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You want to slide a 0.39 kg book across a table. If the coefficient of kinetic friction is .21, what force is required to move the book with an acceleration of 0.18 m/s^2?

Respuesta :

egenriether
Find the force that would be required in the absence of friction first, then calculate the force of friction and add them together.  This is done because the friction force is going to have to be compensated for.  We will need that much more force than we otherwise would to achieve the desired acceleration:

[tex]F_{NoFric}=ma=0.39kg \times0.18 \frac{m}{s^2} =0.0702N[/tex]

The friction force will be given by the normal force times the coefficient of friction.  Here the normal force is just its weight, mg

[tex]F_{Fric}=0.39kg \times 9.8 \frac{m}{s^2} \times 0.21=0.803N [/tex]

Now the total force required is:

0.0702N+0.803N=0.873N

The force that's required to move the book is 0.873N

Mass of book = 0.39kg

Coefficient of kinetic friction = 0.21

Firstly, we need to calculate the force that's needed in the absence of friction. This will be:

F = ma

F = 0.39 × 0.18

F = 0.702N

Then, we will calculate the normal force which will be the weight multiplied by the acceleration due to gravity and this will be:

F = 0.39 × 0.21 × 9.8

F = 0.803N

Therefore, the total force that's required to move the book will be:

= 0.0702N + 0.803N

= 0.873N

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