Unless otherwise stated, all objects are located near the Earth\'s surface, wher

Question

Unless otherwise stated, all objects are located near the Earth's surface, where g = 9.80 { m m/s^2}.
A person has a choice while trying to push a crate across a horizontal pad of concrete: push it at a downward angle of 25 , or pull it at an upward angle 25 . If the crate has a mass of 50.0 kg and the coefficient of kinetic friction between it and the concrete is 0.790, calculate the required force to move it across the concrete at a steady speed for both situations.

What is the F required to push and the F required to pull?

Explanation / Answer

the difference is that when he pushes down, he increases the normal force on the surface thereby increasing friction

in order to move the crate at constant speed, the horizontal pushing force must equal the force of friction; the horizontal moving force = F cos 25; the frictional force is u N where u is the coeff of friction and N is the normal force; we consider vertical equilibrium to find the normal force

if he pushes down, the vertical component of the pushing force is - F sin 25, and vertical equilibrium allows us to write

N - mg - F sin 25 = 0 or N = mg + F sin 25 = 490+0.42F

then, horizontal equilibrium gives us

F cos 25 - u N =0
F cos 25 - u(490+0.42F) =0 where u = 0.79

0.906F - 0.331F = 387.1N
F=673.21N

if he pulls up, the normal force is given by

F ( cos + µ sin ) = µ m g

F( cos + 0.79 * 0.42261.83) = 387.1 ( µ m g )

F ( 0.9063 + 0.33386 ) = 387.1

----1.2016 F =387.1

F = 387.1 / 1.2016 = 322.15 N

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