The volume of every sphere is
Volume = (4/3) (pi) (radius)³
When you say "across", I think you mean the diameter of the ball.
The radius is half of the diameter = 12 inches.
Volume = (4/3) (pi) (12 inches)³
= (4/3) (pi) (1,728 cubic inches)
= 7,238.2 cubic inches . (rounded)
Answer:
159.38 Watts
Explanation:
Initially;
- Mass on the spring is 8.5 kg
- Therefore, compression force is 85 N
- Compression distance is 15 cm or 0.15 m
But;
F = kx
where F is the force of compression, k is the spring constant and x is the compression distance.
Thus;
k = F/x
= 85 N ÷0.15
= 566.67 N/m
We are required to determine the power needed to stretch the same spring for 1.5 m in 4 secs.
Power = Work done ÷ time
Work done is given by 0.5kx²
Therefore;
Power = 0.5kx²÷ t
= (0.5×566.67 N/m × 1.5² ) ÷ 4 seconds
= 159.38 Watts
Thus, the power needed is 159.38 watts
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The 1st quadrant (0-90 degrees) is the only quadrant where none of the components are negative, so that means that any angle larger than 90 degrees will result in one of the components being negative.
To solve this problem it is necessary to use the conservation equations of both kinetic, rotational and potential energy.
By definition we know that
Where,
KE =Kinetic Energy
KR = Rotational Kinetic Energy
PE = Potential Energy
In this way
Where,
m = mass
v= Velocity
I = Moment of Inertia
Angular velocity
g = Gravity
h = Height
We know as well that 
for velocity (v) and Radius (r)
Therefore replacing we have
![[tex]h= \frac{1}{2} \frac{v^2}{g} +\frac{1}{2} \frac{I}{mg}(\frac{v}{r})^2](https://tex.z-dn.net/?f=%5Btex%5Dh%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7Bv%5E2%7D%7Bg%7D%20%2B%5Cfrac%7B1%7D%7B2%7D%20%5Cfrac%7BI%7D%7Bmg%7D%28%5Cfrac%7Bv%7D%7Br%7D%29%5E2)
[/tex]
Therefore the height must be 0.3915 for the yo-yo fall has a linear speed of 0.75m/s
