An electron with a speed of 1.1 × 107 m/s moves horizontally into a region where a constant vertical force of 3.6 × 10-16 N acts on it. The mass of the electron is 9.11 × 10-31 kg. Determine the vertical distance the electron is deflected during the time it has moved 47 mm horizontally.
To determine the vertical distance the electron is deflected, we need to calculate the time it takes for the electron to move 47 mm horizontally, and then use that time to find the vertical distance.
First, let's convert the horizontal distance from millimeters (mm) to meters (m). We have:
Horizontal distance = 47 mm = 47 × 10^-3 m
Next, we need to calculate the time it takes for the electron to move this distance. We can use the formula:
Time = Distance / Speed
Time = (horizontal distance) / (horizontal speed)
= (47 × 10^-3 m) / (1.1 × 10^7 m/s)
Now, let's calculate the time.
Time = 47 × 10^-3 / (1.1 × 10^7)
Once we have calculated the time, we can find the vertical distance using the formula:
Vertical distance = (1/2) * (acceleration due to force) * (time)^2
= (1/2) * (force / mass) * (time)^2
Given that the force acting on the electron is 3.6 × 10^-16 N, and the mass of the electron is 9.11 × 10^-31 kg:
Vertical distance = (1/2) * (3.6 × 10^-16 N / 9.11 × 10^-31 kg) * [(47 × 10^-3) / (1.1 × 10^7 s)]^2
Now, let's calculate the vertical distance.