Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, t
he first having a mass of 150,000 kg and a velocity of 0.300 m/s, and the second having a mass of 110,000 kg and a velocity of (-0.12 m/s). What is their final velocity?
1 answer:
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Answer:
T = 2.4 + 2.4 = 4.8 [s]
Explanation:
In order to solve this problem, we must use the following kinematics equation and calculate the acceleration value.
Vo = inital velocity = 0
x - xo = 15 [m]
t = time = 2.4 [s]
15 = 0.5*a*(2.4)^2
a = 5.208 [m/s^2]
We can use the same equation to find the time.
30 = 15 + 0.5*(5.208)*t^2
t = 2.4 [s]
T = 2.4 + 2.4 = 4.8 [s]
The electron is accelerated through a potential difference of 
, so the kinetic energy gained by the electron is equal to its variation of electrical potential energy:
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
is the potential difference
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B:
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B: