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What is the value of theta such that a 900 newton block is in limiting equilibrium with mu coefficient of friction equal to 1.3?
Wiki User
∙ 14y ago
Note that I will be using x as a replacement for theta, and m as a replacement for the coefficient of friction.
When a block on a ramp is in limiting equilibrium, it means it is literally on the edge of moving forwards. In other words, the force pushing it forwards and backwards cancel each other out. Now we have:
the weight of the block= 900N
Reaction force R (the force perpendicular to the ramp acting against the blocks weight)= 900cos(x)
Force down the block = 900sin(x)
Force up the block = mR = 1.3*900cos(x)
As stated earlier the forces up and down the block need to cancel each other out, in other words Force up-Force down=0 giving
1.3*900cos(x) - 900*sin(x) = 0
=> 1.3*900cos(x) = 900sin(x)
=> 1.3 = tan(x)
=> x = arctan(1.3)
=> x = 52.4314 degrees or 0.9151 rad
Wiki User
∙ 14y ago
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