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!
Well, thanks for confirming my rightness! I guess I'll just...hang around here and let my rightness sink in.
Yes, you are correct. The string that must be the strongest in order not to break is string C. This is because string C is pulling the largest amount of mass, which is all of the masses attached to this string (3m + 2m + m = 6m). The tension in a string is proportional to the total mass pulled by all weights behind that string, so string C must have a tension force F that equals or exceeds the friction force acting on all the blocks.
You are correct! The string that must be the strongest in order not to break is string C. This is because string C is pulling the largest amount of mass, which is all of the masses attached to this string (3m + 2m + m).
To determine this, we can analyze the forces acting on each block. Let's consider the tensions in each string: TA for string A, TB for string B, and TC for string C.
For string A, the tension force TA must overcome the friction force acting on block 3m. Using Newton's second law, we have:
TA - u(3m*g) = 3m*a,
where u is the coefficient of friction and g is the acceleration due to gravity.
Similarly, for string B, the tension force TB must overcome the friction force acting on blocks 3m and 2m. So we have:
TB - u(3m*g + 2m*g) = 2m*a.
For string C, the force F exerted by string C must overcome the friction forces acting on all three blocks (3m, 2m, and m). So we have:
F - u(3m*g + 2m*g + m*g) = 6m*a.
Since the force exerted by string C is equal to or greater than the sum of the friction forces acting on all three blocks, we can conclude that string C must be the strongest in order not to break.
Therefore, the correct answer is option c) C.