A model of a spring/mass system is 4x'' + e−0.1tx = 0. By inspection of the differential equation only, discuss the behavior of

Explanation:

The formula for the electric field produced by an infinite sheet of charge is outlined below.

               E =

where,   is the surface charge density

Following this, the formula for the electric force acting on a proton is given as:

             F = eE

where,    e is the charge of a proton

According to Newton's second law of motion, the overall force on the proton can be expressed as follows.

                       F = ma

                 a =

                    =

                     =

According to kinematic equations, the proton's speed in the perpendicular direction can be described as follows.

                     =

                     =

                     = 683.974 m/s

Thus, the overall speed of the proton can be calculated as follows.

                v' =

                    =

                    = 1178.73 m/s

Consequently, we conclude that the proton's speed is 1178.73 m/s.

Answer:

The work performed by air resistance totals -0.0782 J

Explanation:

Hello!

According to the principle of conservation of energy, the energy of a raindrop must remain constant.

At the outset, the raindrop possesses only gravitational potential energy:

PE = m · g · h

Where:

PE = potential energy.

m = mass of the raindrop.

g = gravitational acceleration (9.8 m/s²)

h = height.

Let's determine the initial potential energy of the raindrop:

(4 mg should be converted into kg: 4 mg · 1 kg / 1 × 10⁶ mg = 4 × 10⁻⁶ kg)

PE = 4 × 10⁻⁶ kg · 9.8 m/s² · 2000 m

PE = 0.0784 J

As the raindrop descends, some of its potential energy converts into kinetic energy while the rest is lost to the air resistance. Upon reaching the ground, all initial potential energy has been either turned into kinetic energy or spent overcoming air resistance:

initial PE = final KE + Work by air

Where:

KE = kinetic energy.

Work by air = work done by air resistance.

The kinetic energy at ground level is computed as follows:

KE = 1/2 · m · v²

Where:

m = mass

v = velocity

KE = 1/2 · 4 × 10⁻⁶ kg · (10 m/s)²

KE = 2 × 10⁻⁴ J

Now, we can find the work done by air resistance:

initial PE = final KE + Work by air

0.0784 J = 2 × 10⁻⁴ J + Work by air

Work by air = 0.0784 J - 2 × 10⁻⁴ J

Work by air = 0.0782 J

Since work is performed in the opposite direction to movement, this results in a negative value. Therefore, the work done by air resistance is -0.0782 J.

Explanation:

= initial resistance

= temperature coefficient of resistivity

= final temperature    

= initial temperature

= 3 ohm

= 0.0045

        R =

        36 =

Thus, it can be concluded that the temperature of the light bulb at 12.0 V is 7626.33 K.