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
