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Which requires more work?

Two inclines have the same height and same coefficients of friction. However, incline A is much steeper than incline B. If two identical blocks were pushed up the ramp, which block requires more work to get to the top of the inclines?

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Arturo O. | Experienced Physics Teacher for Physics TutoringExperienced Physics Teacher for Physics ...
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The incline where more energy is lost from friction will require more work.
 
E = energy lost from friction
L = length of incline (longer for B, since B is less steep)
θ = angle above horizontal (higher for A, since A is more steep)
h = height (same for both inclines)
b = length of horizontal base of incline (longer for B, since B is less steep)
 
E = μmg cosθ L
 
Note that 
 
L cosθ = b ⇒
 
E = μmgb
 
Since b is greater for incline B, the energy lost is greater on B than on A, so incline B requires more work under the conditions of this problem.