Chapter 9.1, Problem 4PP

a.

To determine

To Sketch: Event showing initial and final situation.

Explanation of Solution

Introduction:

Momentum is simply a ‘mass in motion’. When any object having mass is moving, it has momentum. It is the product of mass of an object and its velocity.

Mathematically,

  $p=mv$

Where, $p$ is momentum, $m$ is mass and $v$ is velocity of object.

Let, initial speed of the snowmobile is $v_i$ and final speed is $v_f$ and distance covered is $x$ .

The initial and final situation is shown below

  

b.

To determine

Change in momentum.

Answer to Problem 4PP

The change in momentum is $\Delta p=5.28\times {10}^3\text{kg}\text{.m/s}$

Explanation of Solution

Given:

Mass of snowmobile, $m=240\text{kg}$

Initial speed, $v_i=6\text{m/s}$

Final speed, $v_f=28\text{m/s}$

Time taken, $t=60\text{s}$

Formula used:

Change in momentum is,

  $\Delta p=F\Delta t=m\left(v_f-v_i\right)$

Where, $m$ is mass, $v_i$ is initial speed and $v_f$ is final speed.

Calculation:

On putting the values, change in momentum is

  $\begin{array}{l}\Delta p=240\times \left(28-6\right)\\ =5.28\times {10}^3\text{kg}\text{.m/s}\end{array}$

Conclusion:

Therefore, the change in momentum is $\Delta p=5.28\times {10}^3\text{kg}\cdot \text{m/s}$ .

c.

To determine

Magnitude of average force exerted.

Answer to Problem 4PP

  $F=88\text{N}$

Explanation of Solution

Given:

Mass of snowmobile, $m=240\text{kg}$

Initial speed, $v_i=6\text{m/s}$

Final speed, $v_f=28\text{m/s}$

Time taken, $t=60\text{s}$

Formula used:

Change in momentum is,

  $\Delta p=F\Delta t$

Where, $F$ is force exerted and $\Delta t$ is change in time.

Calculation:

As $\Delta p=5.28\times {10}^3\text{kg}\cdot \text{m/s}$ from previous calculation.

So, on putting the values,

  $\begin{array}{c}5.28\times {10}^3=F\times 60\\ F=\frac{5.28\times {10}^3}{60}\\ =88\text{N}\end{array}$

Conclusion:

Therefore, magnitude of average force exerted on the snowmobile is $F=88\text{N}$ .