Answer:
a) x_{cm} = m₂/ (m₁ + m₂) d
, b) x_{cm} = 52.97 pm
Explanation:
The expression for the center of mass is
= 1 / M ∑
Where M is the total masses, mI and xi are the mass and position of each element of the system.
Let's fix our reference system on the oxygen atom and the molecule aligned on the x-axis, let's use index 1 for oxygen and index 2 for carbon
x_{cm} = 1 / (m₁ + m₂) (0+ m₂ x₂)
Let's reduce the magnitudes to the SI system
m₁ = 17 u = 17 1,661 10⁻²⁷ kg = 28,237 10⁻²⁷ kg
m₂ = 12 u = 12 1,661 10⁻²⁷ kg = 19,932 10⁻²⁷ kg
d = 128 pm = 128 10⁻¹² m
The equation for the center of mass is
x_{cm} = m₂/ (m₁ + m₂) d
b) let's calculate the value
x_{cm} = 19.932 10⁻²⁷ /(19.932+ 28.237) 10⁻²⁷ 128 10-12
x_{cm} = 52.97 10⁻¹² m
x_{cm} = 52.97 pm
Answer:
See the answers below.
Explanation:
To solve this problem we must use the following equation of kinematics.
![v_{f}=v_{o}-a*t](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D-a%2At)
where:
Vf = final velocity = 10 [m/s]
Vo = initial velocity = 40 [m/s]
t = time = 5 [s]
a = acceleration [m/s²]
Now replacing:
![10=40-a*5\\40-10=a*5\\30=5*a\\a=6[m/s^{2}]](https://tex.z-dn.net/?f=10%3D40-a%2A5%5C%5C40-10%3Da%2A5%5C%5C30%3D5%2Aa%5C%5Ca%3D6%5Bm%2Fs%5E%7B2%7D%5D)
Note: The negative sign in the above equation means that the velecity is decreasing.
2)
To solve this second part we must use the following equation of kinematics.
![v_{f}^{2} =v_{o}^{2} -2*a*x\\](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%20%3Dv_%7Bo%7D%5E%7B2%7D%20-2%2Aa%2Ax%5C%5C)
where:
x = distance [m]
![(10)^{2} =(40)^{2} -2*6*x\\100=1600-12*x\\12*x=1600-100\\12*x=1500\\x=125[m]](https://tex.z-dn.net/?f=%2810%29%5E%7B2%7D%20%3D%2840%29%5E%7B2%7D%20-2%2A6%2Ax%5C%5C100%3D1600-12%2Ax%5C%5C12%2Ax%3D1600-100%5C%5C12%2Ax%3D1500%5C%5Cx%3D125%5Bm%5D)
1 plane, because a point has no dimensions. Just location.
Both actually
Hope this helps!!