Answer:
Magnitude of gravitational force between this planet and its moon: approximately [tex]1.37 \times 10^{20}\; \rm N[/tex].
Acceleration of this moon towards the planet: approximately [tex]5.49 \times 10^{-3}\; \rm m \cdot s^{-2}[/tex].
Acceleration of this planet towards its moon: approximately [tex]2.29 \times 10^{-5}\; \rm m \cdot s^{-2}[/tex].
Explanation:
Look up the gravitational constant, [tex]G[/tex]:
[tex]G \approx 6.67 \times 10^{-11}\; \rm m^3\cdot kg^{-1} \cdot s^{-2}[/tex].
Assume that both this planet and its moon are spheres of uniform density. When studying the gravitational interaction between this planet and its moon, this assumption allows them to be considered as two point masses.
The formula for the size of gravitational force between two point masses [tex]m_1[/tex] and [tex]m_2[/tex] with a distance of [tex]r[/tex] in between is:
[tex]\displaystyle F = \frac{G \cdot m_1 \cdot m_2}{r^2}[/tex],
where [tex]G[/tex] is the gravitational constant.
Let [tex]m_1[/tex] and [tex]m_2[/tex] denote the mass of this planet and its moon, respectively.
Calculate the size of gravitational force between this planet and its moon:
[tex]\begin{aligned} F &= \frac{G \cdot m_1 \cdot m_2}{r^2} \\ &\approx \frac{6.67 \times 10^{-11}\; \rm m^3 \cdot kg^{-1} \cdot s^{-2} \times 6.00 \times 10^{24}\; \rm kg \times 2.50 \times 10^{22}\; \rm kg}{{\left(2.70 \times 10^{8}\; \rm m\right)}^2} \\ &\approx 1.37 \times 10^{20}\; \rm N\end{aligned}[/tex].
Assume that other than the gravitational force between this planet and its moon, all other forces (e.g., gravitational force between this planet and the star) are negligible. The magnitude of the net force on the planet and on the moon should both be approximately [tex]1.37 \times 10^{20}\; \rm N[/tex].
Apply Newton's Second Law of motion to find the acceleration of this planet and its moon:
[tex]\displaystyle \text{acceleration} = \frac{\text{net force}}{\text{mass}}[/tex].
For this moon:
[tex]\displaystyle \frac{1.37 \times 10^{20}\; \rm N}{2.50 \times 10^{22}\; \rm kg} \approx 5.49\times 10^{-3}\; \rm m \cdot s^{-2}[/tex].
For this planet:
[tex]\displaystyle \frac{1.37 \times 10^{20}\; \rm N}{6.00 \times 10^{24}\; \rm kg} \approx 2.29 \times 10^{-5}\; \rm m \cdot s^{-2}[/tex].
How many stars are in the universe (approximately)? O 40 sixtillion 0 365 billion O 86.4 million O one
Answer:
a i belive
Explanation:
the univerce is VERY large so a, if im wrong i apologise :(
* WILL GIVE BRAINLIEST TO CORRECT ANSWER *
Name a product that people commonly purchase by mass and not by weight.
I would say food but like they take weight too
When you turn off your bedroom lights, the kitchen lights can stay on. This is because your home is wired using which of the following? (AKS 10b / DOK 1)
A.
Fuses
B.
Series circuits
C.
Batteries
D.
Parallel circuits
When you turn off your bedroom lights, the kitchen lights can stay on. This is because your home is wired by using the series circuit. Hence, option B is correct.
What is a Series circuit?The amount of current in the flow circuits of each element in a series circuit is the same. This is due to the recent flow having a single path. The flow rate (marble speed) at any point in a circuit (tube) at any given moment in time has to be equal because electric current moves through a conductor like marble in a duct.
The requirement that all values (voltage, current, resistance, and power) relate to one another in terms of the identical two places in a circuit is a significant exception to Ohm's law.
Therefore, the wiring of the home is in series combination. So, option B is correct.
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2. Heather and Matthew walk with an average velocity of +0.87 m/s eastward.
If it takes them 27 minutes to walk to the store, what is their
displacement? (include direction)
(5 points)
The second-order dark fringe in a single-slit diffraction pattern is 1.40 mm from the center of the central maximum. Assuming the screen is 89.0 cm from a slit of width 0.710 mm and assuming monochromatic incident light, calculate the wavelength of the incident light.
We know, for single slit :
[tex]y =\dfrac{ n\lambda L}{a}\\\\\lambda = \dfrac{ya}{nL}[/tex] ...1)
[tex]y = 1.4\ mm = 1.4 \times 10^{-3}\ m[/tex]
n = 2
L = 89 cm = 0.89 m
[tex]a=7.1\times 10^{-4}\ m[/tex]
Putting all these in equation 1), we get :
[tex]\lambda = \dfrac{ya}{nL}\\\\\lambda = \dfrac{1.4\times 10^{-3}\times 7.1\times 10^{-4}}{2\times 0.89 }\\\\\lambda = 5.584 \times 10^{-7}\ m[/tex]
Therefore, wavelength of the incident light is [tex]5.584 \times 10^{-7}\ m[/tex] or 558.4 nm.
Hence, this is the required solution.
Why does a watched pot never boil?
Help me guys please with this question
Answer:
[tex]\mid \vec C\mid=31.9[/tex]
Explanation:
Consider the vectors:
[tex]\vec A=9.4\mathbf{\hat{i}}-3.6\mathbf{\hat{j}}[/tex]
[tex]\vec B=-9.5\mathbf{\hat{i}}-13.4\mathbf{\hat{j}}[/tex]
Calculate the magnitude of
[tex]\vec C=-2\vec B-\vec A[/tex]
Substitute the values of the vectors:
[tex]\vec C=-2(-9.5\mathbf{\hat{i}}-13.4\mathbf{\hat{j}})-(9.4\mathbf{\hat{i}}-3.6\mathbf{\hat{j}})[/tex]
Operate and remove parentheses:
[tex]\vec C=19\mathbf{\hat{i}}+26.8\mathbf{\hat{j}}-9.4\mathbf{\hat{i}}+3.6\mathbf {\hat{j}}[/tex]
Operating both components separately:
[tex]\vec C=9.6\mathbf{\hat{i}}+30.4\mathbf{\hat{j}}[/tex]
Now find the magnitude of C:
[tex]\mid \vec C\mid=\sqrt{9.6^2+30.4^2}[/tex]
[tex]\mid \vec C\mid=\sqrt{1016.32}[/tex]
[tex]\mathbf{\mid \vec C\mid=31.9}[/tex]
A spring gun fires a ball horizontally at 15 m/s. It is mounted on a flat car moving in a straight line at 25 m/s. relative to the ground, what is the horizontal speed of the ball when the gun is aimed forward?
Answer:
15 m/s
Explanation:
The Speed Of The Car Does Not Add To The Speed Of The Bullet
In football we see unbalanced forces. When 1 player exerts an unbalanced force on another player and causes a player to
Answer:
Fall
Explanation:
In ultimate the disc may be passed in any direction.
True
False
I think is True: Because...
when you throw a disc you can throw it in any direction, many people call it "Flying Saucer" I'll give you an example ... When you throw something, for example a paper, you want to throw it at your classmate. You already know what address you want to send it to, then I say it is: True ...
Sorry if it's wrong :(
significance of practicals in the discipline of geography
Catching a wave, a 77 kg surfer starts with a speed of 1.3 m/s, drops through a height of 1.65 m, and ends with a speed of 8.2 m/s. How much non-conservative work was done on the surfer?
Answer:
Explanation:
The total work done by the wave is expressed as;
Workdone = Potential energy + Kinetic energy
Workdone = mgh + 1/2mv²
m is the mass = 77kg
g is the acceleration due to gravity = 9.8m/s²
v is the velocity = 8.2m/s
h is the height = 1.65m
Substitute into the formula;
Workdone = 77(9.8)(1.65) + 1/2(77)8.2²
Workdone = 1245.09 + 2588.74
Workdone = 3833.83Joules
Hence the amount of non conservative work done on the sofa is 3833.83Joules
Given:
Velocity, v = 8.2 m/sHeight, h = 1.65 mMass, m = 77 kgWe know,
→ [tex]Work \ done = Potential \ energy +Kinetic \ energy[/tex]
or,
[tex]= mgh +\frac{1}{2} mv^2[/tex]
By putting the values,
[tex]= 77\times 9.8\times 1.65+\frac{1}{2}\times 77\times (8.2)^2[/tex]
[tex]= 1245.09+2588.74[/tex]
[tex]= 3833.83 \ Joules[/tex]
Thus the above approach is right.
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Which statement is part of Dalton's atomic theory?
Matter is composed of small particles called atoms.
Atoms can be divided into their subatomic particles.
Atoms are able to be seen with proper spectroscopy equipment.
Chemical reactions can change atoms from one type to another.
Answer:
Dalton’s atomic theory was a scientific theory on the nature of matter put forward by the English physicist and chemist John Dalton in the year 1808. It stated that all matter was made up of small, indivisible particles known as ‘atoms’.
Explanation:
Atoms can be divided into their subatomic particles.
The statement that is part of Dalton's atomic theory is as follows: Matter is composed of small particles called atoms.
What is Dalton's atomic theory?John Dalton is a scientist that first stated the theory of chemical combination in 1803.
The components of these theory are as follows:
Elements consist of indivisible small particles called atoms.All atoms of the same element are identical i.e. different elements have different types of atom. Atoms can neither be created nor destroyedTherefore, according to this question, the statement that is part of Dalton's atomic theory is as follows: Matter is composed of small particles called atoms.
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If you are riding your bike west to your friend’s house, and you ride the 1.25 miles in 5 minutes, what is your velocity, in miles per hour?
Answer:
velocity = 15 miles / hourExplanation:
distance = 1.25 mile
time traveled = 5 min.
find velocity in miles / hour
solution:
use the formula: velocity = distance / time
velocity = 1.25 mile x 60 min
5 min 1 hour
velocity = 15 miles / hour
a heavty downpour and thundrstorm is probably caused by
A 4.80 g bullet moves with a speed of 170 m/s perpendicular to the Earth's magnetic field of 5.00×10−5T.
Part A
If the bullet possesses a net charge of 1.06×10−8 C , by what distance will it be deflected from its path due to the Earth's magnetic field after it has traveled 1.00 km ?
Answer:
[tex]3.24\times 10^{-7}\ \text{m}[/tex]
Explanation:
m = Mass of bullet = 4.8 g
v = Velocity of bullet = 170 m/s
B = Magnetic field of Earth = [tex]5\times 10^{-5}\ \text{T}[/tex]
q = Charge of bullet = [tex]1.06\times 10^{-8}\ \text{C}[/tex]
a = Acceleration
Time the bullet will be in the air for is [tex]t=\dfrac{1000}{170}=5.88\ \text{s}[/tex]
Force is given by
[tex]F=ma[/tex]
Magnetic force is given by
[tex]F=qvB[/tex]
So
[tex]ma=qvB\\\Rightarrow a=\dfrac{qvB}{m}\\\Rightarrow a=\dfrac{1.06\times 10^{-8}\times 170\times 5\times 10^{-5}}{4.8\times 10^{-3}}\ \text{m/s}^2[/tex]
From the linear equations of motion we have
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0+\dfrac{1}{2}\times \dfrac{1.06\times 10^{-8}\times 170\times 5\times 10^{-5}}{4.8\times 10^{-3}}\times 5.88^2\\\Rightarrow s=3.24\times 10^{-7}\ \text{m}[/tex]
The defelection of the bullet is [tex]3.24\times 10^{-7}\ \text{m}[/tex]
A golf ball (m=26.7g) is struck a blow that makes an angle of 33.6 degrees with the horizontal. The drive lands 190m away on a flat fairway. The acceleration of gravity is 9.8 m/s^2 . If the golf club and ball are in contact for 7.13 ms, what is the average force of impact?
Answer:
Th average force impact is [tex]F = 168.298 \ N[/tex]
Explanation:
From the question we are told that
The mass of the golf ball is [tex]m_g = 26.7 \ g = 0.0267 \ kg[/tex]
The angle made is [tex]\theta = 33.6 ^o[/tex]
The range of the golf ball is [tex]R = 190 \ m[/tex]
The duration of contact is [tex]\Delta t = 7.13 \ ms = 7.13 *10^{-3} \ s[/tex]
Generally the range of the golf ball is mathematically represented as
[tex]R = \frac{v^2 sin2(\theta)}{g}[/tex]
Here v is the velocity with which the golf club propelled it with, making v the subject
[tex]v = \sqrt{\frac{R * g}{sin 2 (\theta)} }[/tex]
=> [tex]v = \sqrt{\frac{190 * 9.8}{sin 2 (33.6)} }[/tex]
=> [tex]v = 44.94 \ m/s[/tex]
Generally the change in momentum of the golf ball is mathematically represented as
[tex]\Delta p = m * (v - u )[/tex]
here u is the initial velocity of the ball before being stroked and the value is 0 m/s
[tex]\Delta p = 0.0267 * ( 44.94 - 0 )[/tex]
=> [tex]\Delta p = 1.19996 \ kg \cdot m/s[/tex]
Generally the average force of impact is mathematically represented as
[tex]F = \frac{\Delta p }{\Delta t}[/tex]
=> [tex]F = \frac{1.19996 }{7.13 *10^{-3}}[/tex]
=> [tex]F = 168.298 \ N[/tex]
Zookeepers carry a stretcher that holds a sleeping lion. The total mass of the stretcher and lion is 175 kg. The lion's forward acceleration is 2 m/s2. What is the force necessary to produce this acceleration?
Answer:
350 N
Explanation:
Newton's second law:
∑F = ma
∑F = (175 kg) (2 m/s²)
∑F = 350 N
The metric unit of power is _____.
Answer:
Watt
Explanation:
Power is defined as the work done by an object per unit time. Its mathematical form is given by :
[tex]P=\dfrac{W}{t}[/tex]
The SI unit of work done is Joules (J) and that of time is seconds (s).
J/s is equal to watts. Watt is the metric unit of power.
Calculate the average induced voltage between the tips of the wings of a Boeing 747 flying at 970 km/hr above East Lansing. The downward component of the earth's magnetic field at this place is
This question is incomplete, the complete question is;
Calculate the average induced voltage between the tips of the wings of a Boeing 747 flying at 970 km/hr above East Lansing. The downward component of the earth's magnetic field at this place is 0.7 × 10⁻⁴ T. (DATA: Assume that the wingspan is 60 meters.)
Answer:
the average induced voltage between the tips of the wings of a Boeing 747 flying is 1.132 Volts
Explanation:
Given that;
Speed S = 970 KM/hr
downward component of the earth's magnetic field B = 0.7 × 10⁻⁴
wingspan 1 = 60min
Velocity V = (970 × 10³) / 3600 = 269.44 m/s
So Average Induced Voltage E = VBI
we substitute
E = 269.44 × (0.7 × 10⁻⁴) × 60
E = 1.132 Volts
Therefore the average induced voltage between the tips of the wings of a Boeing 747 flying is 1.132 Volts
Morgan does 50 J of work with a lever
that has an efficiency of 92%. What is
the output work of the lever?
Answer:
46 J
Explanation:
Simply calculate the 92% of 50 Joules as:
0.92 * 50 J = 46 J
Hmmm... Who can answer this question?
How did life begin?
Just a practice
Answer:
The earliest known life-forms are putative fossilized microorganisms, found in hydrothermal vent precipitates, that may have lived as early as 4.28 Gya (billion years ago), relatively soon after the oceans formed 4.41 Gya, and not long after the formation of the Earth 4.54 Gya.
Explanation:
Is this what your looking for?
1.) There was an earthquake in Salt Lake City, Utah, on March 18, 2020, in the morning at 9 hours, 9 minutes, and 45 seconds Mountain Standard Time (9:9:45 MST). If the velocity of the p-wave is 7.3 km/sec and the velocity of the s-wave is 5.1 km/sec and the s-p time lag is 16 seconds, what is the distance in kilometers from Salt Lake City to the focus of the earthquake? Explain how you calculated the answer.
Answer:
7 because salt lake and Southis weat
A force of 1.50 N acts on a 0.20 kg trolley so as to accelerate it along an air track.
The track and force are horizontal and in line. How fast is the trolley going after acceleration from rest through 30 cm, if friction is negligible?
Answer: The trolley is moving at 2.12m/s
Explanation:
Given from the question that the track and force are horizontal and inline, we have that
F= ma
where F= force= 1.50 N
m= mass = 0.2kg
therefore Acceleration , a = F/ m= 1.50/0.2 =7.5 m/s^2
To find how fast the trolley is going ie the Velocity, v
Having that
initial velocity at rest , u = 0,
acceleration a = 7.5 and
and distance, s = 30 cm = 30/100 = 0.30 m
we use motion equation that
v² = u² + 2 a s
v² = 0² + 2 x 7.5 x 0.30
v² = 4.5
v = [tex]\sqrt{4.5}[/tex]
v = 2.12 m/s
from a flying aeroplane abody should be dropped in advance to hit the target why
From a flying plane a body should dropped in advance to hit the target,Why? ... The body should be dropped in advance as when the body is dropped it has the velocity of the plane. So, in air the body moves forward which we have to take into consideration in order to hit the target.
How much thermal energy (in kcal) is required to change a 43 g ice cube from a solid at - 16.5 oC to steam at 11.5 oC above boiling
Answer:
The total thermal energy required is 8.93 Kcal
Explanation:
Given;
mass of the ice cube, m = 43 g
specific heat capacity of water, Cp = 4.18 J/gc
specific latent heat of fusion of ice, Cf = 334 J/g
First step, determine the heat needed to raise the temperature of the ice from -16.5 °C to 0° C
Q₁ = mCp[0 - (-16.5)]
Q₁ = 43 x 4.18(16.5)
Q₁ = 2965.71 J
Second step, determine the latent heat of fusion of ice at 0°C
Q₂ = mCf
Q₂ = 43 x 334
Q₂ = 14362 J
Third step, determine the quantity of heat required to raise the temperature of the water initially at 0°C to above 11.5 °C of boiling point of water.
The final temperature of the water = 11.5 °C + 100° C = 111.5 °C
Q₃ = mCp Δθ
Q₃ = 43 x 4.18 (111.5 - 0)
Q₃ = 20041 J
Total thermal energy required = Q₁ + Q₂ + Q₃
Total thermal energy required = 2965.71 J + 14362 J + 20041 J
Total thermal energy required = 37,368.71 J
Total thermal energy required = 8.93 Kcal
C4. A 50.0 kg boy runs at 10.0 m/s, jumps on a cart and rolls off at 2.50 m/s. What is the mass of the cart
Answer:
The mass of the cart is 150 kg.
Explanation:
Given that,
Mass of a boy, m₁ = 50 kg
Initial speed of boy, u₁ = 10 m/s
Initial speed of car, u₂ = 0 (at rest)
The speed of the cart with the boy on it is 2.50 m/s, V = 2.5 m/s
Let m₂ is the mass of the cart. Using the conservation of momentum as follows :
[tex]m_1u_1+m_2u_2=(m_1+m_2)V\\\\50(10)+m_2(0)=(50+m_2)(2.5)\\\\500=125+2.5m_2\\\\375=2.5m_2\\\\m_2=150\ kg[/tex]
So, the mass of the cart is 150 kg.
Objects are lighter on the moon than they are on earth. if an object A weighs 25lbs on the Moon and another object B weighs 25 Newtons on earth, which has more mass?
a. Object a
b. Object b
c. Same mass
d. Other
Answer:
a. Object A
Explanation:
The mass of an object implies the quantity of matter in it, while the weight is the amount of gravitational force applied on an object.
The object A has a mass of 25 lbs, but object B on the earth has a weight, W, of 25 N.
So that,
For object A on the moon, mass = 25 lbs
For object B on the earth, W = 25 N,
W = m x g
25 = m x 10 (g = 10 m/[tex]s^{2}[/tex])
m = [tex]\frac{25}{10}[/tex]
= 2.5 lbs
Mass of object B is 2.5 lbs.
Therefore, the mass of the object A is more than that of B.
Fast and safe heart rate for workouts is called muscular strength? True or false
Answer:
False
Explanation:
Answer:
False
Explanation:
Hope this helped, Have a Wonderful Day/Night!!
If you jump upward with a speed of 1.70 m/s how high will you be when you stop rising?
Answer:
How long do you jump (sec) ?
Explanation: