An electron ( mass = 9.11×10−31 kg) leaves one end of a TV picture tube with zero initial speed and travels in a straight line to the accelerating grid, which is 1.85 cm away. It reaches the grid with a speed of 2.95×10^6 m/s . (You can ignore the gravitational force on the electron.)

If the accelerating force is constant, compute the acceleration of the electron. If the accelerating force is constant, compute the time it takes the electron to reach the grid. If the accelerating force is constant, compute the net force that is accelerating the electron, in newtons.

Why did the electron leave its TV show? Because it couldn't find the remote control!

To compute the acceleration of the electron, we can use the second equation of motion:

v² = u² + 2as

Where:
v = final velocity = 2.95×10^6 m/s
u = initial velocity = 0 m/s
s = displacement = 1.85 cm = 0.0185 m
a = acceleration (what we're trying to find)

Plugging in the values, we get:

(2.95×10^6 m/s)² = (0 m/s)² + 2a(0.0185 m)

a = (2.95×10^6 m/s)² / (2 * 0.0185 m) ≈ 2.51 × 10^14 m/s²

So, the acceleration of the electron is approximately 2.51 × 10^14 m/s². That's quite a speedy electron!

Now, let's calculate the time it takes for the electron to reach the grid. We can use the first equation of motion:

s = ut + (1/2)at²

Where:
s = displacement = 0.0185 m
u = initial velocity = 0 m/s
t = time (what we're trying to find)
a = acceleration ≈ 2.51 × 10^14 m/s²

Plugging in the values, we get:

0.0185 m = 0 m/s * t + (1/2)(2.51 × 10^14 m/s²)(t²)

0.0185 m = (1.255 × 10^14 m/s²)(t²)

t² ≈ 0.0185 m / (1.255 × 10^14 m/s²)

t² ≈ 1.47 × 10^-16 s²

Taking the square root of both sides, we get:

t ≈ √(1.47 × 10^-16 s²)

t ≈ 3.83 × 10^-8 s

So, it takes approximately 3.83 × 10^-8 seconds for the electron to reach the grid.

Now, let's find the net force accelerating the electron. We can use Newton's second law of motion:

F = ma

Where:
F = net force (what we're trying to find)
m = mass = 9.11 × 10^-31 kg
a = acceleration ≈ 2.51 × 10^14 m/s²

Plugging in the values, we get:

F = (9.11 × 10^-31 kg)(2.51 × 10^14 m/s²)

F ≈ 2.29 × 10^-16 N

So, the net force accelerating the electron is approximately 2.29 × 10^-16 newtons. That's a tiny force for such a speedy electron!

To find the acceleration of the electron, we can use the formula:

acceleration = (final velocity - initial velocity) / time

Given:
Mass of the electron (m) = 9.11 x 10^-31 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 2.95 x 10^6 m/s

Substituting the known values:
acceleration = (2.95 x 10^6 m/s - 0 m/s) / time

Now, we need to find the time taken by the electron to reach the grid. We can use the formula:

distance = (initial velocity * time) + (0.5 * acceleration * time^2)

Given:
Distance (d) = 1.85 cm = 0.0185 m
Initial velocity (u) = 0 m/s
Acceleration (a) = ?

Substituting the known values:
0.0185 m = (0 m/s * time) + (0.5 * acceleration * time^2)

Next, let's calculate the net force acting on the electron. We can use Newton's second law of motion:

net force = mass * acceleration

Given:
Mass (m) = 9.11 x 10^-31 kg
Acceleration (a) = ?

Substituting the known values:
net force = (9.11 x 10^-31 kg) * acceleration

Now, let's solve for each of the unknown values step-by-step.

1. Acceleration:
acceleration = (2.95 x 10^6 m/s - 0 m/s) / time

2. Time:
0.0185 m = (0 m/s * time) + (0.5 * acceleration * time^2)

3. Net force:
net force = (9.11 x 10^-31 kg) * acceleration

To solve this problem, we can use kinematic equations. Let's break it down into three parts and find each value step by step.

1. Compute the acceleration of the electron:
We can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Given:
Initial velocity, u = 0 m/s (since the electron starts with zero initial speed)
Final velocity, v = 2.95 × 10^6 m/s
Displacement, s = 1.85 cm = 0.0185 m

Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)

Plugging in the values:
a = (2.95 × 10^6)^2 / (2 × 0.0185)

Calculating this will give you the acceleration of the electron.

2. Compute the time it takes the electron to reach the grid:
We can use another equation of motion: s = ut + (1/2)at^2
Given:
Initial velocity, u = 0 m/s
Displacement, s = 0.0185 m
Acceleration, a = calculated in the previous step

Rearranging the equation, we get a quadratic equation:
(1/2)at^2 = s
(1/2)at^2 - s = 0

Solving this quadratic equation will give you the value of t, which is the time taken by the electron to reach the grid.

3. Compute the net force accelerating the electron:
We can use Newton's second law of motion: F = ma, where F is the force, m is the mass, and a is the acceleration.
Given:
Mass of the electron, m = 9.11 × 10^-31 kg
Acceleration, a = calculated in the first step

Plugging in the values will give you the net force exerted on the electron.

Please note that all calculations should be done using consistent units (e.g., meters for distance and seconds for time).

(a) Vfinal = sqrt(2 a X)

where X = 0.0185 m and Vfinal = 2.95*1-^6 m/s
Solve for acceleration, a.

(b) (1/2)*a*t^2 = 0.0185 m
Solve for t.

(c) F = m a
Solve for F.