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2. A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp that is inclined at 19.0° above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes (a) parallel to the incline and (b) parallel to the floor.

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Snor1ax

Answer: See below

Explanation:

Part (a):

As the velocity of the piano is constant, the net force on the piano is zero. The friction is also zero.

Here, F is the force applied by the man towards the inclined plane, mg is the weight of the piano and N is the normal force.

Applying Newton's law we get,

[tex]F = mg\sin \theta[/tex]

Substituting we get,

[tex]F &= \left( {180\;{\rm{kg}}} \right) \times \left( {9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) \times \sin 19.0^\circ \\ &= 574.3\;{\rm{N}}[/tex]

Therefore, the force is 574.3 N

Part (b)

Here, the force F is applied parallel to the floor.

The friction is zero.

Applying Newton's law we get,

[tex]F\cos \theta &= mg\sin \theta \\ F &= mg\tan \theta[/tex]

Substituting we get,

[tex]F &= \left( {180\;{\rm{kg}}} \right) \times \left( {9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}} \right) \times \tan 19.0^\circ \\ &= 607.4\;{\rm{N}}[/tex]

Therefore, the force is 607.4 N

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