How Do You Solve a Kinetic Friction Problem Involving Two Blocks?

AI Thread Summary
The discussion centers on solving a kinetic friction problem involving two blocks, where a tension force of 20 N acts on the lower block. The coefficients of kinetic friction for both the lower block with the surface and between the two blocks are both 0.30. Initially, the user attempted to calculate the acceleration of the 2.0 kg block but arrived at an incorrect answer of 2.75 m/s². After reevaluating the equations and incorporating the friction between the two blocks, the user proposed a new acceleration of 5/3 m/s², which was also incorrect; the correct answer was identified as 1.77 m/s². The discussion highlights the importance of considering all frictional forces in such problems.
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Homework Statement


The lower block in the figure is pulled on by a rope with a tension force of 20 N. The coefficient of kinetic friction between the lower block and the surface is 0.30. The coefficient of kinetic friction between the lower block and the upper block is also 0.30.
knight_Figure_08_28.jpg


Find the acceleration of the 2.0kg block

Homework Equations


The Attempt at a Solution

I set m1a= T - (0.3)m1g and m2a= 20 - T - 0.3m1+2g. After which I added them and isolating a, giving me a=(20 - 0.3m1+2g - 0.3m1g)/(m1+m2), which gave me the answer 2.75, but apparently it is not correct.

Never mind, I solved it. I forgot the friction between block 1 and 2 for movement of block 2
 
Last edited:
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m1a= T - (0.3)m1g
m2a= 20 - T - 0.3m1+2g-0.3m1g

==>a=[20-(m1+m2)g*0.3-2*0.3*m1g]/(m1+m2)=5/3 (ms^-2)

is it right?
 
Yep, you got the equation set up right, but the answer is 1.77, not 5/3
 
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