Why is less force needed to pull a block at an angle compared to pushing it?

[DrummingAtom]

Homework Statement

A block rests on a level floor. To move it at a constant velocity, why do you exert less force if you pull it at an angle above the horizontal than if you push it at the same angle below the horizontal?

Homework Equations

The Attempt at a Solution

I know that pushing at an angle below the horizontal is going to add to the weight (w) of the block. I've come up with these expressions:

1) F_pull = w*sin(θ)
2) F_push = w/sin(θ)

Since w in 1) is going to be multiplied by a number less than 1 it's going to decrease the magnitude of F. And since w in 2) is going to be divided by a number less than 1 it's going to increase the magnitude of F.

Is this the best way to express this relationship? Thanks for any help.

 

[fzero]

It's better to consider kinetic friction and the sum of vertical forces. The expressions you wrote down are incorrect. The applied force is independent of the weight. You need to draw a force diagram and examine the sums of forces.

 

[PhanthomJay]

If you apply a force F and it moves at constant velocity on a level floor, then some other force must be acting equal and opposite to that horizontal component of the applied force, per Newton's 1st Law. What is that other force?