While looking at bromine (Br) on the periodic table, a student needs to find another element with very similar chemical properti
es but with a different atomic mass. Which best describes the student’s options? There are two possible elements, and they are directly to the left and right of bromine. There are two possible elements, and they are directly above and below bromine. There are many possible elements, and they are all in the same vertical column as bromine. There are many possible elements, and they are all in the same horizontal row as bromine.
2 answers:
Answer: There are many possible elements, and they are all in the same vertical column as bromine
Explanation: All the elements in the same vertical columns or same groups have similar chemical properties due to the presence of similar valence shell configurations but have different masses as the number of protons and neutrons keep on increasing on moving down the group.
All the halogens (members of fluorine group) are short of one electron each to attain their stable noble gas configuration and hence behave similarly.
The elements present in the same horizontal row or same period differ in the chemical properties as they have different valence shell configurations.
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Explanation:
A) To prove the motion of the center of mass of the cylinders is simple harmonic:
System diagram for given situation is shown in attached Fig. 1
We can prove the motion of the center of mass of the cylinders is simple harmonic if
where aₓ is acceleration when attached cylinders move in horizontal direction:
<h3>PROOF:</h3>rotational inertia for cylinders is given as:
-----(1)
Newton's second law for angular motion is:
∑τ = Iα ------(2)
For linear motion in horizontal direction it is:
∑Fₓ = Maₓ ------ (3)
By definition of torque:
τ = RF --------(4)
Put (4) and (1) in (2)
from Fig 3 it can be seen that fs is force by which the cylinders roll without slipping as they oscillate
So above equation becomes
------ (5)
As angular acceleration is related to linear by:
Eq (5) becomes
---- (6)
aₓ shows displacement in horizontal direction
From (3)
∑Fₓ = Maₓ
Fₓ is sum of fs and restoring force that spring exerts:
----(7)
Put (7) in (3)
[/tex] -----(8)
Using (6) in (8)
--- (9)
For spring mass system
----- (10)
Equating (9) and (10)
then (9) becomes
(The minus sign says that x and aₓ have opposite directions as shown in fig 3)
This proves that the motion of the center of mass of the cylinders is simple harmonic.
<h3 /><h3>B) Time Period</h3>Time period is related to angular frequency as:
Answer:
.
Explanation:
This problem can be solved using Newton's law of universal gravitation: ,
where F is the gravitational force between two masses and
,
is the distance between the masses (their center of mass), and
is the gravitational constant.
We know the weight of the astronout on the surface, with this we can find his mass. Letting be the weight on the surface:
,
,
,
since we now that we get that the mass is
.
Now we can use Newton's law of universal gravitation
,
where is the mass of the astronaut and
is the mass of the earth. From Newton's second law we know that
,
in this case the acceleration is the gravity so
, (<u>becarefull, gravity at this point is no longer</u>
<u>because we are not in the surface anymore</u>)
and this get us to
, where
is his new weight.
We need to remember that the mass of the earth is and its radius is
.
The total distance between the astronaut and the earth is
meters.
Now we can compute his weigh:
,
,
.
m = mass = 5 kg
= initial velocity = 100 m/s
= final velocity = ?
I = impulse = 30 Ns
Using the impulse-change in momentum equation
I = m( -
)
30 = 5 ( - 100)
= 106 m/s