Add forces as vectors help - Thanks

[nukeman]

Homework Statement

I am not understanding this. This is the question, and the correct solutions for the question I need help with.

I really don't understand how to get the answer here! Can anyone help me? First steps?

Question:

Answer:

Homework Equations

The Attempt at a Solution

 

[technician]

Are you confident with the idea that you have 2 forces which are vectors.
In the first case the vectors (20N and 15N) are at 90 degrees. To find acceleration you divide F by m (5kg) giving 2 acceleration vectors 4 and 3 at 90 degrees.
You need to find the resultant of these 2 perpendicular vectors (pythagoras !)
In the second case the logic is the same but the angle is not 90 degrees.
Is this any help?

 

[nukeman]

I understand how to get (4i + 3j) but how did they eventually come up with 5 m/s^2 at 36.9 degreeS?

 

[DrewD]

The magnitude of the vector comes from the pythagorean theorem by treating the two vectors as perpendicular sides of a triangle. Trig is the best way to get the angle. How's your trig?

 

[asteriatic]

I am happy to assist you with your question. The concept of adding forces as vectors can be confusing at first, but it is a fundamental concept in physics. Essentially, when we add forces as vectors, we are considering both the magnitude and direction of each force in relation to each other. This allows us to determine the overall effect of multiple forces acting on an object.

To get started, it is important to draw a diagram showing all the forces acting on the object. This will help you visualize the direction and magnitude of each force. Next, we can use vector addition to find the resultant force. This involves adding the individual components of each force in a specific order, typically using the head-to-tail method.

Once you have determined the resultant force, you can use it to solve for any other variables in the problem, such as acceleration or velocity. It is also important to keep in mind the principles of Newton's Laws of Motion when working with forces.

I hope this helps you understand the concept of adding forces as vectors. If you have any further questions or need clarification, please don't hesitate to ask. Remember, practice makes perfect, so keep practicing and you will become more comfortable with this concept. Good luck with your homework!