An object with a mass of $2 k g$ $2 kg$ is on a surface with a kinetic friction coefficient of $9$ $9$ . How much force is necessary to accelerate the object horizontally at $6$ $6$ $m s^{- 2}$ $ms^-2$ ?

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An object with a mass of $2 k g$ $2 kg$ is on a surface with a kinetic friction coefficient of $9$ $9$ . How much force is necessary to accelerate the object horizontally at $6$ $6$ $m s^{- 2}$ $ms^-2$ ?

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Answer 1 · 2016-01-25T04:00:35

If the object were on a frictionless surface the force required would be $12$ $12$ $N$ $N$ , but including the frictional force it is $188.4$ $188.4$ $N$ $N$ , but see the explanation: this is a silly answer because there is a problem with the question.

Explanation:

This is a very badly written question: the friction coefficient should have values between 0 and 1. Very rarely it can have values greater than one, and perhaps as high as 2, but 9 is a ridiculous and non-physical number. Are you sure it wasn't 0.9 and you missed something when writing down the question?

First we can calculate the required force due to the object's inertia:

$F = m a = 2 \cdot 6 = 12$ $F = ma = 2*6 = 12$ $N$ $N$

This is the force we'd need on a frictionless surface.

To calculate the frictional force, use:

$F_{f} = μ F_{N}$ $F_f = muF_N$ where $F_{N}$ $F_N$ is the normal force acting - in this case the weight force of the object, $m g = 2 \cdot 9.8 = 19.6$ $mg = 2*9.8 = 19.6$ $N$ $N$ .

$F_{f} = μ F_{N} = 9 \cdot 19.6 = 176.4$ $F_f = muF_N = 9*19.6 = 176.4$ $N$ $N$

To find the total force required we would add this to the $12$ $12$ $N$ $N$ above, but this is a silly number...

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An object with a mass of $2 k g$ $2 kg$ is on a surface with a kinetic friction coefficient of $9$ $9$ . How much force is necessary to accelerate the object horizontally at $6$ $6$ $m s^{- 2}$ $ms^-2$ ?

1 Answer

Explanation:

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An object with a mass of 2 kg2kg2 kg is on a surface with a kinetic friction coefficient of 9 9 9 . How much force is necessary to accelerate the object horizontally at 666 ms^-2ms−2ms^-2?

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An object with a mass of $2 k g$ $2 kg$ is on a surface with a kinetic friction coefficient of $9$ $9$ . How much force is necessary to accelerate the object horizontally at $6$ $6$ $m s^{- 2}$ $ms^-2$ ?