Question

00-64 Figure 5-56 shows a box of mass m2 = 1.0 kg on a friction- less plane inclined at angle θ= 30°. It is connected by a cord of negligible mass to a box of mass m 3.0 kg on a horizontal fric- tionless surface. The pulley is frictionless and massless. (a) If the magnitude of horizontal force F is 2.3 N, what is the tension in the connecting cord? (b) What is the largest value the magnitude of F may have without the cord becoming slack? mi mo Fig. 5-56 Problem 64.

Answer 1

Given,
m1 = 3 kg
m2 = 1 kg
θ = 30 degree
F = 2.3 N

a)
m2*g*sinθ - T = m2*a
T + F = m1*a
solve these equations and get
T = m2*(m1*g*sinθ - F)/(m1 + m2)
Plug values ,
T = (3*9.8*sin30 - 2.3)/(4)
=> T = 3.1 N

b)
If T = 0 then m1*g*sinθ - F = 0
so
F = m1*g*sinθ
= 3*9.8*sin30
= 14.7 N