In a TV set, a beam of electrons is shot horizontally from the rear of the TV tube toward the screen with a speed about 1x10^7 m/s. If the distance from the rear of the TV set to the front is .5m, approximately how far do the electrons drop because of the gravity as they move across the tube?
1.2×10–4 m
To determine how far the electrons drop due to gravity as they move across the TV tube, we can use the equations of motion. We'll assume that the electrons are under free fall motion, meaning the only force acting on them is gravity.
The initial horizontal velocity of the electrons is given as 1x10^7 m/s, and the distance from the rear to the front of the TV set is 0.5 m. Since the time of motion is the same horizontally and vertically, we can find the time it takes for the electrons to move across the tube using the horizontal distance and initial velocity.
First, let's find the time taken for the horizontal motion:
Distance = 0.5 m
Initial velocity = 1x10^7 m/s
Using the formula:
Distance = Initial velocity * Time
0.5 m = (1x10^7 m/s) * Time
Time = 0.5 m / (1x10^7 m/s)
Time ≈ 5x10^-8 s
Now, let's find the vertical distance (drop) during this time using the equation of motion for vertical motion under constant acceleration.
Using the formula for vertical displacement:
Displacement = Initial velocity * Time + 0.5 * Acceleration * Time^2
Since the initial vertical velocity is 0 m/s (starting from rest), the equation simplifies to:
Displacement = 0.5 * Acceleration * Time^2
The acceleration due to gravity is approximately 9.8 m/s^2.
Substituting the values:
Displacement = 0.5 * (9.8 m/s^2) * (5x10^-8 s)^2
Displacement ≈ 1.225x10^-14 m
Therefore, the electrons drop approximately 1.225x10^-14 meters, or about 0.00000000000001225 meters due to the effects of gravity as they move horizontally across the TV tube.
To find the distance the electrons drop due to gravity as they move across the tube, we can use the equations of motion. The horizontal velocity of the electrons does not change, so we only need to consider the vertical motion.
The equation for the distance fallen due to gravity can be expressed as:
d = 0.5 * g * t^2
Where:
d is the distance fallen
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time taken to cross the tube
To find the time taken, we can use the formula:
t = d / v
Where:
v is the horizontal velocity of the electrons (1x10^7 m/s)
Substituting this back into the equation for distance fallen due to gravity, we get:
d = 0.5 * g * (d / v)^2
Now we can solve this equation for d.
0.5 * g * (d / v)^2 = d
0.5 * g * d^2 / v^2 = d
0.5 * g * d^2 = d * v^2
0.5 * g * d = v^2
d = (v^2) / (0.5 * g)
Now we can substitute the given values:
v = 1 x 10^7 m/s
g = 9.8 m/s^2
d = (1 x 10^7 m/s)^2 / (0.5 * 9.8 m/s^2)
d = 1 x 10^14 m^2/s^2 / 4.9 m/s^2
d = 2 x 10^13 m
Therefore, the electrons drop approximately 2 x 10^13 meters due to gravity as they move across the tube.
Please indicate your subject as the "school subject", not your grade level.
First calculate how long it takes the electrons to travel the length of the TV tube:
t = 0.5 m / 10^7 m/s = 5.0*10^-8 s
The distance they fall in this time is Y = (1/2) g t^2
g is the acceleration of gravity
Compute Y