You swing a 2.2 kg stone in a circle of radius 75 cm. At what speed should you swing it so its centripetal acceleration will be 9.8 m/s^2
so if i do a=w^2 R....
and i plug everything in
so... 9.8 = w^2 (75)
9.8 (-75) = w^2
735 = w^2
Square root (735) and get 27.11
Is this correct cause the book gets 2.7 m/s do i need to move a decimal??
so... 9.8 = v^2 (.75)
9.8 (.75) = v^2
735 = v^2
Square root (7.35) and get 2.711
... You swing a 2.2 kg stone in a circle of radius 75 cm.
Can you take it from here?
using the a = w^2 R... equation right
well R is going to = 75 cm and we are searching for w^2 so i would put 2.2 kg as A????
2.2 = w^2 (75)
No, mass has nothing to do with it.
9.8m/s^3=v^2/r
and r=.75 m
solve for v.
Excellent!
Well, it seems like you might have made a slight mistake in your calculations. Let's go through it again and find out what went wrong.
First, we can rearrange the formula to solve for angular velocity, w:
a = w^2 * R
where a is the centripetal acceleration and R is the radius of the circle.
So, plugging in the values:
9.8 m/s^2 = w^2 * 0.75 m
Now, let's solve for w:
w^2 = 9.8 m/s^2 / 0.75 m
w^2 = 13.07 rad/s^2
Taking the square root of both sides:
w ≈ √13.07 rad/s
w ≈ 3.61 rad/s
So, the angular speed required for a centripetal acceleration of 9.8 m/s^2 is approximately 3.61 rad/s.
Note that the book's answer of 2.7 m/s seems incorrect as it should be measured in rad/s and not m/s.
To solve this problem, you're on the right track using the formula a = ω^2 R, where a is the centripetal acceleration, ω is the angular velocity, and R is the radius of the circle.
However, there seems to be a mistake in your calculations. Let's go through the steps again:
1. Substitute the given values into the formula: a = 9.8 m/s^2 and R = 0.75 m (since 75 cm is equal to 0.75 m).
9.8 = ω^2 * 0.75
2. Rearrange the equation to solve for ω^2:
ω^2 = 9.8 / 0.75
3. Evaluate the right side of the equation:
ω^2 = 13.067
4. Take the square root of both sides of the equation to solve for ω:
ω = sqrt(13.067)
Using a calculator to find the square root of 13.067, you should get approximately 3.611 rad/s as the value of ω.
Therefore, the correct angular velocity for the stone to have a centripetal acceleration of 9.8 m/s^2 is approximately 3.611 rad/s.
Keep in mind that this value represents only the magnitude of the angular velocity, so the book's answer of 2.7 m/s may be labeled as such because it refers to the linear velocity (magnitude of tangential velocity) of the stone, which is related to the angular velocity by v = ωR.