- #1

- 293

- 39

- Homework Statement
- the arrangement in the figure

- Relevant Equations
- sum(F)=ma

in the opposite problem that has three pulleys and two masses, the book is asking for :

1- the tension on the string.

2- the acceleration of pulley p1.

3- the acceleration of mass m2.

4- what should the mass "m" be such that m1 does not accelerate?

note : pulley p1 has mass m, in the diagram of P1 there should be mg also along with T on pulley 1 , I assume!

the solution

1-

$$

T-m_{1}g=m_{1}a_{1},\quad,\quad T=m_{1}(g+a_{1})

$$

2-

$$

m_{2}g-T_{2}=m_{2}a_{2},\quad,\quad a_{2}=(m_{2}g-T_{2})/m_{2}

$$

3-

$$

2T-T-mg=ma_{p1}\quad,\quad a_{p1}=T/m-g

$$

4- now for a_{1} to equal zero the system will be in equilibrium and

$$

T=m1g\quad, T/m=g\quad, m=m_{1}

$$

I just want to check my answer or if I am missing something, thanks in advance.

1- the tension on the string.

2- the acceleration of pulley p1.

3- the acceleration of mass m2.

4- what should the mass "m" be such that m1 does not accelerate?

note : pulley p1 has mass m, in the diagram of P1 there should be mg also along with T on pulley 1 , I assume!

the solution

1-

$$

T-m_{1}g=m_{1}a_{1},\quad,\quad T=m_{1}(g+a_{1})

$$

2-

$$

m_{2}g-T_{2}=m_{2}a_{2},\quad,\quad a_{2}=(m_{2}g-T_{2})/m_{2}

$$

3-

$$

2T-T-mg=ma_{p1}\quad,\quad a_{p1}=T/m-g

$$

4- now for a_{1} to equal zero the system will be in equilibrium and

$$

T=m1g\quad, T/m=g\quad, m=m_{1}

$$

I just want to check my answer or if I am missing something, thanks in advance.