- #1

BurpHa

- 44

- 13

- Homework Statement
- For the system of Fig. 4–32 (see below), how large

a mass would box A have to have to prevent any motion

from occurring? Assume the coefficient of the static friction = 0.30.

- Relevant Equations
- Newton's Third Law, Newton's Second Law.

Ok, logically, it must be that the static friction force of block A equal to the force of gravity on block B, so mass of block A is:

m_A * 9.8 * 0.30 = m_B * 9.8

m_A * 2.94 = 2 * 9.8

m_A * 2.94 = 19.6

m_A \approx 6.7 kg.

However, when I look at block A individually, there is one thing confuses me.

Say block A's mass is x, then in the frictionless scenario, tension force on block A is:

\frac 19.6 {x + 2} * x

I wonder how about if the static friction of block A is equal to the tension force on block A, because then block A should be stopped. Then:

9.8 * x * 0.3 = \frac 19.6 {x + 2} * x

9.8 * 0.3 = \frac 19.6 {x + 2}

2.94 = \frac 19.6 {x + 2}

x \approx 4.7 kg.

According to Newton's second law, then block A cannot move, because the force of tension and the force of static friction cancel out, thus, block B cannot move. So what is wrong about this thinking?

This is why it is confusing. I can understand how all of this work at the bird's eye view, but when I get to the individual level, it starts to confuse. I know my question is kind of silly, but please clarify for me.

Thank you for your help.

m_A * 9.8 * 0.30 = m_B * 9.8

m_A * 2.94 = 2 * 9.8

m_A * 2.94 = 19.6

m_A \approx 6.7 kg.

However, when I look at block A individually, there is one thing confuses me.

Say block A's mass is x, then in the frictionless scenario, tension force on block A is:

\frac 19.6 {x + 2} * x

I wonder how about if the static friction of block A is equal to the tension force on block A, because then block A should be stopped. Then:

9.8 * x * 0.3 = \frac 19.6 {x + 2} * x

9.8 * 0.3 = \frac 19.6 {x + 2}

2.94 = \frac 19.6 {x + 2}

x \approx 4.7 kg.

According to Newton's second law, then block A cannot move, because the force of tension and the force of static friction cancel out, thus, block B cannot move. So what is wrong about this thinking?

This is why it is confusing. I can understand how all of this work at the bird's eye view, but when I get to the individual level, it starts to confuse. I know my question is kind of silly, but please clarify for me.

Thank you for your help.