A crate of mass 2 kg is pulled along the floor a distance of 3m with a force of

Question

A crate of mass 2 kg is pulled along the floor a distance of 3m with a force of 9N. The coefficient of kinetic friction is k = 0.4. Calculate the work done by the applied force F , friction Fk , the normal force N , and gravity W for two cases when (a) the applied force F is parallel to the floor, and (b) F makes an angle of 30 with the horizontal. Compare the work done in both cases and explain any differences. University Physics I Ponderable Definition of work A crate of mass 2 kg is pulled along the floor a distance of 3an with a force of 9N. The cocficient cf kinetic friction is =0.4. Calculate the work done by the applied force F, friction F., the normal force N, and gravity W for two cascs when (a) the applied force F is parallel to the floor, and (b) F makes an angle of 30 with the horizontal. Compare the work done in both cases and explain any differences. Ar

Explanation / Answer

a] When force is parallel to the floor:

Work Done by the force will be:

W = 9 x 3 = 27 J

Work Done by friction force will be:

Wf = - ukNS = - 0.4(2 x 9.8)(3) = - 23.52 J

Work Done by Normal force N is zero since it is perpendicular to the displacement.

Similarly, work done by gravity will be again will zero.

b]

Work Done by the force will be:

W = FScos30 = 27cos30 = 23.382 J

Work Done by Friction will be:

Wf = - ukNS = - 0.4(mg - Fsin30)S = - 0.4((2x9.8) - 4.5)(3) = - 18.12 J

And like in the previous cases, work done by both gravity and Normal Force N will be zero since both are perpendicular to the displacement.

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