Answer:
r = 4.44 m
Explanation:
For this exercise we use the Archimedes principle, which states that the buoyant force is equal to the weight of the dislodged fluid
B = ρ g V
Now let's use Newton's equilibrium relationship
B - W = 0
B = W
The weight of the system is the weight of the man and his accessories (W₁) plus the material weight of the ball (W)
σ = W / A
W = σ A
The area of a sphere is
A = 4π r²
W = W₁ + σ 4π r²
The volume of a sphere is
V = 4/3 π r³
Let's replace
ρ g 4/3 π r³ = W₁ + σ 4π r²
If we use the ideal gas equation
P V = n RT
P = ρ RT
ρ = P / RT
P / RT g 4/3 π r³ - σ 4 π r² = W₁
r² 4π (P/3RT r - σ) = W₁
Let's replace the values
r² 4π (1.01 10⁵ / (3 8.314 (70 + 273)) r - 0.060) = 13000
r² (11.81 r -0.060) = 13000 / 4pi
r² (11.81 r - 0.060) = 1034.51
As the independent term is very small we can despise it, to find the solution
r = 4.44 m
Answer:
An aircraft flying at sea level with a speed of 220 m/s, has a highest pressure of 29136.8 N/m²
Explanation:
Applying Bernoulli's equation, we determine the highest pressure on the aircraft.

where;
P is the highest pressure on the aircraft
is the density of air = 1.204 kg/m³ at sea level temperature.
V is the velocity of the aircraft = 220 m/s
P = 0.5*1.204*(220)² = 29136.8 N/m²
Therefore, an aircraft flying at sea level with a speed of 220 m/s, has a highest pressure of 29136.8 N/m²
A is the answer for the problem
Answer:
K.E = 100 J
Final P.E = 100 J
Explanation:
The kinetic energy of any object can be given by the following formula:

where,
K.E = Kinetic Energy
m = mass of ball = 2 kg
v = speed of ball
Initially, v = 10 m/s. Therefore, the initial K.E is given as:

<u>K.E = 100 J</u>
Now, at the highest point the K.E of the ball becomes zero. because the ball stops for a moment at the highest point and its velocity becomes zero. So, from Law of Conservation of energy:
Initial K.E + Initial P.E = Final K.E + Final P.E
Initial P.E is also zero due to zero height initially.
K.E + 0 = 0 + Final P.E
<u>Final P.E = 100 J</u>