The Physics of Pushing vs. Pulling
Have you ever noticed that pulling a heavy object like a suitcase or a sled feels much easier than pushing it? This isn't just subjective—it is rooted in the fundamental laws of classical mechanics, specifically regarding friction and normal force.
The Normal Force Factor
Friction is directly proportional to the normal force ($N$), which is the force exerted by a surface perpendicular to the object. The formula for limiting friction ($f$) is:
$$f = \mu N$$
where $\mu$ is the coefficient of friction.
Scenario 1: Pushing
When you push an object at an angle $\theta$ below the horizontal, you exert a downward component of force ($F \sin \theta$). This component adds to the weight ($mg$) of the object, increasing the total normal force:
$$N_{push} = mg + F \sin \theta$$
Because the normal force increases, the frictional force increases, making it harder to move the object.
Scenario 2: Pulling
When you pull an object at an angle $\theta$ above the horizontal, you exert an upward component of force ($F \sin \theta$). This component acts in opposition to the weight ($mg$):
$$N_{pull} = mg - F \sin \theta$$
Because the normal force decreases, the frictional force decreases, making it significantly easier to set the object in motion.
Conclusion
By pulling, you effectively 'lighten' the load by counteracting gravity, thereby reducing the friction that opposes motion. By pushing, you increase the load, thereby increasing the resistance.