The first thing to note is that we don't know what many of the forces are originally, but that is fine. Filling the forces diagram in is almost a puzzle itself. I started vertically. Each block has a mass of 5kg, so has a weight force upon it due to its own weight of 5 x 9.8 ( gravitational strength) or 5g. There is then a reaction force from the ground or block below on each block. Then Newton's third law dictates that the upper block must place an equal and opposite reaction force on the block below. That is all the vertical forces. Horizontally we need to start at the second block. The system is in equilibrium so we know opposing the 20N force is a frictional force. There is a frictional force from the blocks above and below. Again we use Newton's Third law to say that one block imposes a frictional force on a block an equal and opposite force is imparted on the other block. When all the forces are filled in, the diagram should look like the above.
Now we need to consider that the system is in equilibrium. That means that there are no resultant forces on any of the blocks. However, from the diagram it appears that the top block has a resultant frictional force to the right, I. We know this can't be the case. Therefore, we know that I=0. That means the force of I on the third block is also 0. Then for the same reason as before we know H=0, otherwise there would be a resultant force on the third block. Therefore, The diagram becomes much simpler.
Now we can apply Newton's Second law on the second block. Resolving horizontally, gives the equation. below.
20 - F =0
It is easy to see that F = 20N.
20 - F =0
To resolve vertically we need to start on the top block. We get the equation below on the top block.
U -5g = 0
U is obviously 5g or 49N
On the third block resolving vertically we get the equation.
T - 5g -5g = 0
T is obviously 10g or 98N
Then on the second block resolving vertically we get
S -10g -5g = 0
Therefore S=15g or 147N.
Now we are nearly finished. The formula for the coefficient of friction on an object is below.
Frictional force= Coefficient of friction x reaction force ( during motion or limiting equilibrium)
We can use this equation because we are dealing with limiting equilibrium, which is when the block is just on the point where any more force will cause it to start moving. If the block is not moving the frictional force is only less than the coefficient of friction x the reaction force.
Therefore, the coefficient of fiction = 20/147.6 = 0.136 (3.s.f)
I hope you enjoyed that puzzle.
The next puzzle will be up soon!
