Tuesday, 30 January 2018

homework and exercises - A block on a wedge


The system is as follows -



Friction exists only between the 2 blocks.


I am trying to find out the accelerations of m1 and m2.


Let a2 be acceleration of m2, and ax and ay be the accelerations of m1 in the respective directions. Let R be the normal reaction between the 2 blocks, and N be the normal reaction between m2 and floor. Balancing components across the axes, I get the following equations - N=m2g+Rcosθ

m2a2=Rsinθ
ax=R(sinθ+μscosθ)
ay=R(cosθ+μssinθ)m1g


I don’t think (1) is necessary, since friction is not involved between the blocks and the ground. Leaving that aside, I have 3 equations in 4 variables: ax,ay,a2,R.


Is there are any way I could perhaps get a 4th equation so that the system of equations could be solved? I can get |a1| in terms of R from the expressions for ax and ay, but I don’t think that would help.





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