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11 days ago

A sleepy student drops a calculator out of a window that's 20.7\text{ m}20.7 m20, point, 7, start text, space, m, end text off t

he ground. We can ignore air resistance.
What is the velocity of the calculator after falling for 1.8\,\text s1.8s1, point, 8, start text, s, end text?

Physics

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Two electrodes, separated by a distance d, in a vacuum are maintained at a constant potential difference. An electron, accelerat

Yuliya22 [3333]

Answer:

Explanation:

The distance between the electrodes is denoted as d.

The kinetic energy of the electron is represented as Ek when the electrodes are positioned at a distance of "d" apart.

Our goal is to determine the kinetic energy when they are separated by a distance of d/3.

K.E = ½mv²

It’s important to note that the mass remains constant; only velocity varies.

Additionally,

K.E = Work done by the electron

K.E = F × d

K.E = W = ma × d

Assuming constant acceleration

Hence, m and a are fixed,

therefore,

K.E is directly related to d

Thus, as d increases, K.E increases, and conversely, when d decreases, K.E decreases.

Consequently,

K.E_1 / d_1 = K.E_2 / d_2

With K.E_1 equating to E_k

and d_1 being d

while d_2 is represented as d/3

This leads to K.E_2 = K.E_1 / d_1 × d_2

Thus, K.E_2 = E_k × ⅓d / d

Finally,

K.E_2 = ⅓E_k

Therefore, the resultant kinetic energy is one third of the original E_k

7 0

2 months ago

To study torque experimentally, you apply a force to a beam. One end of the beam is attached to a pivot that allows the beam to

kicyunya [3294]

Answer:

a) τ = i ^ (y $F_{z}$ - z $F_{y}$ ) + j ^ (z Fₓ - x $F_{z}$ ) + k ^ (x $F_{y}$ - y Fₓ)

b) τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

Explanation:

a) The torque can be expressed as

τ = r x F

To tackle this equation, using the determinant approach is the most straightforward method

$\tau =\left[\begin{array}{ccc}i&j&k\\x&y&z\\F_{x}&F_{y} &F_{z}\end{array}\right]$

The resulting expression is

τ = i ^ (y $F_{z}$ - z $F_{y}$ ) + j ^ (z Fₓ - x $F_{z}$ ) + k ^ (x $F_{y}$ - y Fₓ)

b) Now let's compute

τ = i ^ (0.075 1.4 -0.035 8.4) + j ^ (0.035 2.8 - 4.07 1.4) + k ^ (4.07 8.4 - 0.075 2.8)

τ = i ^ (- 0.189) + j ^ (-5.6) + k ^ (33,978)

τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m

c) To find angular acceleration, we use

τ = I α

α = τ / I

The moment of inertia being a scalar means that only the magnitude of each component changes, orientation remains constant.

α = (-0.189i^ -5.6 j^ + 33.978k^) / 241

α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²

8 0

2 months ago

A boat is floating in a small pond. the boat then sinks so that it is completely submerged. what happens to the level of the pon

ValentinkaMS [3465]

When the boat submerges completely in the pond, the water level of the pond rises.

4 0

1 month ago

Newton’s law of cooling states that dx dt = −k(x−A) where x is the temperature,t is time, A is the ambient temperature, and k &g

Maru [3345]

Answer:

a) $X= kA_o\dfrac{1}{k^2+\omega^2}\left ( kcos\omega t+\omega sin\omega t \right )+Ce^{-kt}$

b) D does not influence the long-term results.

Explanation:

Given that

$\dfrac{dx}{dt}=-k(x-A)$

A = A0 cos(ωt)

$\dfrac{dx}{dt}=-k(x-A_o cos(\omega t))$

$\dfrac{dx}{dt}+kx=kA_o cos(\omega t)$ This is a linear equation hence the integration factor, I

$I=e^{\int kdt}$

$I=e^{kt}$ Now using the characteristics of linear equations

$e^{kt} X=\int e^{kt} kA_o cos(\omega t) dt +C$

$e^{kt} X= kA_o \dfrac{e^{kt}}{k^2+\omega^2}\left ( kcos\omega t+\omega sin\omega t \right )+C$

b) At t= 0

$X= kA_o\dfrac{1}{k^2+\omega^2}\left ( kcos\omega t+\omega sin\omega t \right )+Ce^{-kt}$

Thus, the initial condition

does not affect the long-term outcome.

$X(0)=\dfrac{k^2A_o}{\omega^2+k^2}+C$

5 0

2 months ago

A pressure cooker is a pot whose lid can be tightly sealed to prevent gas from entering or escaping. even without knowing how bi

Sav [3153]

Even if we lack details about the size of the pressure cooker or the altitude of its operation, we can reliably assess the force on the lid based on prior knowledge because, similar to boiling water, the pressure buildup inside the cooker increases in line with the rising temperature.

5 0

3 months ago