In a cathode-ray tube, electrons are projected horizontally at 6.4 x 106 m/s and travel a horizontal distance of 4.7 cm across the tube. Find the vertical distance the electrons fall under the influence of gravity during their flight. Give your answer in femtometers.
time to fall= 4.6e-2/6.4e6 sec=7.2e-9 sec
fall distance= .5*9.8*(7.2e-9)^2=2.5e-16m= .25fm
To find the vertical distance the electrons fall under the influence of gravity during their flight, we need to calculate the time it takes for the electrons to travel horizontally across the tube.
First, we can calculate the time of flight using the horizontal distance and the horizontal velocity of the electrons. The formula to calculate time is:
time = distance / velocity
Plugging in the values, we have:
time = 4.7 cm / (6.4 x 10^6 m/s)
Note that we need to convert centimeters to meters to ensure consistent units.
time = 0.047 m / (6.4 x 10^6 m/s) = 7.34375 x 10^(-9) s
Now that we have the time of flight, we can proceed to find the vertical distance the electrons fall due to gravity. The formula for the vertical distance fallen under gravity in a free fall is given by:
distance = (1/2) * acceleration * time^2
In this case, the acceleration is the acceleration due to gravity, which is approximately 9.8 m/s^2. Plugging in the values, we have:
distance = (1/2) * 9.8 m/s^2 * (7.34375 x 10^(-9) s)^2
Simplifying the equation, we have:
distance = (1/2) * 9.8 m/s^2 * 5.39399707 x 10^(-17) s^2
distance ≈ 2.647199152 x 10^(-17) m
To convert the distance to femtometers, we need to multiply by a conversion factor:
1 m = 1 x 10^15 femtometers
distance in femtometers = 2.647199152 x 10^(-17) m * (1 x 10^15 femtometers / 1 m)
Simplifying the equation, we have:
distance in femtometers ≈ 2.647199152 x 10^(-2) femtometers
Therefore, the vertical distance the electrons fall under the influence of gravity during their flight is approximately 2.647199152 x 10^(-2) femtometers.