Understanding the Physics of Pushing vs. Pulling
In classical mechanics, the ease of moving an object depends not just on the applied force, but on how that force affects the normal reaction (the force exerted by the ground back onto the object).
When we apply a force $F$ at an angle $\theta$ to the horizontal, we can resolve this force into two perpendicular components:
- Horizontal component ($F \cos \theta$): Responsible for moving the object forward.
- Vertical component ($F \sin \theta$): Affects the total weight pressing down on the ground.
The Case of Pushing
When you push a roller, you apply force downwards. The vertical component $F \sin \theta$ acts in the same direction as the weight ($mg$) of the roller.
- Normal reaction $N = mg + F \sin \theta$.
- Since the frictional force is proportional to the normal reaction ($f = \mu N$), the friction becomes $f = \mu(mg + F \sin \theta)$.
- This increase in normal reaction increases the friction, making it harder to move the roller.
The Case of Pulling
When you pull a roller, the vertical component $F \sin \theta$ acts upwards, opposing the weight of the roller.
- Normal reaction $N = mg - F \sin \theta$.
- The effective normal reaction is decreased, which in turn reduces the frictional force $f = \mu(mg - F \sin \theta)$.
- Because there is less resistance from friction, it is significantly easier to pull the roller than to push it.
Conclusion
While the forward force ($F \cos \theta$) remains the same for both, the difference lies in the frictional resistance. Pulling effectively 'lifts' the roller slightly, reducing the contact pressure between the roller and the ground.