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Part A

A 10 kg box slides at a constant speed of 2 m/s along a smooth floor. What is the magnitude of the normal force exerted on the box by the floor?

System: Box as point particle subject to external influences from the earth (gravity) and the floor (normal force).

Model: Point Particle Dynamics.

Approach: We begin with a free body diagram for the box:

From the free body diagram, we can write the equations of Newton's 2nd Law. We ignore the x-direction, since there are no forces acting.

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\begin

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[ \sum F_

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= N - mg = ma_

]\end

Because the box is sliding over level ground, it is not moving at all in the y direction. Thus, it certainly has no y-acceleration. Setting ay = 0 in the above equation gives:

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\begin

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[ N = mg = \mbox

Unknown macro: {98 N}

]\end

Part B

A person pushes a 10 kg box along a smooth floor by applying a perfectly horizontal force of 20 N. The box accelerates horizontally at 2 m/s2. What is the magnitude of the normal force exerted on the box by the floor?

System: Box as point particle subject to external influences from the earth (gravity), the floor (normal force) and the person (applied force).

Model: Point Particle Dynamics.

Approach: We begin with a free body diagram for the box:

From the free body diagram, we can write the equations of Newton's 2nd Law.

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\begin

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[ \sum F_

Unknown macro: {x}

= F_

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= ma_

]
[ \sum F_

Unknown macro: {y}

= N - mg = ma_

]\end

Because the box is sliding over level ground, it is not moving at all in the y direction. Thus, it certainly has no y-acceleration. Setting ay = 0 in the y direction equation gives:

Unknown macro: {latex}

\begin

Unknown macro: {large}

[ N = mg = \mbox

Unknown macro: {98 N}

]\end

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