Classical Mechanics Challenge
Inclined Planes
The inclined plane makes a 30 degree angle with the ground. The masses of crates A and B are 80 kg and x kg respectively. The coefficient of kinetic friction at the surface of the inclined plane is mu = sqrt(3)/10, and the pulley is fricionless. If crate A is sliding up at a constant speed, what is the value of x?
Solution
A major key to solving any mechanics problem is to annotate the diagram with appropriate forces.
As the crates are moving at a constant speed, we know from Newton’s Second Law that the net force applied to the crates must be equal to zero.
The downward force of gravity exerted on crate B is
The formula for the frictional force given the coefficient of friction is
This means the frictional force on crate A is
The net force on A is therefore
We know that the net forces must be zero.
and that
Well done!
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Barry 🍩