Answer:
a)30.14 rad/s2
b)43.5 rad/s
c)60633 J
d)42 kW
e)84 kW
Explanation:
If we treat the propeller is a slender rod, then its moments of inertia is

a. The angular acceleration is Torque divided by moments of inertia:

b. 5 revolution would be equals to
rad, or 31.4 rad. Since the engine just got started


c. Work done during the first 5 revolution would be torque times angular displacement:

d. The time it takes to spin the first 5 revolutions is

The average power output is work per unit time
or 42 kW
e.The instantaneous power at the instant of 5 rev would be Torque times angular speed at that time:
or 84 kW
Answer:
2.41 L
Explanation:
We can solve the problem by using the ideal gas equation, which can be rewritten as:

where we have:
(initial pressure is stp pressure)
is the initial volume
is the initial temperature (stp temperature)
is the final pressure
is the final volume
is the final temperature
By substituting the numbers inside the formula and solving for V2, we find the final volume:

which corresponds to 2.41 L.
Answer:
= 0.0298V
Explanation:
Electric field between two conductor = σ / ε₀
σ = 33pC/m²
= 33 × 10⁻¹²C/m²
ε₀ = 8.85 × 10 ⁻¹²C²/Nm²
E = 33 × 10⁻¹² / 8.85 × 10 ⁻¹²
= 3.7288N/C
potential difference between two conductors = Ed
where d = 8mm = 8 × 10 ⁻³m
V = 3.7288 × 8 × 10 ⁻³
= 29.83 × 10 ⁻³
= 0.0298V
Answer:
a) F_b = 6.62 N
b) F_net = 5.583 N
Explanation:
Given:
- Conditions of He gas: T = 0 C , P = 1 atm , ρ = 0.179 kg/m^3
- The mass of balloon m = 0.012 kg
- The radius of balloon r = 0.5 m
Find:
a)What is the magnitude of the buoyant force acting on the balloon?
b)What is the magnitude of the net force acting on the balloon?
Solution:
- The buoyant force F_b acting on the balloon is equal to the weight of the air it displaces.The mass of the displaced air ρ*V is the volume of the balloon times the density of the. Multiplying that by acceleration due to gravity gives its weight.
F_b = ρ*V*g
F_b = 4*ρ*g*pi*r^3 / 3
F_b = 4*1.29*9.81*pi*.5^3 / 3
F_b = 6.62 N
- The net force will be the difference between the balloon’s weight and the buoyant force. The weight of the balloon is the density of the helium times the volume of the balloon added to the mass of the empty balloon.
F_g = ρ*V*g + m*g
F_g = 4*ρ*g*pi*r^3 / 3 + 0.012*9.81
F_g = 4*0.179*9.81*pi*.5^3 / 3 + 0.012*9.81
F_g = 1.037 N
- The net force is the difference between weight and buoyant force
F_net = F_g - F_b
F_net = 6.62 - 1.037
F_net = 5.583 N