Force and Motion with two unknows

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The discussion revolves around solving a physics problem involving two bodies with different weights and friction coefficients on an incline. Body A weighs 100 N and body B weighs 77 N, with a friction coefficient of μs = 0.52 and μk = 0.28 at an angle of θ = 31°. Participants are attempting to derive equations for the forces acting on both bodies, focusing on tension and acceleration as the two unknowns. Despite having two equations, users express difficulty in solving for the unknowns, prompting requests for numerical substitution to clarify the calculations. The conversation highlights the challenges of applying Newton's laws in multi-body systems with friction.
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Body A in Fig. 6-36 weighs 100 N, and body B weighs 77 N. The coefficients of friction between A and the incline are μs = 0.52 and μk = 0.28. Angle θ is 31°. Let the positive direction of an x-axis be down the slope. What is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down the incline?
http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c06/fig06_34.gif

=S m stuck @ -FT + mgsintheta = ma and i am stuck with two unknowns.. Tension and acceleration
 
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Welcome to PF!

ankitp3 said:
-FT + mgsintheta = ma and i am stuck with two unknowns.. Tension and acceleration

Hi ankitp3! Welcome to PF! :smile:

Yes, you do have two unknowns.. tension and acceleration …

but you also have two equations, one for body A and one for body B. :wink:
 


still having hard time solving this problem :S
 
ankitp3 said:
still having hard time solving this problem :S

ok, show us your two equations, and we'll see what we can do … :smile:
 
FK + mgsingtheta - FT = m1ax (block A)

Ft - Fg = m2gy (block b)

ukmgcostheta - mgsintheta - FT = m1ax

Ft - (wB) = (wB/9.8)a

ukmgcostheta + mgsintheta - Ft (< sub in Ft from the last equation)
 
ankitp3 said:
FK + mgsingtheta - FT = m1ax (block A)

Ft - Fg = m2gy (block b)

ukmgcostheta - mgsintheta - FT = m1ax

Ft - (wB) = (wB/9.8)a

ukmgcostheta + mgsintheta - Ft (< sub in Ft from the last equation)

Sorry … I've stared at this for several minutes and I can't follow it. :confused:

Can you put the numbers in? :smile:
 

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