Q. 51 An object at rest on a flat, hor... [FREE SOLUTION]

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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,

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

Now, evaluating the velocities,

For heavier:

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

For lighter:

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

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

Step 3. Applying conservation principle

On applying conservation of momentum we have,

$0 = m_{h e a v i e r} v_{h e a v i e r} 鈭� m_{l i g h t e r} v_{l i g h t e r} m_{h e a v i e r} \sqrt{2 \frac{渭_{k} g}{m_{h e a v i e r}} d_{h e a v i e r}} - m_{h e a v i e r} \sqrt{2 \frac{渭_{k} g}{m_{h e a v i e r}} d_{l i g h t e r}} = 0 d_{l i g h t e r} = 49 脳 8.2 鈮� 400 m$

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91影视

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.

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91影视

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

Translational Dynamics

Medical Physics

Nuclear Physics

Electricity and Magnetism

Further Mechanics and Thermal Physics

Classical Mechanics

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