Question

Anyone know the answer?

Answer 1

`<b><u>Answer</u></b>`

The magnitude of the acceleration to the nearest hundredth is
`3.39ms^(-2)`


`<b><u>Explanation</u></b>`

We have to analyze the external forces acting on the two solid blocks.

The tension,
`T` in the string, the weight
`w_1=12.4g` and
`w_2=25.5g` are all illustrated in the diagram in the attachment.

Recall from Newton's law of motion that,


`F=ma`, where
`m` is mass measured in kilograms and
`a` is the acceleration in
`ms^(-2)`.

For the
`12.4kg` mass the resultant upward force is


`T-12.4g`.

Applying
`F=ma` to the
`12.4kg` mass gives


`T-12.4g=12.4a...eqn(1)`.

For the
`25.5kg` mass the resultant downward force is


`25.5g-T`

Applying
`F=ma` to the
`25.5kg` mass gives,


`25.5g-T=25.5a...eqn(2)`

Adding the two equations gives us,


`25.5g-12.4g=25.5a+12.4a`

This simplifies to


`13.1g=37.9a`

We divide both sides by
`37.9` to obtain,


`(13.1g)/(37.9)=a`

We were given
`g=9.8ms^(-2)`

We substitute this value to obtain,


`a=(13.1)/(37.9) * 9.8`


`a=3.3873 \ms^(-2)`

Hence the magnitude of the acceleration to the nearest hundredth is
`3.39ms^(-2)`