Friction Force on a System at Rest

[odie5533]

Homework Statement

http://img337.imageshack.us/img337/2514/diagramfn4.png

The Attempt at a Solution

$$\sum F_{x} = w_{x} - T = m_{x}a$$
$$T = (6.9)g - (6.9)a$$

$$\sum F_{a} = T - w_{a} - f_{s} = m_{a}a$$
$$T - m_{a}g - m_{a}a = f_{s}$$
$$(6.9g - 6.9a) - m_{a}g - m_{a}a = f_{s}$$
I don't see a 5kg block with friction, but I do see a 3kg block with friction:
$$6.9g - 6.9a - 3g - 3a = f_{s}$$
$$3.9g - 9.9a = f_{s}$$

Since the system is at rest, $$a = 0$$
$$38N = f_{s}$$
So the answer is B

But I have two problems with my answer:
1) $$f_{s-max} = (0.40)(50) = 20N < 38N$$ in my answer
2) Using the "5kg" block, $$f_{s} = 19N$$

Am I missing something?

 

[Doc Al]

Looks to me like the 3 kg was a typo and they meant to write 5 kg. (Otherwise the problem doesn't work, as you point out.)

 

[ogb p]

I would like to clarify a few things about your response. First, it is important to note that the homework statement provided does not specify the mass of the block with friction, so it is possible that the 5kg block is indeed the one with friction. However, assuming that the 3kg block is the one with friction, your solution is correct.

Regarding your concerns, it is important to remember that the maximum static friction force (f_{s-max}) is the maximum force that can act before the object starts to move. In this case, since the system is at rest, the static friction force must be less than or equal to the maximum static friction force. Therefore, your answer of 38N is still within the limit of the maximum static friction force of 20N.

In addition, the value of f_{s} can vary depending on the mass of the block and the coefficient of friction. In your calculation, you used a mass of 5kg, while in the homework statement, the mass of the block is not specified. Therefore, it is possible that the value of f_{s} can be different in different scenarios.

Overall, your solution is correct and you have not missed anything. It is important to carefully consider the given information and assumptions when solving problems in physics.