Why Does a String Need to Be Parallel to the Plane in Physics Problems?

[ironhawk316]

Homework Statement

Why is it important that the string be parallel to the plane? Use Diagrams to illustrate.

Homework Equations

F = ma

The Attempt at a Solution

I believe that if the string is parallel to the plane it requires more force than if it were inclined because pulling up on the cart reduces the FN. This makes the cart less heavy, reducing the friction.

I have included an attachment of my diagram that I made.

 

[jbsteele]

As the diagram shows, when the string is parallel to the plane, the force (F) is acting in the same direction as the acceleration (a). This means that the force will be working in tandem with the acceleration of the cart. The force and acceleration are both working together to propel the cart forward. However, if the string is inclined, then the force would not be acting in the same direction as the acceleration. This would cause the force to be pushing against the acceleration, thus slowing down the cart's movement. So, it is important that the string be parallel to the plane in order to maximize the force and acceleration, and ensure that the cart moves at the fastest possible speed.

 

[nlightner]

I would like to clarify and expand on this explanation. It is important for the string to be parallel to the plane because it minimizes the effect of the normal force acting on the object being pulled. The normal force, represented by FN in the equation F=ma, is the force exerted by the surface on the object in the direction perpendicular to the surface. In this case, the surface is the plane and the object is the cart. When the string is parallel to the plane, the normal force acts in a direction that is perpendicular to the string, thus not affecting its movement. This reduces the friction force acting against the cart, making it easier to pull and requiring less force to move it.

In contrast, if the string is inclined, the normal force acts in a direction that is not perpendicular to the string. This creates a component of the normal force that acts against the direction of motion, adding to the friction force and making it more difficult to move the cart. This can be seen in the diagram, where the inclined string creates a larger angle between the normal force and the direction of motion compared to the parallel string.

Therefore, it is important for the string to be parallel to the plane in order to minimize the effect of the normal force and reduce the friction force acting against the object. This allows for a more accurate and efficient application of the equation F=ma, as shown in the diagram where the parallel string requires less force to move the cart compared to the inclined string.