Newton's Laws for Systems of Particles - Example Problem 5.7-3

 

The coefficients of friction between block B and block A are μ_s = 0.5 and μ_k = 0.3 and the coefficients of friction between block A and the incline are μ_s = 0.62 and μ_k = 0.4. Block A weighs 30 lb and block B weighs 10 lb. Knowing that the system is released from rest in the position shown, determine the acceleration of B relative to A. The angle of the ramp is 40^o.

 

 

Given:

• W_A = 30 lb
• W_B = 10 lb
• W = W_A + W_B
• v_o = 0
• θ = 40^o
• μ_sB = 0.5
• μ_kB = 0.3
• μ_sA = 0.62
• μ_kA = 0.4

 

Find:

• a_A/B

 

Draw 2 free-body diagrams. One for the system as a whole and one that contains a FBD for each particle.

 

 

 

 

What are the normal forces that act on each block?

 

N_A = lb

 

N_B = lb