Chapter 9, Problem 88A

a.

To determine

The change in momentum of the car if a constant external force changes its speed from $10.0\text{m/s}$ to $44.0\text{m/s}$ in $68.0\text{s}$ .

Answer to Problem 88A

  $2.125\times {10}^4\text{kg}\cdot \text{m/s}$

Explanation of Solution

Given:

The mass of the car, $m=625\text{kg}$

Initial velocity of the car, $v_i=10\text{m/s}$

Final velocity of the car, $v_f=44\text{m/s}$

Time taken, $\Delta t=68.0\text{s}$

Formula used:

Momentum of an object of mass m and moving with velocity v is given by,

  $p=mv$

Calculation:

Using the given values in above formula, the change in momentum will be

  $\begin{array}{c}{p}_f-p_i=m{v}_f-m{v}_i\\ \Delta p=m\left(v_f-v_i\right)\\ =625\left(44-10\right)\\ =2.125\times {10}^4\text{kg}\cdot \text{m/s}\end{array}$

Conclusion:

Thus, the change in momentum of the car is $2.125\times {10}^4\text{kg}\cdot \text{m/s}$ .

b.

To determine

The magnitude of the external constant force applied to the car.

Answer to Problem 88A

  $312.5\text{N}$

Explanation of Solution

The mass of the car, $m=625\text{kg}$

Initial velocity of the car, $v_i=10\text{m/s}$

Final velocity of the car, $v_f=44\text{m/s}$

Time taken, $\Delta t=68.0\text{s}$

From part (a), the change in momentum of the car, $\Delta p=2.125\times {10}^4\text{kg}\cdot \text{m/s}$

Formula used:

Momentum of an object of mass m and moving with velocity v is given by,

  $p=mv$

Impulse on an object is equal to the change in momentum of an object,

  $\text{Impulse = }F\Delta t=p_f-p_i$

Where $F$ is the applied force for time $\Delta t$ , $p_f$ is the final momentum, $p_i$ is the initial momentum.

Calculation:

Then, using the given and calculated values in above formula, the magnitude of the external force will be,

  $\begin{array}{c}F\Delta t=\Delta p\\ F\left(68\right)=2.125\times {10}^4\text{kg}\cdot \text{m/s}\\ F=312.5\text{N}\end{array}$

Conclusion:

Thus, the magnitude of the external, constant force applied on the car is $312.5\text{N}$ .