What equation can be used to calculate either wavelength, frequency or speed?

9) A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M = 0.10 kg, R = 0.10 m) rotating in a horizontal

natima [27]

Answer:

a. ω₂ = 14rad/s

b. ∇K.E = 0.014J

c. The bug does not conserve force while moving on the disk (non-conservative force).

Explanation:

Mass of the bug (m) = 0.02kg

Mass of the cylindrical disk (M) = 0.10kg

Radius of the disk (r) = 0.10m

Initial angular velocity ω₁ = 10rad/s

final angular velocity ω₂ = ?

a.

To calculate the new angular velocity, we relate it to the conservation of angular momentum of the system I.e when the bug was at the edge of the disk and when it is located at the centre of the disk.

I = Mr² / 2

I₁ = Mr₂ / 2 + mr²

I₁ = moment of inertia when the bug was at the edge

I₁ = [(0.10 * 0.10²) / 2 ] + (0.02 * 0.1²)

I₁ = 0.0005 + 0.0002

I₁ = 7.0*10⁻⁴kgm²

I₂ = moment of inertia when yhe bug was at the center of the disk.

I₂ = Mr² / 2

I₂ = (0.01 * 0.01²) 2

I₂ = 0.0005kgm²

for conservation of angular momentum,

I₁ω₁ = I₂ω₂

solve for ω₂

ω₂ = (I₁ * ω₁) / I₂

ω₂ = (7.0*10⁻⁴ * 10) / 5.0*10⁻⁴

ω₂ = 14 rad/s

b. the change in kinetic energy of the system is

∇K = K₂ - K₁

∇K = ½I₂*ω₂² - ½I₁*ω₁²

∇K = ½(I₂*ω₂² - I₁ω₁²)

∇K = ½[(5.0*10⁻⁴ * 14²) - (7.0*10⁻⁴ * 10²)]

∇k = ½(0.098 - 0.07)

∇K = ½ * 0.028

∇K = 0.014J

c.

The cause of the decrease and increase in kinetic energy is because the bug uses a non-conservative force. To conserve the mechanical energy of a system, all the forces acting in it must be conservative.

The work W produced by this force brings the difference in kinetic energy of the system

W = K₂ - K₁

6 0

3 years ago

Three people pull simultaneously on a stubborn donkey. Jack pulls eastward with a force of 83.5 N, Jill pulls with 93.3 N in the

Irina18 [472]

Answer:

235.8 N

Explanation:

Given that

Jack

83.5 east

Jill

93.3√2/2 east

93.3√2/2 north

Jane

121√2/2 east

121√2/2 south

From the above listed, we can calculate the total force component on x axis to be

Fx = 83.5 + 93.3√2/2 + 121√2/2

Fx = 83.5 + 65.97 + 85.56

Fx = 235 N (east)

Again, we calculate the total force component on y axis to be

Fy = 93.3√2/2 - 121√2/2

Fy = 65.97 - 85.56

Fy = -19.59 N (south)

Finding the resultant, we have

F = √(Fx²+Fy²)

F = √(235² + (-19.59)²)

F = √55225 + 383.7681

F = √55608.7681

F = 235.8 N

4 0

3 years ago

A car advertisement claims their car can go from a stopped position to 60 miles per hour in 5 seconds. The advertisement is desc

Komok [63]

Answer:

Acceleration

Explanation:

The advertisement is describing the acceleration of the car.

Acceleration is the rate of change of velocity per unit of time. It can be expressed mathematically as;

Acceleration = $\frac{v - u}{t}$

v is the final velocity

u is the initial velocity

t is the time taken

Any quantity that specifies the rate of change of velocity of a body within a given time frame is describing its acceleration.

5 0

3 years ago

An electron is confined in a harmonic oscillator potential well. What is the longest wavelength of light that the electron can a

kipiarov [429]

Answer:

The longest wavelength of light is 209 nm.

Explanation:

Given that,

Spring constant = 74 N/m

Mass of electron $m= 9.11\times10^{-31}\ kg$

Speed of light $c= 3\times10^{8}\ m/s$

We need to calculate the frequency

Using formula of frequency

$f =\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}$

Where, k= spring constant

m = mass of the particle

Put the value into the formula

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{74}{9.11\times10^{-31}}}$

$f=1.434\times10^{15}\ Hz$

We need to calculate the longest wavelength that the electron can absorb

$\lambda=\dfrac{c}{f}$

Where, c = speed of light

f = frequency

Put the value into the formula

$\lambda =\dfrac{3\times10^{8}}{1.434\times10^{15}}$

$\lambda=2.092\times10^{-7}\ m$

$\lambda=209\ nm$

Hence, The longest wavelength of light is 209 nm.

6 0

3 years ago

Mechanical energy can change to nonmechanical energy as a result of?

Maksim231197 [3]

physics

:p

Mechanical energy is commonly referred to as "the ability to do work." This is a somewhat inaccurate (though still useful) idea of it, as I'll describe.

Mechanical energy is the sum of kinetic energy (energy associated with motion) and potential energy (energy associated with position). Technically speaking, heat energy (the most common example of non-mechanical energy) is small-scale kinetic energy, but for macroscopic systems, this energy is not mechanical. Although it has the ability to do work, it is small-scale and thus not considered "mechanical."

As far as how mechanical energy is transformed into nonmechanical energy, let me provide a couple of examples:

One is the classic example of friction. When two surfaces rub together, they generate thermal energy, or heat. This is a transformation of the mechanical kinetic energy of the objects into the thermal non-mechanical energy (which is small-scale kinetic energy). This is the primary reason why there are no perfect machines--some energy is always lost as heat due to friction.

Another example is a small electric generator. Rotating a small circuit in a magnetic field will induce a voltage and generate electrical non-mechanical energy. This is a transformation of the kinetic energy associated with the rotation into electrical energy.

The primary difference between mechanical energy and non-mechanical energy is the scope. Mechanical energy is generally associated with macroscopic objects (like water wheels), while non-mechanical energy is generally on the sub-microscopic scale (the kinetic energy of individual atoms). Both can do work, though working with mechanical energy is generally more helpful than trying to work with non-mechanical energy.

7 0

4 years ago