Answer:
![r_{cm}=[12.73,12.73]cm](https://tex.z-dn.net/?f=r_%7Bcm%7D%3D%5B12.73%2C12.73%5Dcm)
Explanation:
The general equation to calculate the center of mass is:
Any differential of mass can be calculated as:
Where "a" is the radius of the circle and λ is the linear density of the wire.
The linear density is given by:
So, the differential of mass is:
Now we proceed to calculate X and Y coordinates of the center of mass separately:
Solving both integrals, we get:
Therefore, the position of the center of mass is:
The solution for this problem is through this formula:Ø = w1 t + 1/2 ã t^2
where:Ø - angular displacement w1 - initial angular velocity t - time ã - angular acceleration
128 = w1 x 4 + ½ x 4.5 x 5^2 128 = 4w1 + 56.254w1 = -128 + 56.25 4w1 = 71.75w1 = 71.75/4
w1 = 17.94 or 18 rad s^-1
w1 = wo + ãt
w1 - final angular velocity
wo - initial angular velocity
18 = 0 + 4.5t t = 4 s
Assuming that reaching a height 0 doesn’t stop the ball, and that it accelerates at 9.8 m/s^2, the ball would be traveling at 0.5 + 0.7*9.8 = 7.36 m/s downwards.
The average power output is the ratio between the work done to compress the spring, W, and the time taken, t:
(1)
The work done is equal to the elastic energy stored by the compressed spring:
where
is the spring constant and
is the compression of the spring. If we substitute the numbers, we find:
And now we can use eq.(1) to calculate the average power output:
Conduction involves physical contact to charge, well induction does not.
Learn more at: <span>www.physicsclassroom.com/class/estatics/Lesson-2/Charging-by-Conduction</span>
