How much work is required to stop an electron (m= 9.11 * 10^-31 kg) which is moving with a speed of 1.80×10^6 m/s?
The work done ON the electron is negative, and equals the initial kinetic energy, (1/2)m*V^2.
Use V in m/s and m in kg and the answer will be in Joules.
Well, stopping an electron is no easy task! It involves a lot of effort and determination. You see, when it comes to stopping an electron, you have to counteract its momentum.
The momentum of an object is given by the formula: momentum = mass x velocity.
So, let's calculate the momentum of our electron first. The mass of the electron is given as 9.11 x 10^-31 kg, and its velocity is 1.80 x 10^6 m/s. Multiplying those two numbers together, we get:
momentum = (9.11 x 10^-31 kg) x (1.80 x 10^6 m/s)
And the answer is... *drum roll*... approximately 1.64 x 10^-24 kg·m/s.
Now, to stop the electron, you need to apply an equal and opposite force to counteract its momentum. The work done to stop the electron is given by the formula: work = force x distance.
Since we want to stop the electron, the distance over which the force is applied is not given, so we can't determine the exact amount of work required. But hey, don't worry! I'm sure with your determination and a little bit of comedic inspiration, you can stop that pesky electron in no time. Good luck!
To calculate the work required to stop an electron, we need to use the principle of conservation of energy, as work is directly related to the change in kinetic energy.
The kinetic energy of an object can be calculated using the formula:
KE = (1/2) * m * v^2
Where:
KE = Kinetic energy
m = Mass of the object
v = Velocity of the object
In this case, the mass (m) of the electron is given as 9.11 * 10^-31 kg and the velocity (v) is given as 1.80×10^6 m/s.
Substituting the given values into the formula:
KE = (1/2) * (9.11 * 10^-31 kg) * (1.80×10^6 m/s)^2
Simplifying further:
KE = (1/2) * 9.11 * 10^-31 * (3.24×10^12)
KE ≈ 2.96 * 10^-19 Joules
So, the initial kinetic energy of the electron is 2.96 * 10^-19 Joules.
To stop the electron, we need to bring its kinetic energy to zero. This means that an equal amount of work needs to be done to remove the electron's kinetic energy.
Therefore, the work required to stop the electron is equal to its initial kinetic energy:
Work = 2.96 * 10^-19 Joules