An electron is moving horizontally in a laboratory when a uniform electric field is suddenly turned on. This field points vertic

Answer:

20 cm

Explanation:

The electric potential energy U is calculated with the formula U = kq₁q₂/r, where q₁ = 5 nC (5 × 10⁻⁹ C) and q₂ = -2 nC (-2 × 10⁻⁹ C) and r is determined as √(x - 2)² + (0 - 0)² + (0 - 0)² = x - 2. This leads to U = -0.5 µJ (-0.5 × 10⁻⁶ J), where k = 9 × 10⁹ Nm²/C².

Thus, solving for r gives us r = kq₁q₂/U

which leads to x - 2 = kq₁q₂/U

Then, rearranging gives x = 0.02 + kq₁q₂/U m

So, x = 0.02 + 9 × 10⁹ Nm²/C² × 5 × 10⁻⁹ C × -2 × 10⁻⁹ C/-0.5 × 10⁻⁶ J

Resulting in x = 0.02 - 90 × 10⁻⁹ Nm²/-0.5 × 10⁻⁶ J

This simplifies to x = 0.02 + 0.18 = 0.2 m, or 20 cm

Answer:

The resulting velocity for him will be 0.187 m/s in reverse direction.

Explanation:

Given:

The mass of the man is,

The mass of the ball is,

The initial velocity of the man is,

The initial velocity of the ball is,

The final velocity of the ball is,

The final velocity of the man is,

To determine this scenario, we employ the principle of momentum conservation.

Momentum is calculated by multiplying mass by velocity.

Initial momentum =

Final momentum = Final momentum of the man and the ball

Final momentum =

Hence, the total initial momentum equals the total final momentum

The negative sign indicates that the man moves backward.

Thus, his final velocity ends up being 0.187 m/s backward.

Answer:

The beats frequency measures approximately

Explanation:

The beat frequency arises from the original ultrasound frequency, , and the frequency of the sound reflected off the car, :

(1)

To calculate the frequency of the reflected sound, we apply the Doppler effect formula:

where

v = 340 m/s, the speed of sound

is the velocity of the car

is the frequency of the sound emitted

By substituting values,

Thus, the beat frequency (1) is

Answer:

Explanation:

Let T represent the tension in the swing.

At the peak

where v denotes the velocity needed to maintain the circular motion.

r equals the distance from the rotation point to the center of the ball, which is L+\frac{d}{2} (with d being the ball's diameter).

The threshold velocity can be expressed as

To determine the velocity at the bottom, we can use energy conservation principles at both the top and bottom positions.

At the top

Energy at the bottom

By comparing the two states using conservation of energy, we find

Answer:

The surface area of the dog changes from A to 3A

Explanation:

It is stated that the dog's surface area has increased by a factor of 3 over four years.

We need to calculate the change in the relative surface area of the dog over this timeframe.

Let’s assume the initial surface area is A.

Since the surface area has been multiplied by 3,

it follows that the surface area after four years is equal to 3×A = 3A.

Thus, the dog's surface area transitions from A to 3A.