Answer:
a
The mass is ![m_2 =21.75*10^{-27} \ kg](https://tex.z-dn.net/?f=m_2%20%3D21.75%2A10%5E%7B-27%7D%20%5C%20kg)
b
The velocity is ![v_2 = 3.0*10^{6} m/s](https://tex.z-dn.net/?f=v_2%20%3D%203.0%2A10%5E%7B6%7D%20m%2Fs)
Explanation:
From the question we are told that
The speed of the protons is ![u_1 = 2.10*10^{7} m/s](https://tex.z-dn.net/?f=u_1%20%3D%20%202.10%2A10%5E%7B7%7D%20m%2Fs)
The mass of the protons is ![m](https://tex.z-dn.net/?f=m)
The speed of the rebounding protons are ![v_1 = -1.80 * 10^{7} \ m/s](https://tex.z-dn.net/?f=v_1%20%3D%20%20-1.80%20%2A%2010%5E%7B7%7D%20%5C%20m%2Fs)
The negative sign shows that it is moving in the opposite direction
Now according to the law of energy conservation mass of one nucleus of the unknown element. is mathematically represented as
Where
is the mass of a single proton
So substituting values
![m_2 = \frac{2.10 *10^{7} - (-1.80 *10^{7})} {(2.10 *10^7) + (-1.80 *10^{7})} m_1](https://tex.z-dn.net/?f=m_2%20%3D%20%5Cfrac%7B2.10%20%2A10%5E%7B7%7D%20-%20%28-1.80%20%2A10%5E%7B7%7D%29%7D%20%7B%282.10%20%2A10%5E7%29%20%2B%20%28-1.80%20%2A10%5E%7B7%7D%29%7D%20m_1)
![m_2 =13 m_1](https://tex.z-dn.net/?f=m_2%20%3D13%20m_1)
The mass of on proton is ![m_1 = 1.673 * 10^{-27} \ kg](https://tex.z-dn.net/?f=m_1%20%3D%201.673%20%2A%2010%5E%7B-27%7D%20%5C%20kg)
So ![m_2 =13 ( 1.673 * 10^{-27} )](https://tex.z-dn.net/?f=m_2%20%3D13%20%28%201.673%20%2A%2010%5E%7B-27%7D%20%29)
![m_2 =21.75*10^{-27} \ kg](https://tex.z-dn.net/?f=m_2%20%3D21.75%2A10%5E%7B-27%7D%20%5C%20kg)
Now according to the law of linear momentum conservation the speed of the unknown nucleus immediately after such a collision is mathematically evaluated as
![m_1 u_1 + m_2u_2 = m_1 v_1 + m_2v_2](https://tex.z-dn.net/?f=m_1%20u_1%20%2B%20m_2u_2%20%3D%20m_1%20v_1%20%2B%20m_2v_2)
Now
because before collision the the nucleus was at rest
So
![m_1 u_1 = m_1 v_1 + m_2v_2](https://tex.z-dn.net/?f=m_1%20u_1%20%3D%20%20m_1%20v_1%20%2B%20m_2v_2)
=> ![v_2 = \frac{m_1(u_1 -v_1)}{m_2}](https://tex.z-dn.net/?f=v_2%20%3D%20%20%5Cfrac%7Bm_1%28u_1%20-v_1%29%7D%7Bm_2%7D)
Recall that ![m_2 =13 m_1](https://tex.z-dn.net/?f=m_2%20%3D13%20m_1)
So
![v_2 = \frac{m_1(u_1 -v_1)}{13m_1}](https://tex.z-dn.net/?f=v_2%20%3D%20%20%5Cfrac%7Bm_1%28u_1%20-v_1%29%7D%7B13m_1%7D)
=> ![v_2 = \frac{(u_1 -v_1)}{13}](https://tex.z-dn.net/?f=v_2%20%3D%20%20%5Cfrac%7B%28u_1%20-v_1%29%7D%7B13%7D)
substituting values
![v_2 = \frac{( 2.10*10^{7} -(-1.80 *10^{7}))}{13}](https://tex.z-dn.net/?f=v_2%20%3D%20%20%5Cfrac%7B%28%202.10%2A10%5E%7B7%7D%20-%28-1.80%20%2A10%5E%7B7%7D%29%29%7D%7B13%7D)
![v_2 = 3.0*10^{6} m/s](https://tex.z-dn.net/?f=v_2%20%3D%203.0%2A10%5E%7B6%7D%20m%2Fs)
Answer:
because the car needs gas so why wouldnt it stop working
Explanation:
The law of conservation of linear momentum says that when objects collide, the total initial momentum equals the total final momentum.
The momentum of a body is given by the product of mass and velocity of the object.
Answer:
Explanation:
a ) density = mass / volume
density of mars / density of earth
= (mass of mars/mass of earth) x (volume of earth / volume of mars)
= (mass of mars/mass of earth) x (diameters of earth / diameters of mars)³
= 0.11 x (130/69)³
= .73
b )
gravitational acceleration (g) = GM/R²
Gravitational acceleration on mars / Gravitational acceleration on earth
= (mass of mars / mass of earth) x (radius of earth / radius of mars )²
= .11 x (130/69 )²
= .39
Gravitational acceleration on mars = .39 x Gravitational acceleration on earth
Gravitational acceleration on mars = 9.8 x .39
= 3.82 m/s
c ) Escape velocity ![\sqrt{2gR }](https://tex.z-dn.net/?f=%5Csqrt%7B2gR%20%7D)
c ) escape speed of mars / escape velocity of earth
= [( g on mars / g on earth ) x ( radius of mars / radius of earth )]°⁵
= √(.39 x 69/130)
= .4549
escape speed of mars = .4549 x escape velocity of earth
= .4549 x 11.2km/s
= 5.1 km / s