Respuesta :
Answer:
As the distance is greater than the separation of the electron plates collides with it
X1= 3.02 10⁻² m
Explanation:
To solve that problem we will work with Newton's second law to find acceleration and then we will use the kinematic equations
Electric force is
F = E q
Where E is the electric field and q the charge in this case the charge of an electron e = 1.6 10-19 C, of negative sign and its mass is 3.1 10-31 Kg
F = ma
-E e= m a
a = -Ee / m
As the force is attractive it is directed on the Y axis
a = - Ee / m j ^
a = -4.00 10³ 1.6 10⁻¹⁹ / 3.1 10⁻³¹
a = -2.06 10¹⁵ m / s² j ^
Let's use the parabolic motion equations to find the position of the electron at the end of the plates, let's decompose the velocities
Vox = Vo cos θ
Voy = Vo sin θ
Vox = 7.86 10⁶ cos (-45)
Voy = 7.86 10⁶ sin (-45)
Vox = 5.56 10⁶ m / s
Voy = -5.56 10⁶ m / s
The movement in the X axis is uniform, so we can find the time it takes to cross the plate
X = Vox t
t = X / Vox
t = 5 10⁻² / 5.56 10⁶
t = 8.99 10⁻⁹ s
With this time we can see how much the electron descended
Y = Voy t - ½ a t²
Y = -5.56 10⁶ 8.99 10⁻⁹ - ½ 2.06 10¹⁵ (8.99 10⁻⁹)²
Y = -49.98 10⁻³ - 83.24 10⁻³
Y = -133.22 10⁻³ m = 1.33 10⁻¹ m
In the exercise they give as data that the separation of the plates is 2.00 cm, let's reduce the distance found to centimeters
Y = 133.22 10⁻³ m (100cm / 1m) = 13,322 cm
As the distance is greater than the separation of the electron plates collides with it
Second Part
Let's look for the time it takes to lower the width of the plate
Y = 2.00 cm = 2.00 10⁻² m
Y = Voy t - ½ a t²
-2.00 10⁻² = -5.56 10⁶ t - ½ 2.06 10¹⁵ t²
0 = 2 10⁻² + 5.56 10⁶ t - 1.03 10¹⁵ t²
1.03 10¹⁵ t² - 5.56 10⁶ t - 2 10⁻² = 0
We solve the second degree equation
t = 5.56 10⁶ √ [(5.56 10⁶) 2 - 4 1.03 10¹⁵ 2.10⁻²]} / (2 1.03 10¹⁵)
t = 5.56 10⁶ ±√ [30.91 10¹² - 8.24 10¹¹]} / 2.06 10¹⁵
t = 5.56 10⁶ ± 5.63 10⁶} /2.06 10¹⁵
t1 = 11.19 10⁶ /2.06 1015
t1 = 5.43 10⁻⁹ s
t2= -0.07 10⁻⁹ s
We take the right time as the positive. Let's calculate the horizontal distance
Xi = Vox t1
X1 = 5.56 10⁶ 5.43 10⁻⁹
X1 = 30.19 10⁻³ m
X1= 3.02 10⁻² m
