Velocity of an Object in Uniform Circular Motion

[Argella]

Homework Statement

An object of mass 0.5 kg is swung in uniform circular motion. The radius is 2 meters, and the force exerted is 4 N. Calculate the magnitude of the velocity.

Answer Choices:
a) 0.25 m/s
b) 1 m/s
c) 4 m/s
d) 16 m/s

Homework Equations

v = 2piR/T
F = mv^2/R

The Attempt at a Solution

Since I didn't know the variable time, I couldn't use the velocity equation. Next, I tried plugging in the variables for the centripetal force equation and solving for velocity:

4 = (0.5)v^2/2
4 = 0.5/2 + v^2/2
4 = 0.3 + v^2/2 <- 0.3 because of significant figures
(subtracted 0.3 from both sides)
4 = v^2/2 <- 4 because of significant figures
(multiplied both sides by 2)
8 = v ^2
(took the square root of both sides)
v = 3 which isn't one of my answer choices.

Maybe I'm not doing my algebra correctly or maybe I'm not using the right equation, but I couldn't find another equation using the variables I have. If I knew the time it took for one revolution I could use the velocity equation, but I don't know how to find time and I couldn't find an equation for finding it.

 

[Fightfish]

4 = (0.5)v^2/2
4 = 0.5/2 + v^2/2

There is an algebra mistake in going from the first to the second step. You have essentially turned a product into a sum instead.

On a side note, when taking significant figures into account, do so only on the final answer. If you keep rounding off at each step, you will find that the rounding-off error grows substantially larger after each step, and the final answer you obtain might be significantly off the correct one.

 

[Argella]

Ohh, okay, that makes a lot more sense. I'll be sure to keep that in mind about significant figures in the future, too.

Thanks a lot!