What is the Resultant Force on a Mass in Non-Uniform Circular Motion?

In summary, the conversation discusses a problem involving non-uniform circular motion and a mass attached to a string. The question asks for the magnitude of the resultant force on the mass at a specific moment. The solution involves separating the forces into radial and tangential components and then using Pythagoras to combine them. The final answer is 6.11N for the perpendicular force and 2.25N for the parallel force.
  • #1
[imagine]
9
0
Hi,
I have a multiple choice non-uniform circular motion problem that I am trying to solve, but somehow I keep getting an answer that is not one of the possible answers. Here it is:

A 0.30kg mass attached to the end of a string swings in a vertical circle (R=1.6m) as shown [ In the diagram, x = theta ]. At an instant when x=50, the tension in the string is 8.0N, what is the magnitude of the resultant force on the mass at this instant?

a) 5.6N
b) 6.0N
c) 6.5N
d) 5.1N
e) 2.2N

http://img468.imageshack.us/img468/716/physdiag5xc.png

So.. firstly, I established that the resultant force on the mass is the sum of the net radial force and the net tangential force. The net radial force is equal to [ Tension - Gravity in the Y direction ], and the net tangential force is equal to Gravity in the X direction. So...

Fnet = Sum of Radial Forces + Sum of Tangential Forces
Fnet = (T - mgcosx) + (mgsinx)

Using this formula, I get Fnet= 8.4N ?? What could I be doing wrong here?

Then I thought.. if I just take the tangential force, that is equal to mgsinx = 2.25..which is pretty close to E. Can this be what is meant by resultant force?

I hope someone can help me find my mistake in solving this problem, and point me toward the right solution. Thanks in advance!
 
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  • #2
I think we'd need a diagram..
 
  • #3
Diagram included now.
 
  • #4
Usually once you separate the Forces into components parallel to
and perpendicular to the motion, KEEP THEM SEPARATE!

HERE, you're asked to combine them, using Pythagoras.

I get F perp = 6.11 N , and F parallel = 2.25 N
 
  • #5
Ahhhhh... That clears it all up! Thanks a lot :).
 

1. What is non-uniform circular motion?

Non-uniform circular motion is the motion of an object moving along a circular path at a varying speed. This means that the object is not moving at a constant speed, but rather its speed is changing as it moves along the path.

2. What causes an object to have non-uniform circular motion?

An object can have non-uniform circular motion due to a change in its velocity, which can be caused by a force acting on it. This force can either speed up or slow down the object, resulting in the varying speed along the circular path.

3. How is non-uniform circular motion different from uniform circular motion?

In uniform circular motion, the speed of the object remains constant throughout its motion along the circular path. However, in non-uniform circular motion, the speed of the object changes, resulting in a varying velocity.

4. What is the role of centripetal force in non-uniform circular motion?

Centripetal force is the force that acts on an object in non-uniform circular motion, causing it to continuously change its direction towards the center of the circular path. This force is necessary to keep the object moving along the curved path instead of moving in a straight line.

5. How is the speed in non-uniform circular motion calculated?

The speed in non-uniform circular motion can be calculated by dividing the distance traveled by the time taken to travel that distance. However, since the speed is constantly changing, the instantaneous speed at a particular point can be calculated using calculus by finding the derivative of the distance-time function.

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