Free Body Diagram of both the bodies as shown in Figure. Consider equilibrium of body A.
∑ F_{x} = 0, T = 15 a + μ N_{1}
= 15 a + 0.3 N_{1 }----------- (1)
∑ F_{y} = 0, N_{1} = 15 × 9.81
= 147.15 N ----------- (2)
By Substituting in Eq. (1), we obtain
T = 15 a + 0.3 × 147.15
= 15 a + 44.145 ----------- (3)
Now let us assume equilibrium of body B.
∑ F_{y } = 0, T + 7a = 7 × 9.81
T = 68.67 - 7 a ------------- (4)
From Eqs. (3) and (4), we obtain
T = 15 a + 44.145 = 68.67 - 7 a
∴ 22 a = 24.525
∴ a = 1.115 m / sec.
By Substituting this value of a in either Eqs. (3) or (4), we obtain
T = 15 a + 44.145
= 15 × 1.115 + 44.145 = 60.87 N