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Fantom [35]
3 years ago
7

Starting from Newton’s law of universal gravitation, show how to find the speed of the moon in its orbit from the earth-moon dis

tance of 3.9 × 108 m and the earth’s mass. Assume the orbit is a circle.
Physics
1 answer:
WARRIOR [948]3 years ago
5 0

Answer: 1010.92 m/s

Explanation:

According to Newton's law of universal gravitation:

F=G\frac{Mm}{r^{2}} (1)

Where:

F is the gravitational force between Earth and Moon

G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}} is the Gravitational Constant  

M=5.972(10)^{24} kg is the mass of the Earth

m=7.349(10)^{22} kg is the mass of the Moon

r=3.9(10)^{8} m is the distance between the Earth and Moon

Asuming the orbit of the Moon around the Earth is a circular orbit, the Earth exerts a centripetal force on the moon, which is equal to F:

F=m.a_{C} (2)

Where a_{C} is the centripetal acceleration given by:

a_{C}=\frac{V^{2}}{r} (3)  

Being V the orbital velocity of the moon

Making (1)=(2):

m.a_{C}=G\frac{Mm}{r^{2}} (4)

Simplifying:

a_{C}=G\frac{M}{r^{2}} (5)

Making (5)=(3):

\frac{V^{2}}{r}=G\frac{M}{r^{2}} (6)  

Finding V:

V=\sqrt{\frac{GM}{r}} (7)

V=\sqrt{\frac{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(5.972(10)^{24} kg)}{3.9(10)^{8} m}} (8)

Finally:

V=1010.92 m/s

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A small car with mass m and speed 2v and a large car with mass 2m and speed v both travel the same circular section of an unbank
Alenkasestr [34]

Answer:

(D) F/2

Explanation:

Since the circular section is unbanked, the centripedal acceleration acting on each of the cars is

a_s = \frac{v_s^2}{r} = \frac{(2v)^2}{r} = \frac{4v^2}{r}

a_l = \frac{v_l^2}{r} = \frac{v^2}{r}

Therefore the centripetal force on each car

F_s = m_sa_s = \frac{4mv^2}{r}

F_l = m_la_l = \frac{2mv^2}{r}

Since F_s = 2F_l this means the friction force required to keep the large car on the road is only half of the friction force required to keep the small car on road

So (D) F/2 is the correct answer

5 0
3 years ago
What force controls the movement of the planets around the sun, holds together stars grouped in galaxies, and galaxies grouped i
JulijaS [17]

Answer:

Gravity.

Explanation:

The force that controls the movement of the planets around the sun, holds together stars grouped in galaxies, and galaxies grouped in clusters is called gravity.

This ultimately implies that, gravity is considered to be a universal force of attraction that acts between all objects that has both mass, energy and occupy space. Therefore, it acts in such a way as to bring objects together.

Additionally, the gravity of earth makes it possible for all physical objects to possess weight.

Weight can be defined as the force acting on a body or an object as a result of gravity.

Mathematically, weight is given by the formula;

Weight = mg

Where;

m is the mass of an object.

g is acceleration due to gravity.

4 0
3 years ago
The olive oil in a bottle has a mass of 360 g. If the density of olive oil is 0.9 g/mL, what is its volume?
andreev551 [17]
Mass/density= volume so it will be 360/0.9 which equals to 400 and if you want to find mass you just need to multiple volume•density
4 0
3 years ago
Read 2 more answers
A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable i
Inga [223]

Answer:

The speed  is v  =122.2 \ m/s

Explanation:

From the question we are told that

   The  length of the wire is L  =  100 \ m

    The  mass density is  \mu =  2.01 \ kg/m

    The tension is T  =  3.00 *10^{4} \ N

   

Generally the speed of the transverse cable is mathematically represented as

           v  = \sqrt{\frac{T}{\mu} }

substituting values

         v  = \sqrt{\frac{3.0 *10^{4}}{2.01} }

        v  =122.2 \ m/s

           

3 0
3 years ago
A block of mass 2.5kg is pressed against a spring and compresses the spring to a length of
IrinaK [193]

Answer:

10.032 N.

Explanation:

From the question given above, the following data were obtainedb

Mass (m) = 2.5 Kg

Final length = 10.0 cm

Original length = 21.4 cm

Spring constant (K) = 88 N/m

Force (N) =?

Next, we shall determine the compression of the spring. This can be obtained as follow:

Final length = 10.0 cm

Original length = 21.4 cm

Compression (e) =?

e = Original length – final length

e = 21.4 – 10

e = 11.4 cm

Next, we shall convert 11.4 cm to m. This can be obtained as follow:

100 cm = 1 m

Therefore,

11.4cm = 11.4 cm × 1 m / 100 cm

10 cm = 0.114 m

Finally, we shall determine the force. This can be obtained as illustrated below:

Compression (e) = 0.114 m

Spring constant (K) = 88 N/m

Force (N) =?

F = Ke

F = 88 × 0.114

F = 10.032 N

Thus, the force in the spring is 10.032 N

6 0
3 years ago
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