Question

PHYSICS HELP
PLEASE HELP ITS ABOUT ATWOOD MACHINES

Answer 1

7.23407

Step-by-step explanation:

easy

Answer 2

7.23407
`(m)/(s^2)`

Step-by-step explanation:

(I will not include units in calculations)

I'm assuming FBD's are already drawn, so I will work from there.

Let the 2.2kg block equal
`m_2`, and the 20kg block equal
`m_1`.

Summation equation for
`m_2`:
`\sum F_x=F_t_2-(F_f+F_g_x)=m_2a`,
`\sum F_y=F_n-F_g_y=0`

Summation equation for
`m_1`:
`\sum F_y=F_g-F_t_1=m_1a`

Torque Summation Equation:
`\sum\tau=F_t_1*r-F_t_2*r=I\alpha`

Do some plugging in with the values given:
`\sum\tau=F_t_1*r-F_t_2*r=.5Mr^2\alpha`

Replace
`\alpha` with
`(a)/(r)`, and cancel out the r's.

`\sum\tau=F_t_1-F_t_2=.5Ma`

This step is important: Rearrange the force summation equation to solve for each tension force.

`F_t_2=m_2a+F_f+F_g_x\\F_t_1=m_1g=m_1a`

Perform Substitution:
`\sum\tau=m_1g-m_1a-(m_2a+F_f+F_g_x)=.5Ma`

Now, we need to find the friction force and the horizontal component of the force of gravity.

Note that
`F_f=`μ
`F_n`

And based on our earlier summation equation:
`F_n=F_g_y`

First, break
`F_g` into x and y components.
`F_g_y=F_g\cos(\theta)`,
`F_g_x=F_g\sin(\theta)`

Perform substitution with this and the fact that
`F_g=mg`.

`\sum\tau=m_1g-m_1a-(m_2a+\mu*m_2g\cos(\theta)+m_2g\sin(\theta))=.5Ma`

Solving for a, plugging in numbers yields an answer of 7.23407
`(m)/(s^2)`