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Paul [167]
4 years ago
8

Mary and her younger brother Alex decide to ride the 17-foot-diameter carousel at the State Fair. Mary sits on one of the horses

in the outer section at a distance of 8 feet from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 5 feet from the center.(a) What is Mary's angular speed ?M compared to that of Alex's angular speed ?A? Give your answer as a multiple of ?A.(b) What is Mary's tangential speed vM compared to that of Alex's tangential speed vA? Give your answer as a multiple of vA.
Physics
1 answer:
lorasvet [3.4K]4 years ago
5 0

Answer:

\omege_A=\omega_M

v_M=1.6v_A

Explanation:

A denotes Alex

M denotes Mary

r = Distance from center

Mary and Alex will have the equal displacements in equal interval of time as they are in uniform circular motion. So,

\omega_A=\omega_M

Tangential speed speed is given by

\dfrac{v_M}{v_A}=\dfrac{r_M\omega_M}{r_A\omega_A}\\\Rightarrow \dfrac{v_M}{v_A}=\dfrac{r_M}{r_A}\\\Rightarrow \dfrac{v_M}{v_A}=\dfrac{8}{5}\\\Rightarrow \dfrac{v_M}{v_A}=1.6\\\Rightarrow v_M=1.6v_A

The tangential speed of Mary is v_M=1.6v_A

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What is the energy stored between 2 Carbon nuclei that are 1.00 nm apart from each other? HINT: Carbon nuclei have 6 protons and
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Answer:

A. 8.29\times 10^{-18}\ J

Explanation:

Given that:

p = magnitude of charge on a proton = 1.6\times 10^{-19}\ C

k = Boltzmann constant = 9\times 10^{9}\ Nm^2/C^2

r = distance between the two carbon nuclei = 1.00 nm = 1.00\times 10^{-9}\ m

Since a carbon nucleus contains 6 protons.

So, charge on a carbon nucleus is q = 6p=6\times 1.6\times 10^{-19}\ C=9.6\times 10^{-19}\ C

We know that the electric potential energy between two charges q and Q separated by a distance r is given by:

U = \dfrac{kQq}{r}

So, the potential energy between the two nuclei of carbon is as below:

U= \dfrac{kqq}{r}\\\Rightarrow U = \dfrac{kq^2}{r}\\\Rightarrow U = \dfrac{9\times10^9\times (9.6\times 10^{-19})^2}{1.0\times 10^{-9}}\\\Rightarrow U =8.29\times 10^{-18}\ J

Hence, the energy stored between two nuclei of carbon is 8.29\times 10^{-18}\ J.

8 0
3 years ago
What can one say for sure about element #99, Einsteinium (Es))? a) There's no such element! b) It is an alkali metal. c) It is r
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Answer:

Option (C)

Explanation:

Einsteinium is an element of the periodic table grouped in the Actinide series, with atomic number 99. They are dense element and highly electro-positive. <u>They are highly radioactive</u>, i.e the atoms within the element are unstable and constantly decay until they reach a stable environment. It has 99 number of electrons and protons, 153 number of neutrons.

Due to its high radioactivity, they are health hazardous and can used in making nuclear weapons but their uses are very limited and unknown.

Thus, the correct answer is option (C).

8 0
4 years ago
A 1.0 C charged object and a 2.0 C charged object are separated by 100 m. Where should a -1.0x10-3 C charged object be placed on
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Answer:

x = 41.2 m

Explanation:

The electric force is a vector magnitude, so it must be added as vectors, remember that the force for charges of the same sign is repulsive and for charges of different sign it is negative.

In this case the fixed charges (q₁ and q₂) are positive and separated by a distance (d = 100m), the charge (q₃ = -1.0 10⁻³ C)) is negative so the forces are attractive, such as loads q₃ must be placed between the other two forces subtract

             F = F₁₃ - F₂₃

let's write the expression for each force, let's set a reference frame on the charge q1

           F₁₃ = k \frac{q_1 q_3}{x^2}

           F₂₃ = k \frac{q_2 q_3}{(d-x)^2}

they ask us that the net force be zero

           F = 0

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           F₁₃ = F₂₃

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we substitute

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           100- x = √2  x

           100 = 2.41 x

           x = 41.2 m

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