Why is it more difficult to lean over and push a heavy box across the floor than it is to attach a rope and pull the box at the same angle?

Friction is the force acting between the object and the surface. So, when there will be less force of friction, it is easier  to move the body. Hence, it is easier to pull than to push a heavy box.

So, when there will be less force of friction, it is easier in that case to move the body.

Therefore, it more difficult to lean over and push a heavy box across the floor than it is to attach a rope and pull the box at the same angle.

Here , diagram is attached.

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Case 1: Pushing Diagram 1

Leaning over and Pushing the heavy box from the floor, the push will be divided in to two parts, one is horizontal that can help the box move, and one is vertically downwards, which increases the downward force of the heavy object (an addition to the gravity) and thus increases friction, making it very hard to push.  When you push at certain angle, you are exhibiting two forces as shown in diagram 1.

Case 2: Pulling Diagram 2

Pulling on a rope similar object at the same angle, the pull can be divided into two parts, one is horizontal that can help the box move, and one is vertically upwards, which decreases the downwards force of the box (a subtraction in the gravity) and thus decreases friction, making it very easy to pull. When you pull at a certain angle, you are exhibiting two forces as shown in diagram 2.

So, in the case of pushing, it adds an extra weight on the object, which results in difficulty to push that object at the same angle.  In case of pulling, the upward perpendicular force, it tries to lift the  object upward and divided the weight partially. Thus making it easier to move the object at same angle.

blue light is scattered in different directions by the tiny molecules of air. blue is scattered more than other colours because it has a shorter distance to travel which results in smaller waves. this is why we see a blue sky most of the time.