Consider three scenarios in which a particular box moves downward under the pull of gravity :

(A) In scenario A, the box falls straight down from an initial height h to the ground under the influence of gravity.

(B) In scenario B, the same box, starting from the same initial height, h, slides down to the ground along a frictionless ramp that makes an angle of 30° with the horizontal.

(C) In scenario C, the same box, starting from the same initial height, h, slides down to the ground along a rough ramp with friction that makes an angle of 30° with the horizontal.

Let W A gravity be the work done by gravity on the box in scenario A, let WB gravity be the work done by gravity on the box in scenario B, and let Wc gravity be the work done by gravity on the box in scenario C.

Which of the following is true? Select the correct answer:

1. O WA,gravity > WB,gravity > WC,gravity

2.O WC,gravity > WB,gravity > WA, gravity

3.O WB,gravity > WC,gravity > WA,gravity

4.O WA,gravity > WC,gravity > WB;gravity

In this exercise they give work for several different configurations and ask that we show the relationship between them, the best way to do this is to calculate each work separately.

A) Work is the product of force by distance and the cosine of the angle between them

WA = W h cos 0

WA = mg h

B) On a ramp without rubbing

Sin30 = h / L

L = h / sin 30

WB = F d cos θ

WB = F L cos 30

WB = mf (h / sin30) cos 30

WB = mg h ctan 30

C) Ramp with rubbing

W sin 30 - fr = ma

N- Wcos30 = 0

W sin 30 - μ W cos 30 = ma

F = W (sin30 - μ cos30)

WC = mg (sin30 - μ cos30) h / sin30

Wc = mg (1 - μ ctan30) h

When we review the affirmation it is the work where there is rubbing is the smallest and the work where it comes in free fall at the maximum

Let's review the claims

1. True The work of gravity is the greatest and the work where there is friction is the least

2 False. The job where there is friction is the least

3 False work with rubbing is the least

4 False work with rubbing is the least