IMAT 2014 Q53 [Acceleration]

A book of mass 0.40 kg rests on a horizontal surface with which it has a coefficient of dynamic friction of 0.50.

If this book is now pushed by an external horizontal force of 10 N, what will be its acceleration immediately after it has started to move?

[Assume the gravitational field strength is 10 Nkg­^{-1}, that air resistance is negligible and that the orientation of the book does not change.]

A. 25.0 ms^{-­2}
B. 12.5 ms^{-­2}
C. 50.0 ms^{-­2}
D. 20.0 ms^{-­2}
E. 15.0 ms^{-­2}

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The weight of the book, or the force pulling down on it, would be 4N.

This can be calculated by:

W=mg
W= 0.40 kg\times 10Nkg^{-1}= 4.0 N

The force of friction, which opposes the force of the new external horizontal force, can now we calculated using the coefficient of the mentioned dynamic friction.

The formula for dynamic friction is \mu= F/N, where:
\mu= coefficient
F= frictional force
N= normal force

Using this, we can say:

0.50= F/4
F= 0.50x4= 2N

Our frictional force is 2N. Our opposing external force is 10N. Our resultant force, or driving force of the book, is therefore 8N.

Now we must use newton’s first law, expressed by the formula:

F=ma

To find our acceleration.

8= 0.40a
a= 8/0.40= 20 ms^{-2}

Our answer is now clearly D.

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