VECTORS, NEWTONG SECOND LAW [Chapter 4, question 5 (Focus on Concepts)

[gcombina]

Two vectors acting on a moving object that has a mass of 27kg.One force has a magnitude of 12 N and points due south, while the other force has a magnitude of 17N and points due west,find acceleration of the object?

Calculate the resultant force acting on the object:
RF² = 12² + 17²
RF² = 433
RF = 20.8N

Acceleration =force/mass
Acceleration = 20.8/27
acceleration = 0.770m/s²

Direction:
Tan Θ = 12/17
Tan Θ = 0.7059
Θ = 35.2° south of west


***********************************************************************************I understand everything but the last part under "Direction"

First, I want to know if my graph is ok. Can you please tell me if my graph of the problem is OK?

 

[gneill]

Hi gcombina.

Please use the homework formatting template provided when you begin a new thread to post a question in the Homework sections of PF.

A couple of observations:

Normally the convention is to assume North upwards, South downwards, West to the left, and East to the right. Your plot shows the proposed westward force pointing to the right, which by convention would mean eastwards. So that should be corrected.

The convention for drawing a Free Body Diagram for forces would have the force vectors "rooted" (have their bases) at the center of mass of the object with their tips pointing outward. That removes any confusion that might arise due to the dimensions of the drawn object skewing the angles of the triangle that you completed showing the angle Θ. It's often handy to be able to sketch force vectors roughly to scale so that you can get an intuitive feel for the relative magnitude and direction of the resultant. The size and shape of the object shouldn't change the force vector triangle. What would happen if the object was drawn ten times wider?

Otherwise your calculations of the force magnitude and direction look okay.