Which of the following is a result of gravitational forces in the Solar System?

Exactly one turn of a flexible rope with mass m is wrapped around a uniform cylinder with mass M and radius R.

Dennis_Churaev [7]

Answer:

$\omega=\sqrt{\omega_0^2(\frac{M+m}{M})}$

Explanation:

The rotational kinetic energy when the cylinder is with the rope is:

$E_k=\frac{1}{2}I_c\omega_0^2+\frac{1}{2}I_r\omega_0^2$

where we used the fact that both rope and cylinder hast the same w. This E_k must conserve, that is, E_k must equal E_k when the rope leaves the cylinder. Hence, the final w is given by:

$E_{k1}=E_{k2}\\\\\frac{1}{2}I_c\omega_0^2+\frac{1}{2}I_r\omega_0^{2}=\frac{1}{2}I_c\omega^2\\\\\omega=\sqrt{\omega_0^2(\frac{I_c+I_r}{I_c})}$ (1)

For Ic and Ir we can assume that the rope is a ring of the same radius of the cylinder. Then, we have:

$I_c=\frac{1}{2}MR^2\\\\I_r=mR^2$

Finally, by replacing in (1):

$\omega=\sqrt{\omega_0^2(\frac{M+m}{M})}$

hope this helps!!

7 0

2 years ago

An experiment yielded the above temperature and time information. what is the freezing point of the material in this experiment

Dmitry [639]

The answer is 0 degrees Celsius (0°C). It will be where the line flat lines the first time. The second time would be the boiling point. An experiment yielded the above temperature and time information. The freezing point of the material in this experiment if the material is a solid at time zero is 0 degrees Celsius (0°C) .

7 0

3 years ago

What happens to the gravitational potential energy between two particles if the distance between them is halved? (a) It does not

mr_godi [17]

Answer:

The gravitational potential energy between two particles, if the distance between them is halved, is multiplied by 4 (option c).

Explanation:

The gravitational force is the force of mutual attraction that two objects with mass experience.

The Law of Universal Gravitation enunciated by Newton says that every material particle attracts any other material particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance that separates them. Mathematically this is expressed as:

$F=G*\frac{m1*m2}{r^{2} }$

where m1 and m2 are the masses of the objects, r the distance between them and G a universal constant that receives the name of constant of gravitation.

If the distance between two particles is reduced by half, then, where F' is the new value of the gravitational force:

$F'=G*\frac{m1*m2}{(\frac{r}{2} )^{2} }$

$F'=G*\frac{m1*m2}{\frac{(r )^{2} }{2^{2} } }$

$F'=G*\frac{m1*m2}{\frac{(r )^{2} }{4} }$

$F'=4*G*\frac{m1*m2}{r^{2} }$

F'=4*F

<u><em> The gravitational potential energy between two particles, if the distance between them is halved, is multiplied by 4 (option c).</em></u>

7 0

3 years ago

What is the interaction between surface water and groundwater in a watershed?

Rashid [163]

Answer:

Groundwater occasionally discharges into surface water and then, they flow together as a body of water in a watershed.

Explanation:

According to www.mbgnet.net A watershed describes an area of land that contains a common set of streams and rivers that all drain into a single larger body of water, such as a larger river, a lake or an ocean.

Therefore, when groundwater discharges into a body of surface water, for example a stream, the stream just like several other streams in a watershed would flow into a larger body of water.

3 0

3 years ago

aleksklad [387]

1. Mitosis and Meiosis are both ways cells duplicate DNA
2. They both go through PMAT ( prophase, metaphase, anaphase and telophase)

8 0

3 years ago