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Gnesinka [82]
3 years ago
9

A ball of mass m on a string of length L is attached to a pivot. The ball is released from rest while the string is parallel to

the floor. A bar is placed a distance d vertically below the pivot, such that when the string runs into the bar, it will wrap around the bar. Determine the minimum distance d the bar can be placed such that the ball successfully takes a circular path around the bar. Express your answer in terms of m, L, and physical constants.
Physics
1 answer:
mash [69]3 years ago
8 0

Answer:

L/2

Explanation:

Neglect any air or other resistant, for the ball can wrap its string around the bar, it must rotate a full circle around the bar. This means the ball should be able to swing to the top position where it's directly above the bar. By the law of energy conservation, this happens when the ball is at the same level as where it's previously released vertically. It means the swinging radius around the bar must be at least half of the string length.

So the distance d between the bar and the pivot should be at least L/2

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The constant forces F1 = 8 + 29 + 32 N and F2 = 48 - 59 - 22 N act together on a particle during a displacement from the point A
steposvetlana [31]

Answer:

- 600 J

Explanation:

A (20, 15, 0 ) m

B (0, 0, 7) m

\overrightarrow{F_{1}}=8\widehat{i}+29\widehat{j}+32\widehat{k}

\overrightarrow{F_{2}}=48\widehat{i}-59\widehat{j}-22\widehat{k}

Net force

\overrightarrow{F}=\overrightarrow{F_{1}}+\overrightarrow{F_{2}}

\overrightarrow{F}}=\left ( 8+48 \right )\widehat{i}+\left ( 29-59 \right )\widehat{j}+\left ( 32-22 \right )\widehat{k}

\overrightarrow{F}}=56\widehat{i}-30\widehat{j}+10\widehat{k}

\overrightarrow{S}=\overrightarrow{OB}-\overrightarrow{OA}

\overrightarrow{S}=\left ( 0-20 \right )\widehat{i}+\left ( 0-15 \right )\widehat{j}+\left ( 7-0 \right )\widehat{k}

\overrightarrow{S}=-20\widehat{i}-15\widehat{j}+7\widehat{k}

Work done is defined as

W = \overrightarrow{F}.\overrightarrow{S}

W = \left ( 56\widehat{i}-30\widehat{j}+10\widehat{k} \right ).\left (-20\widehat{i}-15\widehat{j}+7\widehat{k}  \right )

W = -1120 + 450 + 70

W = - 600 J

3 0
3 years ago
Which statements are true concerning Newton's law of gravitation? The gravitational force is related to the mass of each object.
OLEGan [10]

Answer:

The gravitational force is related to the mass of each object.

The gravitational force is an attractive force.

Explanation:

Gravitational force is a long range force of attraction between any two masses.

Mathematically given as :

F=G.\frac{m_1.m_2}{r^2}

where:

m_1 & m_2 are the masses

r= distance between the center of mass of the two objects.

G= gravitational constant = 6.67\times 10^{-11} m^3.kg^{-1}.s^{-2}

From the above relation of eq. (1) it is clear that,

Gravitational force is inversely proportional to the square of the distance and directly proportional to the masses.

The mass of an object is independent of its size due to the fact that density may vary for different objects.

The force of gravity varies with height as:

\frac{g}{g_x} =(\frac{r_x}{r} )^2

where:

g=9.8\,m.s^{-2}

g_x= gravity at height r_x of the center of mass of the object from the center of mass of the earth.

and we know that force:

F=m\times g

where: m= mass of the object.

5 0
3 years ago
Earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.
kobusy [5.1K]

The Earth’s average orbital speed expressed in kilometers per hours is 107225.5 Km/hr and the mass of the sun is 2.58 x 10^{24} Kg

<h3>Relationship between Linear and angular speed</h3>

Linear speed is the product of angular speed and the maximum displacement of the particle. That is,

V = Wr

Where

  • V = Linear speed
  • W = Angular speed
  • r = Radius

Given that the earth orbits the sun at an average circular radius of about 149.60 million kilometers every 365.26 Earth days.

a) To determine the Earth’s average orbital speed, we will make use of the below formula to calculate angular speed

W = 2\pi/T

W = (2 x 3.143) / (365.26 x 24)

W = 6.283 / 876624

W = 7.2 x 10^{-4} Rad/hr

The Earth’s average orbital speed V = Wr

V = 7.2 x  10^{-4} x 149.6 x 10^{6}

V = 107225.5 kilometers per hours.

b) Based on the information given in this question, to calculate the approximate mass of the Sun, we will use Kepler's 3rd law

M = (4\pi ^{2}r^{3}) / GT^{2}

M = (4 x 9.8696 x 3.35 x 10^{24}) / (6.67 x 10^{-11} x 7.68 x 10^{11}<em>)</em>

<em>M = 1.32 x </em>10^{26} / 51.226

M = 2.58 x 10^{24} Kg

Therefore, the Earth’s average orbital speed expressed in kilometers per hours is 107225.5 Km/hr and the mass of the sun is 2.58 x 10^{24} Kg

Learn more about Orbital Speed here: brainly.com/question/22247460

#SPJ1

3 0
1 year ago
a group of students is asking people whether they use plastic bags. what are the students doing? a. stating a problem b. analyzi
notsponge [240]
I believe the correct answer from the choices listed above is option C. A group of students is asking people whether they use plastic bags. By doing such, the students are <span>collecting data. They are collecting data of how many people uses plastic bags. Hope this answers the question.</span>
6 0
3 years ago
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dlinn [17]
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3 years ago
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