Chapter 11: Q. 51 (page 289)

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides $8.2$ m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction

Short Answer

Expert verified

The distance traveled by the lighter fragment side is $400 m$

Step by step solution

Step 1. Given information

One fragment is seven times as massive as the other fragment.

The distance traveled by heavier fragment, $8.2 m$

Step 2. Evaluating the velocities

Use the Newton's second law of motion,

$\begin{matrix} F_{heavier} = a_{heavier} m_{heavier} = μ_{k} g \\ F_{lighter} = a_{lighter} m_{lighter} = μ_{k} g \end{matrix}$

Now, evaluating the velocities,

For heavier:

$\begin{array}{r} v_{heavier}^{2} = 2 d_{heavier} \\ v_{heavier} = \sqrt{2 \frac{μ_{k} g}{m_{heavier}} d_{heavier}} \end{array}$

For lighter:

$\begin{array}{r} v_{lighter}^{2} = 2 a_{lighter} d_{lighter} \\ v_{lighter} = \sqrt{2 \frac{μ_{k} g}{m_{lighter}} d_{lighter}} \end{array}$

$\begin{array}{l} \frac{{v_{l i g h t e r}}^{2}}{{v_{h e a v i e r}}^{2}} = \frac{d_{l i g h t e r}}{d_{h e a v i e r}} \\ \Rightarrow \frac{d_{l i g h t e r}}{d_{h e a v i e r}} = 49 \\ \Rightarrow d_{l i g h t e r} = 49 d_{h e a v i e r} \end{array}$

Step 3. Applying conservation principle

On applying conservation of momentum we have,

$0 = m_{h e a v i e r} v_{h e a v i e r} - m_{l i g h t e r} v_{l i g h t e r} m_{h e a v i e r} \sqrt{2 \frac{μ_{k} g}{m_{h e a v i e r}} d_{h e a v i e r}} - m_{h e a v i e r} \sqrt{2 \frac{μ_{k} g}{m_{h e a v i e r}} d_{l i g h t e r}} = 0 d_{l i g h t e r} = 49 \times 8.2 \approx 400 m$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides $8.2$ m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating the velocities

Step 3. Applying conservation principle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Torque and Rotational Motion

Further Mechanics and Thermal Physics

Famous Physicists

Astrophysics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides 8.2m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating the velocities

Step 3. Applying conservation principle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Dynamics

Torque and Rotational Motion

Further Mechanics and Thermal Physics

Famous Physicists

Astrophysics

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

An object at rest on a flat, horizontal surface explodes into two fragments, one seven times as massive as the other. The heavier fragment slides $8.2$ m before stopping. How far does the lighter fragment slide? Assume that both fragments have the same coefficient of kinetic friction