# physics

posted by on .

THree blocks of masses 3m, 2m and m are connected to strings A,B, and C. The blocks are pulled along a rough surface by a force of magnitude F exerted by string C. The coefficient of friction between each block and the surface is the same. Which string must be the strongest in order not to break?
a) A
b) B
c) C
d) they must all be the same strength
e) It is impossible to determine without knowing the coefficient of friction

I think the answer is c) because it's the string that is pulling the largest amount of mass (which is all of the masses attached to this string).

If A pulls only mass 3m and B is between 3m and m, like this:

3m--A--2m--B--m--C-->F

Then string C has tension force F, which equals or exceeds the friction force acting on A, B, and C together, assuming there is motion.
F - u (3m + 2m + m) g = 6 m a
F = 6m (a + ug)

The tension in A is TA, and
TA - u (3m g) = 3m a
TA = 3m (a + ug)

One could write a similar equation for string B

The tension in any string is proportional to the total mass pulled by all weights behind that string. Thus the answer is C.

So you are right again!