Two blocks with masses m 1 and m 2 are stacked on a horizontal smooth surface- Coefficient of friction between the blocks is - A force F is applied at angle - with the horizontal on block of mass m 1- Find the maximum force F so that the blocks move together-

N=(m_1g + Fsinθ) F_f=uN Fcosθ F_f=m_1a Fcosθ u(m_1g + Fsinθ)=m_1 #160; #160;.......(1) Fcosθ=(m_1 +m_2)a #160; #160; # ...

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Standard XII

Physics

Principle of Superposition

Two blocks wi...

Question

Two blocks with masses $m_{1}$ and $m_{2}$ are stacked on a horizontal smooth surface. Coefficient of friction between the blocks is $μ$ . A force $F$ is applied at angle $θ$ with the horizontal on block of mass $m_{1}$ . Find the maximum force $F$ so that the blocks move together.

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Solution

$N = (m_{1} g + F s i n θ)$
$F_{f} = u N$
$F c o s θ - F_{f} = m_{1} a$
$F c o s θ - u (m_{1} g + F s i n θ) = m_{1}$ .......(1)
$F c o s θ = (m_{1} + m_{2}) a$ ..............(2)
From equation 1 and 2:
$F c o s θ - u (m_{1} g + F s i n θ) = \frac{m_{1} F c o s θ}{m_{1} + m_{2}}$
$F = \frac{u m_{1} (m_{1} + m_{2}) g}{m_{2} c o s θ - u (m_{1} + m_{2}) s i n θ}$

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Two blocks with masses m1 and m2 are stacked on a horizontal smooth surface. Coefficient of friction between the blocks is μ. A force F is applied at angle θ with the horizontal on block of mass m1. Find the maximum force F so that the blocks move together.

N=(m1g+Fsinθ)Ff=uNFcosθ−Ff=m1aFcosθ−u(m1g+Fsinθ)=m1 .......(1)Fcosθ=(m1+m2)a ..............(2)From equation 1 and 2:Fcosθ−u(m1g+Fsinθ)=m1Fcosθm1+m2F=um1(m1+m2)gm2cosθ−u(m1+m2)sinθ

Two blocks with masses $m_{1}$ and $m_{2}$ are stacked on a horizontal smooth surface. Coefficient of friction between the blocks is $μ$ . A force $F$ is applied at angle $θ$ with the horizontal on block of mass $m_{1}$ . Find the maximum force $F$ so that the blocks move together.