Components of A Resultant Force

[Bashyboy]

The following problem is one I have contrived by my own ability, so if there is any error please let me know.

Say I have a box, with a chain attached at one of the edges of the box, and I apply 10 N pull at a 40° angle with the surface of the box. Now I know we sometimes resolve vectors into their components for mere convenience of the addition of vectors. So in this case, we have a horizontal component of 7.7 N, and vertical component of 6.4 N. My question is: if I to pull with 6.4 N vertically, and a friend pull with 7.7 N horizontally, would the box accelerate in the same way if I were to only one force of 10 N at a 40° angle with the surface of the box?

 

[Naty1]

you got it!
Two component vectors ARE equivalent to their total... just like 6.4 plus 7.7 equals 14.1...in that case the vectors point in the same direction...and if they were in opposite directions 6.4 - 7.7 is equivalent to -1.3...[signs are arbitrary]

 

[Bashyboy]

Wow, thanks!

 

[thebrainstorm]

Yes, the accelaration in both cases would be the same because in both cases, he forces acting in the parallel and perpendicular directions would be the same, and since there is no question of variable mass, so the forces will produce the same accelaration.

 

[asteriatic]

I would like to start by saying that your problem is well-constructed and does not contain any errors. Now, to answer your question, the box will indeed accelerate in the same way whether you apply a single force of 10 N at a 40° angle or two separate forces of 6.4 N vertically and 7.7 N horizontally. This is because the resultant force, which is the net force acting on the box, is the same in both cases. The resultant force is the vector sum of all the individual forces acting on the box, and in this case, it will be equal to 10 N at a 40° angle.

To understand this concept better, let's look at the components of a resultant force. A resultant force has two components - magnitude and direction. The magnitude of the resultant force is the total amount of force acting on the object, which in this case is 10 N. The direction of the resultant force is the direction in which the object will accelerate, which is at a 40° angle in this case.

Now, when we break down the 10 N force into its horizontal and vertical components, we are essentially finding the individual forces that contribute to the overall resultant force. These components are still acting on the box and will result in the same acceleration, as long as their vector sum is equal to the resultant force. This is why the box will accelerate in the same way in both scenarios.

In conclusion, the components of a resultant force are the individual forces that contribute to the overall net force acting on an object. Whether these forces are applied separately or as a single force, the resultant force and its components will result in the same acceleration of the object.