If an object is moving at 12 m/s over a surface with a kinetic friction coefficient of u_k=5 /g, how far will the object continue to move?

Apr 2, 2017

The distance is $= 14.4 m$

Explanation:

Let the mass of the object be $= m k g$

$v = 12 m {s}^{-} 1$

The coefficient of kinetic friction is

${\mu}_{k} = {F}_{r} / N$

$N = m g$

So,

${F}_{r} = {\mu}_{k} \cdot N$

$= \frac{5}{g} \cdot m g = 5 m N$

The work done by ${F}_{r}$ is equal to the kinetic energy of the object.

${F}_{r} \cdot d = \frac{1}{2} m {v}^{2}$

$d = \frac{\frac{1}{2} m {v}^{2}}{5 m} = {v}^{2} / 10 = {12}^{2} / 10 = \frac{144}{10} = 14.4 m$
The passage contains a physics problem that involves calculating the distance an object will move given its initial velocity and the kinetic friction coefficient. The answer to the question is provided within the explanation.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
If an object is moving at 12 m/s over a surface with a kinetic friction coefficient of u_k=5 /g, how far will the object continue to move?

Apr 2, 2017

The distance is $= 14.4 m$

Explanation:

Let the mass of the object be $= m k g$

$v = 12 m {s}^{-} 1$

The coefficient of kinetic friction is

${\mu}_{k} = {F}_{r} / N$

$N = m g$

So,

${F}_{r} = {\mu}_{k} \cdot N$

$= \frac{5}{g} \cdot m g = 5 m N$

The work done by ${F}_{r}$ is equal to the kinetic energy of the object.

${F}_{r} \cdot d = \frac{1}{2} m {v}^{2}$

$d = \frac{\frac{1}{2} m {v}^{2}}{5 m} = {v}^{2} / 10 = {12}^{2} / 10 = \frac{144}{10} = 14.4 m$
user
The passage contains a physics problem that involves calculating the distance an object will move given its initial velocity and the kinetic friction coefficient. The answer to the question is provided within the explanation.

TYPE: SINGLE_QUESTION_WITH_ANSWER