Work-Kinetic Energy Theorem

In summary, the conversation discusses the components and function of an electron gun in a black-and-white television set. It is mentioned that the gun contains two charged metallic plates 2.80cm apart and that an electric force is responsible for accelerating the electrons in the beam to 9.60% of the speed of light over this distance. The electron's kinetic energy as it leaves the gun is calculated using the formula KE = 1/2mv^2. The magnitude of the constant electric force acting on the electron is determined using the formula F=ma, and the acceleration and time of flight of the electron are also calculated. The conversation also provides the necessary values for electron mass, velocity, and distance between plates.
  • #1
sn3t
5
0

Homework Statement


In the neck of the picture tube of a certain black-and-white television set, an electron gun contains two charged metallic plates 2.80cm apart. An electric force accelerates each electron in the beam from rest to 9.60% of the speed of light over this distance. a) determine the kinetic energy of the electron as it leaves the electron gun. Electrons carry this energy to a phosphorescent material on the inner surface of the television screen material making it glow. For an electron passing between the plates in the electron gun, determine b) the magnitude of the constant electric force acting on the electron, c) the acceleration, and d) the time of flight.

Electron mass = 9.10938188 * 10^-31 kg
C = 299792458 m/s
Electron velocity = 28780075.968 m/s (.0960 * C)
Distance between plates = .028m


Homework Equations



KE = 1/2m* v^2
F= mass * acceleration


The Attempt at a Solution



a) KE = 1/2m * v^2
= 1/2(9.10938188*10^-31kg) * ( 28780075.968m/s)
= 3.77261759 * 10^-16 Joules
b) F=m*a
= (9.10938188*10^-31kg) * [ (28780075.968m/s)^2 / (.028m) ]
= 2.694722685 * 10^-14 N
c) a = F/m
= 2.694722685*10^-14N / 9.10938188*10^-31kg
= 2.9581839*10-46 m/s^2
d) ?

and I am not sure if my parts b and c are correct
 
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  • #2
b is not correct, you should divide the KE by the distance.

ehild
 
  • #3
ah yea you're right it's N*m then when I divide it cancels out.

w= f * d

so ke = f * d
ke/d = f?
 
  • #4
The change of the KE is equal to the work. But initially, KE=0.

Just divide your 3.7726 * 10^-16 Joules by 0.028 m.

ehild
 

What is the Work-Kinetic Energy Theorem?

The Work-Kinetic Energy Theorem is a fundamental principle in physics that relates the work done on an object to the change in its kinetic energy. It states that the net work done on an object is equal to the change in its kinetic energy.

What is the formula for the Work-Kinetic Energy Theorem?

The formula for the Work-Kinetic Energy Theorem is W = ΔK, where W represents the net work done on an object and ΔK represents the change in the object's kinetic energy.

How is the Work-Kinetic Energy Theorem used in real-world applications?

The Work-Kinetic Energy Theorem is used in various real-world applications, such as in the design of roller coasters and other amusement park rides, in analyzing the motion of projectiles, and in determining the efficiency of machines.

What is the relationship between work and kinetic energy in the Work-Kinetic Energy Theorem?

The Work-Kinetic Energy Theorem states that work is directly proportional to the change in kinetic energy. This means that if the work done on an object increases, its kinetic energy will also increase, and vice versa.

What are the key assumptions of the Work-Kinetic Energy Theorem?

The Work-Kinetic Energy Theorem assumes that the net work done on an object is the sum of all the individual works done on it, and that the only forces acting on the object are those that can be accounted for in the work done. It also assumes that the object has a constant mass and that there is no change in potential energy.

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