Rubber is which of the following?

the moon orbits the earth in an average time of 27.3 days at an average distance of 384000 km. use these facts and newtons versi

natulia [17]

Answer:

The mass of the Earth is $6.02x10^{24}Kg$ .

Explanation:

The Universal law of gravitation shows the interaction of gravity between two bodies:

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

Where G is the gravitational constant, M and m are the masses of the two objects and r is the distance between them.

For this particular case, M is the mass of the Earth and m is the mass of the moon. Since it is a circular motion, the centripetal acceleration will be:

$a = \frac{v^{2}}{r}$ (2)

Then Newton's second law ( $F = ma$ ) will be replaced in equation (1):

$ma = G\frac{Mm}{r^{2}}$

By replacing (2) in equation (1) it is gotten:

$m\frac{v^{2}}{r} = G\frac{Mm}{r^{2}}$

$v^{2} = G\frac{Mmr}{mr^{2}}$

$v^{2} = \frac{GM}{r}$ (3)

Since it is a circular motion, the orbital velocity can be represented by:

$v = \frac{2\pi r}{T}$ (4)

Where r is the orbital radius and T is the period.

Then, equation 4 can be replaced in equation 3.

$(\frac{2\pi r}{T})^{2} = \frac{GM}{r}$

$\frac{4\pi^{2} r^{2}}{T^{2}} = \frac{GM}{r}$

Notice that r can be represented by the semi-major axis (a)

$\frac{4\pi^{2} a^{2}}{T^{2}} = \frac{GM}{a}$

$T^{2}GM = 4\pi^{2} a^{2} a$

$T^{2} = \frac{4\pi^{2} a^{3}}{GM}$ (5)

Therefore, the mass of the Earth can be determined if M is isolated from equation (5):

$M = \frac{4\pi^{2} a^{3}}{GT^{2}}$ (6)

Notice that it is necessary to express a in units of meters and T in units of seconds.

$a = 384000Km . \frac{1000m}{1Km}$ --- $3.84x10^{8}m$

$T = 27.3days . \frac{24hrs}{1day}$ --- $655.2hours.\frac{3600s}{1hour}$ --- $2358720s$

$M = \frac{4\pi^{2} (3.84x10^{8}m)^{3}}{(6.67x10^{-11}kg.m/s^{2}.m^{2}/kg^{2})(2358720s)^{2}}$

$M = 6.02x10^{24}Kg$

Hence, the mass of the Earth is $6.02x10^{24}Kg$ .

6 0

3 years ago

A bowling ball encounters a 0.760 m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictiona

xxMikexx [17]

Answer:

v = 2.31 m/s

Explanation:

Kinetic energy will be converted partially into potential energy and rest will remain in the form of kinetic energy .

Initial kinetic energy = 1/2 mu²

u is initial velocity at the bottom .

Potential energy at the top

= mgh

Kinetic energy at the top

= 1/2 m v²

According to conservation of energy

1/2 mu² = mgh + 1/2 m v²

1/2 u² = gh + 1/2 v²

.5 x 4.5² = 9.8 x .76 + .5 v²

10.125 = 7.448 + .5 x v²

v = 2.31 m/s

5 0

4 years ago

Amber applies a net force of 35 N to pull her younger brother (32 kg) in a wagon (3 kg). at what rate does the wagon accerlerate

Ket [755]

Answer:

C. 1.00 m/s^2

Explanation:

We can solve the problem by using Newton's second law:

$F=ma$

where

F is the net force acting on an object

m is the mass of the object

a is its acceleration

In this case, the net force applied by Amber is F=35 N, while the total mass of the brother+the wagon is

$m=32 kg+3 kg=35 kg$

Therefore, we can re-arrange the previous equation to find the acceleration:

$a=\frac{F}{m}=\frac{35 N}{35 kg}=1.00 m/s^2$

6 0

3 years ago

A car advertisement states that a certain car can accelerate from rest to 70 km/h in 7 seconds. Calculate the acceleration of th

ankoles [38]

Answer:

10 km/h

Explanation:

3 0

3 years ago

11. How many marine mammals from Figure 1 can hear sounds under 100 Hz? 12. If there was a sound that was 100,000 Hz, which mamm

bagirrra123 [75]

Answer:i think that the answer is 2 because bullfrogs and racoons can hear sounds under 100hz

Explanation:

i REALLY HOPE you get this DUB

3 0

3 years ago