Chapter 5, Problem 2TS

A car with a mass of $1000\text{kg}$ moves at $20\text{m}/\text{s}$. Show that the braking force needed to bring the car to a halt in $10\text{s}$ is $2000\text{N}$.

To determine

The braking force needed to bring the car to a halt.

Answer to Problem 2TS

The braking force needed to bring the car to a halt is $2000\text{N}$.

Explanation of Solution

Given Info: The mass of the car is $1000\text{kg}$, speed of the car is $20\text{m}/\text{s}$, time for the braking force is $10\text{s}$.

Write the expression to calculate the momentum of the car.

$P=m\cdot v$

Here,

$P$ is the momentum of the car

$m$ is the mass of the car

$v$ is the speed of the car

Write the expression to calculate the impulse of the car.

$I=F\cdot t$

Here,

$I$ is the impulse of the car

$F$ is the braking force

$t$ is the time for which the braking force applies

The momentum of the car is same as the impulse of the car, so equate the above two expressions to calculate the braking force.

$\begin{array}{c}I=P\\ F\cdot t=m\cdot v\\ F=\frac{m\cdot v}{t}\end{array}$

Substitute $1000\text{kg}$ for $m$, $20\text{m}/\text{s}$ for $v$ and $10\text{s}$ for $t$ to find the $F$.

$\begin{array}{c}F=\frac{\left(1000\text{kg}\right)\left(20\text{m}/\text{s}\right)}{10\text{s}}\\ =2000\text{kg}\cdot \text{m}/{\text{s}}^2\\ =\left(2000\text{kg}\cdot \text{m}/{\text{s}}^2\right)\left(\frac{1\text{N}}{1\text{kg}\cdot \text{m}/{\text{s}}^2}\right)\\ =2000\text{N}\end{array}$

Conclusion:

Therefore, the braking force needed to bring the car to a halt is $2000\text{N}$.