I need to explain and demonstrate mathematically why it is easier to pull a wheelbarrow than it is to push it.
Also, what effect does the component of force parallel to a bicycle crank have?
To explain why it is easier to pull a wheelbarrow than to push it mathematically, we can analyze the forces involved using Newton's laws of motion.
Let's assume that the wheelbarrow is on a level surface and there is no friction. When you pull the wheelbarrow, there are two forces acting on it:
1. Tension force applied by you: Let's define this force as T.
2. Weight of the wheelbarrow: Let's denote it as W.
When you pull the wheelbarrow, the tension force T acts in the forward direction, opposing the weight W. This causes a net force in the forward direction.
Using Newton's second law, we can express this relationship mathematically as:
T - W = mass × acceleration
Now, let's consider pushing the wheelbarrow. When you push the wheelbarrow, there are still two forces acting on it:
1. Normal force exerted on the wheelbarrow by the ground: Let's denote it as N.
2. Frictional force between the wheelbarrow and the ground: Let's denote it as F.
When you push the wheelbarrow, the normal force N acts in the upward direction and friction force F acts in the opposite direction of your push. The friction force opposes the motion and is greater when pushing compared to pulling due to the geometry and design of the wheelbarrow.
The relationship between these forces can be expressed as:
F - N = mass × acceleration
Since the friction force F is generally greater than the tension force T, it requires more force to overcome the friction when pushing the wheelbarrow compared to pulling it. This is why it is easier to pull a wheelbarrow than to push it.
Regarding the effect of the component of force parallel to a bicycle crank, it plays a significant role in propelling the bicycle forward.
When you pedal a bicycle, there are two components of force acting on the crank:
1. Force parallel to the crank: Denote it as F_parallel.
2. Force perpendicular to the crank: Denote it as F_perpendicular.
The force parallel to the crank (F_parallel) is responsible for generating torque and transferring power to the bicycle's drivetrain. It creates a rotational force on the chainring, which then moves the chain and ultimately propels the bicycle forward.
By applying force on the crank at the appropriate angle, you optimize the efficiency and effectiveness of the force transfer, allowing you to generate more power and speed.
In summary, the component of force parallel to the bicycle crank is essential for propelling the bicycle forward by creating torque and transferring power through the drivetrain.