Where is the distance on a position time graph
1 answer:
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Answer:
1) elastic shock, the velocity of the center of mass does not change
2) inelastic shock, he velocity of the mass center change
Explanation:
The position of the center of mass of your system is defined by
=
in this case we have two bodies
x_{cm} = (x₁m₁ + x₂ m₂)
the velocity of the center of mass is
x_{cm} = dx_{cm} / dt =
x_{cm} =
where M is the total mass of the system.
Therefore to answer this question we have to find the velocity of the body after the collision.
Let's use momentum conservation, where the system is formed by the two bodies, so that the forces have been internal during the collision.
Let's solve each case separately.
2) inelastic shock
initial instant. Before the crash
p₀ = m₁ v₀ + 0
final instant. After the collision with the cars together
p_f = (m₁ + m₂) v
p₀ = p_f
m₁ v₀ = (m₁ + m₂) v
v = v₀
let's find the velocity of the center of mass
M = m₁ + m₂
initial.
=
(m₁ vo)
final
=
( v) = v
v_{cm f} =
Let's find the ratio of the velocities of the center of mass
vcmf / vcmo =
therefore the velocity of the mass center change
1) elastic shock
initial instant.
p₀ = m₁ v₀
final moment
p_f = m₁ v_{1f} + m₂ v_{2f}
p₀ = p_f
m₁ v₀ = m₁ v_{1f} + m₂ v_{2f}
m₁ (v₀ - v_{2f}) = m₂ v_{2f}
in this case the kinetic energy is conserved
K₀ = K_f
½ m₁ v₀² = ½ m₁ v_{1f}² + ½ m₂ v_{2f}²
m₁ (v₀² - v_{1f}²) = m₂ v_{2f}²
m₁ (v₀ + v_{1f}) (v₀ - v_{1f}) = m₂ v_{2f}
we write our system of equations
m₁ (v₀ - v_{1f}) = m₂ v_{2f} (1)
m₁ (v₀ - v_{1f}) (v₀ + v_{1f}) = m₂ v_{2f}²
we solve the system
v₀ + v_{1f} = v_{2f}
we substitute and look for the final speeds
v_{1f} =
v_{2f} =
now let's find the velocity of the center of mass
initial
=
m₁ v₀
final
=
(m₁ v_{1f} + m₂ v_{2f} )
v_{cm f} = [
+
] v₀
v_{cm f} = ( m₁² - m₁m₂ +2 m₁m₂) v₂
v_{cm f} = (m₁² + m₁ m₂) v₀
let's look for the relationship
v_{cm f} / v_{cm o} = M
v_{cm f} / v_{cm o} = 1
therefore the velocity of the center of mass does not change
we see in either case the velocity of the center of mass does not change.
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The Ranking of the curve according to their speed would be equal Rank because
b
The first frequency would have a higher rank compared to the other two which will have the same ranking when ranked with respect to their angular velocities because
c
The ranking of the second third frequency would be the same but their ranking would be greater than that of the first frequency because
Explanation:
Mathematically Frequency can be represented as
Where is the wavelength and v is the velocity
Now looking at the diagram we see that
For the first frequency we have
Let the wavelength be , and the frequency
For the second frequency
Let the wavelength be , and the frequency
For the third frequency
Let the wavelength be , and the frequency
To obtain v for each of the frequency we make v the subject in the equation above for each frequency
So,
For the first frequency we have
For the second frequency
For the third frequency
Hence
The Ranking of the curve according to their speed would be equal Rank because
Mathematically angular speed can be represented as
For the first frequency we have
For the second frequency
For the third frequency
Hence
The first frequency would have a higher rank compared to the other two which will have the same ranking when ranked with respect to their angular velocities because
Mathematically the relationship between the angular velocity and the linear velocity can be represented as
=>
Since the linear velocity is constant we have that
This means that r varies inversely to the angular velocity ,What this means for ranking due to the radius is that the ranking of the second third frequency would be the same but their ranking would be greater than that of the first frequency because
