I need to explain and demonstrate mathematically why it is easier to pull a wheelbarrow than it is to push it
To mathematically explain why it is easier to pull a wheelbarrow than to push it, let's consider the forces involved. We can use Newton's laws of motion and vector addition to analyze the situation.
When you push a wheelbarrow, the force you apply is mostly perpendicular to the ground since you are trying to keep the wheelbarrow upright. Let's call this force "Fp" (pushing force).
On the other hand, when you pull a wheelbarrow, the force you apply is mostly parallel to the ground, which helps in moving the wheelbarrow forward. We will call this force "Fpl" (pulling force).
Now, to demonstrate mathematically why pulling is easier than pushing, we need to analyze the angles and forces involved, assuming that the force applied by you remains constant in both cases.
Let's say the angle between the direction of the pushing force and the wheelbarrow's axis is θp, and the angle between the direction of the pulling force and the wheelbarrow's axis is θpl.
When pushing, the effective force that helps in moving the wheelbarrow forward, which we can call "Feffp," is given by Feffp = Fp * cos(θp).
When pulling, the effective force that helps in moving the wheelbarrow forward, which we can call "Feffpl," is given by Feffpl = Fpl * cos(θpl).
Here's the key difference: when pushing (θp > 0), the value of cos(θp) is less than 1, meaning that the effective force is smaller than the actual force applied. On the other hand, when pulling (θpl = 0), the value of cos(θpl) is equal to 1, so the effective force is equal to the actual force applied.
Therefore, for the same applied force, Feffpl > Feffp. This means that when you pull the wheelbarrow, there is a greater component of force in the direction of motion, making it easier to move compared to when you push it.
Note: The values of θp and θpl can vary depending on how you push or pull the wheelbarrow, but the general principle remains the same.