_____________ and ____________ can fly in the stratosphere. Fill in blanks
2 answers:
You might be interested in
Answer:
A) = 1.44 kg m², B) moment of inertia must increase
Explanation:
The moment of inertia is defined by
I = ∫ r² dm
For figures with symmetry it is tabulated, in the case of a cylinder the moment of inertia with respect to a vertical axis is
I = ½ m R²
A very useful theorem is the parallel axis theorem that states that the moment of inertia with respect to another axis parallel to the center of mass is
I = + m D²
Let's apply these equations to our case
The moment of inertia is a scalar quantity, so we can add the moment of inertia of the body and both arms
=
+ 2
= ½ M R²
The total mass is 64 kg, 1/8 corresponds to the arms and the rest to the body
M = 7/8 m total
M = 7/8 64
M = 56 kg
The mass of the arms is
m’= 1/8 m total
m’= 1/8 64
m’= 8 kg
As it has two arms the mass of each arm is half
m = ½ m ’
m = 4 kg
The arms are very thin, we will approximate them as a particle
= M D²
Let's write the equation
= ½ M R² + 2 (m D²)
Let's calculate
= ½ 56 0.20² + 2 4 0.20²
= 1.12 + 0.32
= 1.44 kg m²
b) if you separate the arms from the body, the distance D increases quadratically, so the moment of inertia must increase
Answer:
The volume of water displaced by the raft is 0.233 m³
Explanation:
The question relates to Archimedes' principle which states that the buoyant force experienced by an object immersed in a fluid is equal to the weight of (the force of gravity on) the displaced fluid
The given parameters are;
The combined mass of the person and the raft, m = 233 kg
The liquid on which the raft is located = Water
The density of water, = 1000 kg/m³
Weight = Mass, m × g
Where;
m = The mass of the object
g = The acceleration due to gravity = 9.8 m/s²
Given that the raft is on the surface of the water (floating), the buoyant force is equal to the combined weight of the person and the raft = 233 kg
The combined weight of the person and the raft, = 233 kg × 9.8 m/s² = 2,283.4 N
Therefore;
The buoyant force = 2,283.4 N = The weight of the water displaced
The mass of the water displaced, , = 2,283.4 N/(9.8 m/s²) = 233 kg
Density = Mass/Volume
The volume of water displaced by the raft = The mass of the water displaced/(The density of the water) = 233 kg/(1,000 kg/m³) = 0.233 m³.
Answer:
(i) 12 seconds
(ii) 216 meters from the initial position
(iii) 132 meters from the initial position
(iv) No
Explanation:
Speed of express train =36 m/s
Speed of local train =11 m/s
The initial distance between the local train and passenger train =100 m.
Due to the application of breaks, the express train slows at the rare of
So, the acceleration of the express train, .
(i) Let t be the time the express train takes to stop.
From the equation of motion,
v=u+at
where, v: final velocity, u: initial velocity, a: constant acceleration, t: time taken to change the speed from u to v.
In this case, v=0, u=36 m/s,
So, 0=36+(-3)t
seconds.
(ii) To compute the distance traveled, s, till the express train stops, using
meters.
(iii) The local train is moving at a speed of 11 m/s
So, in 12 seconds, the distance, d, traveled by the local train
d= 11x12=132 meters [as distance= speed x time]
(iv) Let 0 be the reference position which is the initial position of the express train.
So, at the initial time, the position of the local train is at 100m.
After 12 seconds:
The position of the express train is at 216 m [using part (ii)]
and the position of the local train is at 100+132=232m [using part (iii)].
So, the local train is still ahead of the express train, hence the trains didn't collide.