Question

Blocks with masses of $1kg,2kg\text{and}3kg$are lined up in a row on a frictionless table. All three are pushed forward by a $12N$force applied to the $1kg$block.

a. How much force does the $2kg$block exert on the $3kg$block?

b. How much force does the $2kg$block exert on the$1kg$block?

Short answer

a. The $2kg$block exerts a force of $6N$on the $3kg$block.

b. The $2kg$block exerts a force of$10N$ on the $1kg$block.

Step-by-step solution

Part (a) Step 1 : Given information

Three blocks of $1kg,2kg\text{and}3kg$are lined up in a row on a frictionless table. All three are pushed forward by a $12\hspace{0.17em}N$force applied to the $1kg$block.

Part (a) Step 2 : Calculation

The force applied on the blocks is $12\mathrm{N}$and the acceleration of the total system due to all masses is given by :-

localid="1650268035922" $$\begin{gathered} F=ma \\ a=F/\left(m_1+m_2+m_3\right) \\ a=12N/(1kg+2kg+3kg) \\ a=12N/6kg \\ a=2\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

The $2kg$must push on the $3kg$block hard enough to accelerate it at $2m/s^2$and Force on 3 kg is given by :-

$$\begin{gathered} F=ma \\ F=3kg\times 2m/s^2 \\ F=6\mathrm{N} \end{gathered}$$

Part (a) Step 3 : Final answer

The $2kg$block exerts a force of $6\hspace{0.17em}N$on the role="math" localid="1649451571902" $3kg$ block.

Part (b) Step 4 : Given information

Three blocks of $1kg,2kg\text{and}3kg$ are lined up in a row on a frictionless table. All three are pushed forward by a force of $12N$applied to the$1kg$ block.

Part (b) Step 5 : Calculation

The total force on the $1kg$block would be $12-F$. here force 'F' is the force $2kg$block exerted on the $1kg$block in backward direction.

Net force on 1 kg is given by :-

$$\begin{gathered} 12-F=ma \\ 12-F=1kg\times 2m/s^2 \\ F=12-2 \\ F=10\mathrm{N} \end{gathered}$$

Part (a) Step 6 : Final answer

The $2kg$block exerts a force of localid="1650268222629" $10N$on the $1kg$block.