Question

Anyone know the answer?

Answer 1

$Answer$

The magnitude of the acceleration to the nearest hundredth is $3.39ms^{-2}$

$Explanation$

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,

$\frac{13.1g}{37.9}=a$

We were given $g=9.8ms^{-2}$

We substitute this value to obtain,

$a=\frac{13.1}{37.9} \times 9.8$

$a=3.3873 \ms^{-2}$

Hence the magnitude of the acceleration to the nearest hundredth is $3.39ms^{-2}$