) A hot air balloon along with its cargo has a mass of 4.0 x 105 kg, and it holds 7.0 x 10 5 m3 of hot air. It is floating at a
1 answer:
You might be interested in
Answer:
a). C = b/2 and C = b/4
b).
c). m = 63.4 kg (approx.)
Explanation:
Ex. 2.4.4
The total force acting on mass m is , where x is the displacement from the equilibrium position.
The equation of motion is
or or
, where
The solution is , where A and Ф are constants.
A is amplitude of motion
is the angular frequency of motion
Ф is the phase angle.
Now,
or
Given
a).
b).
or
Ex. 2.4.5
a). Total force acting on the mass m is
The equation of motion is
or , angular frequency of the undamped oscillation.
γ = b/2m is called the damping coefficient (γ=C)
for 1 kg weight (= 9.8 N), = 1.1 Hz
k = 4 x (3.14)² x (9.8) x 1.1² = 4.6 x 10² N/m
For 2 kg weight (= 19.6 N), = 0.8 Hz
k = 4 x 9.8596 x 2 x 9.8 x 0.8² = 5 x N/m
or
γ = b/2 (for 1 kg) and γ = b/4 (for 2 kg)
C = b/2 and C = b/4
b).
For two particle problem,
where, μ is the reduced mass.
This time period is same for both the particles.
c).
( approx.)