What is the relationship between the following forces?

Weight, normal force, applied force, and friction force.

a. A homeowner is applying southwest force on a lawn mower, friction force is going to the East, normal force is North, weight is South.

This was a multiple choice question and the answer was Applied force > Friction force and Normal force > Weight

b. A dude is pulling a box Northeast direction, normal force North, weight is South, and friction West.

Ans: Pulling force > friction and Normal force < weight.

Can someone people explain why those are the correct answers?

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Weight, normal force, applied force, and friction force.

a. A homeowner is applying southwest force on a lawn mower, friction force is going to the East, normal force is North, weight is South.

This was a multiple choice question and the answer was Applied force > Friction force and Normal force > Weight

b. A dude is pulling a box Northeast direction, normal force North, weight is South, and friction West.

Ans: Pulling force > friction and Normal force < weight.

Can someone people explain why those are the correct answers?
Hello, Chuckfados. Welcome to PF!

I assume you are describing some sort of diagram you had as part of a multiple choice question, and in the diagram the following forces were depicted as acting on a lawnmower.

The homeowner is applying a force (the Applied Force) down and to the left (you called it southwest, as if you were looking at map).

Friction force is acting toward the right.

Normal force is acting upward.

The weight (force of gravity) is acting downward.

I assume the mower is moving at constant velocity, so that the net force on the mower is zero.

What are the vertical forces acting on the mower?

What are the horizontal forces acting on the mower?