Resultant Force on an object during Non-Uniform Motion

[mldavis086]

Homework Statement

A 0.30-kg mass attached to the end of a string swings in a vertical circle
(R = 1.6 m), as shown. At an instant when θ = 50°, the tension in the string is
8.0 N. What is the magnitude of the resultant force on the mass at this instant?

http://www.flickr.com/photos/89533422@N08/8142258633/in/photostream/lightbox/

Homework Equations

m*centripetal acceleration=m*v^2/r
mg
basic trig

The Attempt at a Solution

I've figured out
mg = 2.94 N
mg sin 50 = 2.25 N (which acts opposite of the direction of the mass)
mg cos 50 =1.89 N (the tension due to gravity)
8-1.89 = 6.11 N (the tension due to motion of the mass)

8=0.3*v^2/1.6 (v=5.71 m/s)
-2.25=0.3*a (a=-7.5 m/s^2)

I'm not 100% on the last 2

But I still don't know what the resultant force is? Or even what force they are referring to. If anyone can help it would be greatly appreciated!

 

[SammyS]

Homework Statement

A 0.30-kg mass attached to the end of a string swings in a vertical circle
(R = 1.6 m), as shown. At an instant when θ = 50°, the tension in the string is
8.0 N. What is the magnitude of the resultant force on the mass at this instant?

http://www.flickr.com/photos/89533422@N08/8142258633/in/photostream/lightbox/

Homework Equations

m*centripetal acceleration=m*v^2/r
mg
basic trig

The Attempt at a Solution

I've figured out
mg = 2.94 N
mg sin 50 = 2.25 N (which acts opposite of the direction of the mass)
mg cos 50 =1.89 N (the tension due to gravity)
8-1.89 = 6.11 N (the tension due to motion of the mass)

8=0.3*v^2/1.6 (v=5.71 m/s)
-2.25=0.3*a (a=-7.5 m/s^2)

I'm not 100% on the last 2

But I still don't know what the resultant force is? Or even what force they are referring to. If anyone can help it would be greatly appreciated!

What are all of the forces acting on the mass ?

 

[mldavis086]

The only force acting on it is gravity right? Does that make the 'resultant force' the 2.25N opposite of it's direction at the moment?

 

[mldavis086]

Or is it just mg=2.94N? I am confused with the term 'resultant force' I think

 

[mldavis086]

Wait the centripetal acceleration is a force too right? 8N towards the center of the circle.

 

[mldavis086]

I think I get it. The 2 forces are the force towards the center, and the force of gravity straight down. If I calculate the 'resultant' of these 2 vectors. I get a force of 2.2N up and 6.13N left. Then using Pythagoreans Theorem. The magnitude of the resulting vector is 6.51N. Can anyone out there confirm if I am looking at this problem properly? I really want to make sure I understand. Thanks