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krok68 [10]
3 years ago
6

What is the moment of inertia of an object that rolls without slipping down a 3.5-m- high incline starting from rest, and has a

final velocity of 7.3 m/s? Express the moment of inertia as a multiple of MR2, where M is the mass of the object and R is its radius. (Hint: Use total conservation of mechanical energy)
Physics
1 answer:
Daniel [21]3 years ago
3 0

Answer:

I = 0.287 MR²

Explanation:

given,

height of the object = 3.5 m

initial velocity = 0 m/s

final velocity  = 7.3 m/s

moment of inertia = ?

Using total conservation of mechanical energy

change in potential energy will be equal to change in KE (rotational) and KE(transnational)

PE = KE(transnational) + KE (rotational)

mgh = \dfrac{1}{2}mv^2 + \dfrac{1}{2}I\omega^2

v = r ω

mgh = \dfrac{1}{2}mv^2 + \dfrac{1}{2}\dfrac{Iv^2}{r^2}

I = \dfrac{m(2gh - v^2)r^2}{v^2}

I = \dfrac{mr^2(2\times 9.8 \times 3.5 - 7.3^2)}{7.3^2}

I =mr^2(0.287)

I = 0.287 MR²

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. A vertical electric field is set up in space to compensate for the gravitational force on a point charge. What is the required
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(a) The required magnitude of the electric field when the point charge is an electron is 5.57 x 10⁻¹¹ N/C.

(b) The required magnitude of the electric field when the point charge is an proton is 1.02 x 10⁻⁷ N/C.

<h3>Magnitude of electric field </h3>

The magnitude of electric field is given by the following equation.

F = qE

But F = mg

mg = qE

E = mg/q

where;

  • E is the electric field
  • m is mass of the particle
  • g is acceleration due to gravity
  • q is charge of the particle
<h3>For an electron</h3>

E = (9.11 x 10⁻³¹ x 9.8)/(1.602 x 10⁻¹⁹)

E = 5.57 x 10⁻¹¹ N/C

<h3>For proton</h3>

E = (1.67 x 10⁻²⁷ x 9.8)/(1.602 x 10⁻¹⁹)

E = 1.02 x 10⁻⁷ N/C

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4 0
2 years ago
Two taut strings of identical mass and length are stretched with their ends fixed, but the tension in one string is 1.10 times g
ollegr [7]

Answer:

The  beat frequency when each string is vibrating at its fundamental frequency is 12.6 Hz

Explanation:

Given;

velocity of wave on the string with lower tension, v₁ = 35.2 m/s

the fundamental frequency of the string, F₁ = 258 Hz

<u>velocity of wave on the string with greater tension;</u>

v_1 = \sqrt{\frac{T_1}{\mu }

where;

v₁ is the velocity of wave on the string with lower tension

T₁ is tension on the string

μ is mass per unit length

v_1 = \sqrt{\frac{T_1}{\mu} } \\\\v_1^2 = \frac{T_1}{\mu} \\\\\mu = \frac{T_1}{v_1^2} \\\\ \frac{T_1}{v_1^2} =  \frac{T_2}{v_2^2}\\\\v_2^2 = \frac{T_2v_1^2}{T_1}

Where;

T₁ lower tension

T₂ greater tension

v₁ velocity of wave in string with lower tension

v₂ velocity of wave in string with greater tension

From the given question;

T₂ = 1.1 T₁

v_2^2 = \frac{T_2v_1^2}{T_1}  \\\\v_2 = \sqrt{\frac{T_2v_1^2}{T_1}} \\\\v_2 = \sqrt{\frac{1.1T_1*(35.2)^2}{T_1}}\\\\v_2 = \sqrt{1.1(35.2)^2} = 36.92 \ m/s

<u>Fundamental frequency of wave on the string with greater tension;</u>

<u />f = \frac{v}{2l} \\\\2l = \frac{v}{f} \\\\thus, \frac{v_1}{f_1}  =\frac{v_2}{f_2} \\\\f_2 = \frac{f_1v_2}{v_1} \\\\f_2 =\frac{258*36.92}{35.2} \\\\f_2 = 270.6 \ Hz<u />

Beat frequency = F₂ - F₁

                          = 270.6 - 258

                          = 12.6 Hz

Therefore, the  beat frequency when each string is vibrating at its fundamental frequency is 12.6 Hz

6 0
3 years ago
A plane rises from​ take-off and flies at an angle of 5 degrees5° with the horizontal runway. When it has gained 800800 ​feet, f
dedylja [7]

Answer:

distance=9188149.567feet

Explanation:

Given Data

Angle α=5°

height h=800800 feet

To find

Distance r

Solution  

As we Know that

Sin\alpha =(\frac{Perpendicular}{hypotenuse} )\\Sin\alpha =\frac{h}{r}\\ r=\frac{h}{Sin\alpha}\\ r=\frac{800800feet}{Sin(5^{o} )}\\ r=9188149.567feet

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