Chapter 4, Problem 2TS

If you increase the speed of a $2.0\text{-kg}$ air puck by $3.0\text{m/s}$ in $4.0\text{ s}$, show that the force you exert on it is $1.5\text{ N}$.

To determine

The force exerted on air puck is $1.5\text{N}$.

Answer to Problem 2TS

The force exerted on air puck is $1.5\text{N}$.

Explanation of Solution

Given info: Mass of air puck is $2.0\text{kg}$, change in speed is $3.0\text{m/s}$ and total time taken is $4.0\text{ s}$.

Write the expression for the acceleration.

$a=\frac{\Delta V}{t}$

Here,

$\Delta V$ is the change in speed

$t$ is the total time taken

Substitute $3.0\text{m/s}$ is $\Delta V$ and $4.0\text{ s}$ for $t$ in the above expression to get $a$.

$\begin{array}{ccc}a& =& \frac{3.0\text{m/s}}{4.0\text{ s}}\\ a& =& 0.75{\text{m/s}}^2\end{array}$

Thus, the acceleration is $0.75{\text{m/s}}^2$.

Write the expression for the force.

$F=m\times a$

Here,

$m$ is the mass of air puck

$a$ is the acceleration

Substitute $2.0\text{kg}$ for $m$ and $0.75{\text{m/s}}^2$ for $a$ in the above expression to get $F$.

$\begin{array}{ccc}F& =& 2.0\text{kg}\times 0.75{\text{m/s}}^2\\ F& =& 1.5\text{N}\end{array}$

Conclusion:

Therefore, the force exerted on air puck is $1.5\text{N}$.