Answer:
Her angular speed (in rev/s) when her arms and one leg open outward is 1.4 rev/s
Explanation:
given information:
moment inertia of arm and leg when in, I₁ = 0.9 kgm²
moment inertia of arm and leg when extended, I₂ = 2.9 kgm²
angular speed when in, ω₁ = 4.5 rev/s
so, her angular speed (in rev/s) when her arms and one leg open outward is
L₁ = L₂
I₁ω₁ = I₂ω₂
ω₂ = I₁ω₁/I₂
= 0.9 x 4.5/2,9
= 1.4 rev/s
B. Engineers perform lots of trials.
Answer: 1.14 N
Explanation :
As any body submerged in a fluid, it receives an upward force equal to the weight of the fluid removed by the body, which can be expressed as follows:
Fb = δair . Vb . g = 1.29 kg/m3 . 4/3 π (0.294)3 m3. 9.8 m/s2
Fb = 1.34 N
In the downward direction, we have 2 external forces acting upon the balloon: gravity and the tension in the line, which sum must be equal to the buoyant force, as the balloon is at rest.
We can get the gravity force as follows:
Fg = (mb +mhe) g
The mass of helium can be calculated as the product of the density of the helium times the volume of the balloon (assumed to be a perfect sphere), as follows:
MHe = δHe . 4/3 π (0.294)3 m3 = 0.019 kg
Fg = (0.012 kg + 0.019 kg) . 9.8 m/s2 = 0.2 N
Equating both sides of Newton´s 2nd Law in the vertical direction:
T + Fg = Fb
T = Fb – Fg = 1.34 N – 0.2 N = 1.14 N
Answer:
27.3 meters
Explanation:
A train travels up a hill that is 100 meters long. If the train has climbed 50 meters vertically, it traveled 27.3 meters vertically. Therefore, the answer is 27.3 meters.
(100)² = (50)²+x²
10000 - 2500 = x²
7500 = x²
x = 27.3 or 27.3 meters
Hope this helped!
