The answer is yes because of conservation of momentum. That is, the momentum before collision is equal to the momentum after collision.
What is Momentum ?Momentum is the product of mass and velocity. It is a vector quantity. And it is measured in Kgm/s
If two vehicles have a head-on collision, the vehicles essentially stick together and travel a certain distance for 20 seconds before coming to a complete stop. The final velocity for both vehicles immediately after the crash can be obtain by using the formula
v = u - at
Where
v = final velocityu = initial velocitya = accelerationt = timeIf you are able to obtain the mass of both vehicles, the initial velocity for Vehicle A, and the final velocity for both vehicles immediately after the crash, then you can determine the momentum of both vehicles before the collision by calculating the momentum of both after the collision because momentum is always conserved.
Or by first calculating the initial velocity for vehicle B by using the formula below
[tex]M_{1}U_{1} - M_{2}U_{2} = (M_{1} + M_{2} )V[/tex]
where
M1 = mass of the first objectU1 = initial velocity of the first objectM2 = mass of the second objectU2 = initial velocity of the second objectV = common final velocityAfter we obtain initial velocity for vehicle B, we can calculate the momentum of both vehicles before the collision
Therefore, the momentum of both vehicles before the collision can be determined.
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A catapult launches a rock at a spy satellite 400 km above the earth. If it leaves the ground with an initial velocity of 367.0m/s [up] and an acceleration of 9.81m/s^2 [down]. The rock reaches its maximum height in 30.6s. Does the rock knock the spy satellite out of the sky?
The rock did not knock the spy satellite out of the sky. Detail below
How to determine the maximum heightTo determine whether the rock will knock out the spy satellite, we shall determine the maximum height reached by the rock. This is obatined as follow:
Initial velocity (u) = 367 m/sFinal velocity (v) = 0 m/s (at maximum height)Acceleration due to gravity (g) = 9.8 m/s²Maximum height (h) =?v² = u² - 2gh (since the ball is going against gravity)
0² = 367² - (2 × 9.8 × h)
0 = 134689 - 19.6h
Collect like terms
0 - 134689 = -19.6h
-134689 = -19.6h
Divide both side by -19.6
h = -134689 / -19.6
h = 6871.89 m
DIvide by 1000 to express in km
h = 6871.89 / 1000
h = 6.87 Km
From the calculation made, we can see that the maximum height reached by the rock is 6.87 Km
Thus, we can conclude that the rock did not knock out the spy satellite becaue the satellite is 400 Km above the ground.
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4. Many of the teachers think that if a student sleeps more on the night before the test, then they
will score higher on the test. This is a(n).
a. theory
b. law
c. inference
d. hypothesis
Answer:
a sleep doesnt get to depict whether you get a good grade or not its what you know.
1. How did you decide whether a substance was a pure substance or a mixture? An element or a compound? A heterogeneous mixture or homogenous mixture? Describe your thought process!
Following are the differences between substance and mixture
A material is said to be pure if it just contains that substance and cannot be broken down into any other components. It is possible to separate a mixture into two or more pure substances. Pure substances have distinct physical and chemical properties, whereas mixtures have various qualities depending on the pure substance amounts and placement within each mixture.
Pure substances might be molecules made up of two or more different elements, or they can be elements composed solely of one type of atom. Depending on how thoroughly the components are combined, mixtures can either be homogeneous or heterogeneous.
Following are the differences between element and compound
Compounds are chemical unions of two or more elements and can potentially be pure substances, whereas elements are invariably pure things. Real-world substances, such as elements and compounds, are rarely pure because they are frequently tainted during manufacturing, storage, or by their environment. In theory, pure denotes the absence of any discernible imperfections. The majority of the time, it is achievable to purify substances to that standard, albeit it frequently necessitates a lot of work.
Following are the differences between heterogeneous and homogeneous mixtures.
Mixtures can be physically separated since they contain multiple types of atoms and molecules. When a combination is homogenous, the particles are so small that the entire mixture appears to be formed of the same substance. When a mixture is heterogeneous, the qualities of the mixture vary depending on which section of the mixture is being analyzed. Typical homogeneous mixtures include solutions. For instance, a salt-water solution is a homogenous combination since it is possible to separate the water and salt using distillation to create pure water and crystalline salt.
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If a pressure of 5Pa is exerted on an area of 15m2, what is the force?
The force required if a pressure of 5Pa is exerted on an area of 15m² is 75N.
How to calculate force?Pressure is a force applied to a surface. It is measured in Pascals denotes by Pa. It can also be defined as the physical force exerted on an object.
The force applied is perpendicular to the surface of objects per unit area. The formula for calculating pressure is as follows:
Pressure = Force ÷ Area
According to this question, the pressure of 5Pa is exerted on an area of 15m². The force required is as follows:
Force = 5Pa × 15m²
Force = 75N
Therefore, the force required is 75N
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Fill in the data tables constant=10 HELP!!!
just substitute whatever number is in the x column for x in the equation, then whatever you get from that equation is the y value
Calculate the current in the 3.0 Ω resistor in the figure above when the current in the 9.0 Ω resistor is 2.4A
The current in the 3.0 Ω resistor is mathematically given as
I_X=1.8A
This is further explained below.
What is current?The proportion of individual resistance to the overall resistance is the same as the current flowing through a branch to the current flowing through the whole system.
When the total current in a parallel circuit is already known, a shortcut approach for finding the branch currents in the circuit may be found via the use of a formula called the current divider formula.
In series circuits, the voltage drops across each resistor, but the current stays the same.
This is analogous to what happens in parallel circuits when the current splits between two branches.
The following diagram illustrates how the entire voltage is distributed across each resistor while maintaining the same amount of current throughout. Ohm's law states that V = I*R.
current dividers ruleis used when current is divided in parallel, such as it is in this case so we employ the current dividers rule as follows
Generally, the equation for current dividers rule is mathematically given as
[tex]I_X=\frac{R_T}{R_X+R_T} I_T[/tex]
where,
I_X = current
R_X = resistor
R_T = total resistance
I_T = sum of the current flowing into a network where R _X is connected in parallel with R_T
Therefore
[tex]I_X=\frac{9}{3+9} 2.4[/tex]
I_X=1.8A
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a magnetic field has a magnitude of , and an electric field has a magnitude of . both fields point in the same direction. a positive charge moves at a speed of in a direction that is perpendicular to both fields. determine the magnitude of the net force that acts on the charge
The magnitude of the net force that acts on the charge is 1.1 x 10^(-2).
What are magnetic and electric forces and how are they calculated?
The Lorentz Force Law, and specifically the magnetic force on a moving charge, is used to define the magnetic field B: F = q (v * B).
The magnetic field B and the charge q's velocity v are both perpendicular to the force.
F = q(v*BsinФ), where Ф is the angle less than 180° between the velocity and the magnetic field, gives the force's magnitude. This suggests that there is no magnetic force acting on a charge that is stationary or travelling perpendicular to the magnetic field.
The right hand rule specifies the force's direction. The aforementioned force relationship takes the shape of a vector product.
Even when they are not in contact, charged particles can nevertheless attract or repel one another. Electric fields are said to be created by charged particles. Additionally, the probes that find an electric field are charged particles. Charged particles experience force from an electric field. The strength of the electric field E that a charged particle at a place P creates is the amount of positive electric force that particle applies to another charged particle at that same position. The force acting on a positive charge is exerted in the direction of the electric field. F = q*E gives the real force acting on a particle with charge q. In the case of a negative charge, it points away from the electric field E.
Let F₁ denote the magnetic field and F₂ denote the electric field.
Since F₁ is perpendicular to F₂, we can use Pythagorian theorem to find the magnitude of the net force(F) by using F = √(F₁² + F₂²)
Therefore, F₁ = qvBsin(90°) = qvB = (1.8 * 3.1 * 1.2)/10³ = 6.70/10³ N
Again, F₂ = q*E = (1.8 * 4.6)/10³ = 8.28/10³ N
Thus, magnitude of the net force = F = √(F₁² + F₂²) = √[(6.70/10³)² + (8.28/10³)²] = 1.1 x 10^(-2) N (approx).
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When you are moving at a
moving at a high rate of speed, inertia makes it hard to stop
True
False
Answer:
the tendency of an object to resists a change in motion depends on its mass. if the net force acting on an above zero, its inertia is also zero.
when you are moving at a high rate of speed, inertia makes it hard to stop . newton's first law of motion applies only to objects that are already moving.
Explanation:
the answer would be TRUE
PLEASE MARK AS BRAINLIEST
Answer:
True
Explanation:
An object thats in motion will stay in motion with the same direction and speed unless an unbalanced force acts upon it. This means that when moving at a high rate of speed, its hard to stop unless you come in contact with an unbalanced force.
Result A 90 kg astronaut, initially at rest, throws a 5 kg oxygen tank at 1 m/s away from himself. What is the new speed and direction of the astronaut?
A 90 kg astronaut, initially at rest, throws a 5 kg oxygen tank at 1 m/s away from himself. The new speed for astronauts is 0.055 meters per second, and they will go in the opposite direction of the thing they are chasing.
This is further explained below.
What is the law of conservation of momentum?Generally, For this, use the law of conservation of momentum
Total final momentum = Total final momentum
P_{a i}+P_{0 i}=P_{a f}+P_{o f}
m_{a v_{a i}}+m_0 v_{o i}=m_{a v_{a f}}+m_0 v_af
0+0=90 v_{a f}+5 *1
90 v_{a f}=-5 a
[tex]v_{a f}=-\frac{5}{90} \mathrm{~m} / \mathrm{sec} \\\\v_{a f}=-0.055 \mathrm{~m} / \mathrm{sec}[/tex]
In conclusion, The new speed of astronauts is 0.055m/second and astronauts will move in the opposite direction of the object.
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an electric dipole is formed from two charges, ±q, spaced 0.700 cm apart. the dipole is at the origin, oriented along the y-axis. the electric field strength at the point (x,y)
In the given electric dipole, the charge q = 0.2 C and the electric field strength at the point (x,y) = (10 cm, 0 cm) N/C is E = 138.37 10⁹ N/C.
What is electric dipole?
Any electromagnetic system has an electric dipole separating the positive and negative charges. A simple illustration of this system is a pair of opposite-sign, equal-sized electric charges that are separated from one another by a relatively short distance. (A permanent electric dipole is known as an electret.)
a) Let's calculate the field for each of the both charge at the point y = 10 cm, x=0 or in the dipole line, for that we calculate the field that creates each charge and add them vectorially
For the Charge 1
y₁ = (0.1 - 0.035) = 0.065 m
(Electric field) E1 = k q / y₁²
E1 = 8.99 10 9 q / 0.065²
E1 = 2127.8 q
For the Charge 2
y₂ = (0.1 - (-0.035) = 0.135 m
(Electric field) E2 = k (-q) / y₂²
E2 = 8.99 109 q / 0.135²
E2 = - 493.3 q
In an electric dipole the value of the two charges is of equal magnitude, but otherwise, suppose the positive charge is the highest
Et = E1 -E2
Et = 2127.8q -493.3q
330 = q (2127.8 -493.3)
q = 330 / 1634.5
q = 0.2 C
Now let the negative charge is higher
Et = (-2127.8 +493.3) q
330 = -1634.5 q
q = -0.2 C
b) calculate the field for the point x = 0.1 m y = 0 m
This is a point perpendicular to the midpoint of the dipole, so that we can use the dipole equation
E = k 2qa / √(x² + a²)³
E = 8.99 10⁹ 2 0.2 0.07 / √(0.1² + 0.07²)³
E = 0.2517 10⁹ / (0.001819)
E = 138.37 10⁹ N/C
Therefore, the charge q is 0.2 C and electric field E is 138.37 10⁹ N/C.
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Complete Question
An electric dipole is formed from two charges, ±q, spaced 0.700 cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point (x,y)=(0cm,10cm) is 330 N/C . What is the charge q? Give your answer in nC what is the electric field strength at the point (x,y) = (10 cm, 0 cm) N/C = ?
What is the area of a box which weighs 95N exerting a pressure of 43Pa?
The area of the ball that weighs 95 N and exerting a pressure of 43 Pa is 1.51 m².
What is area?Area can be defined as the region bounded by a plane shape.
To calculate the area of the ball, we use the formula below.
Formula:
P = F/A.......... Equation 1Where
P = PressureF = Force/WeightA = AreaMake A the subject of the equation
A = F/P.......... Equation 2Froim the question,
Given:
F = 95 NP = 43 PaSubstitute these values into equation 2
A = 95/63A = 1.51 m²Hence, the area of the ball that weighs 95 N and exerting a pressure of 43 Pa is 1.51 m².
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We need to find the launch velocity of our new marble launcher. we know that it will launch a 25g marble to a distance of 73 cm, causing an impact noise of 44 decibels. the marble will then roll up to 6.2 meters befor stopping. with a launch height of 20 cm and a classroom temperature of 15.8 degrees celsius, we can calculate the launch velocity of the marble launcher to be
The launch velocity of the marble launcher is 34.65 m/s
Given that the launch velocity of marble launcher, launches a 25g marble to a distance of 73 cm (0.73 m) and the marble roll up to 6.2 meters before stopping. The launch height is 20 cm (0.2 m).
The time for landing can be calculated by the second equation of motion formula:
h = ut + [tex]\frac{1}{2}[/tex]g[tex]t^{2}[/tex]
Let u = 0
0.2 = 0×t + [tex]\frac{1}{2}[/tex] × 9.8 × [tex]t^{2}[/tex]
[tex]t^{2}[/tex] = [tex]\frac{0.2}{4.9}[/tex]
[tex]t^{2}[/tex] = 0.04
t = 0.2s
Now, the launch velocity of the marble launcher can be calculated by:
Speed = Distance / Time
Speed = [tex]\frac{0.73 + 6.3}{0.2}[/tex]
Speed = [tex]\frac{6.93}{0.2}[/tex]
Speed = 34.65 m/s
Therefore, the launch velocity of the marble launcher is 34.65 m/s
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PLEASE HELP!!!!
It’s due tmr and i dont know how to do this
The magnitude of the gravitational field strength is 2.76 * 10^-18 N/Kg.
What is the gravitational force?The gravitational force is the force that acts on an object that is found in the earth's gravitational field. Let us recall that if an object is thrown up, the object must surely and definitely come down. This is because, there is a force of gravity that is acting on the object on the earth gravitational filed and that the direction of this force as it were is always towards the center of the earth.
In this case we are asked by the question that we ought to be able to obtain the gravitational field strength of the Hubble telescope as we have in the question and this we want to do.
Hence;
g = Gm/r^2
G = gravitational constant
m = mass of the object
r = distance covered
g = 6.67 * 10^-11 * 1.3 * 10^4/(5.6 * 10^5)^2
g = 2.76 * 10^-18 N/Kg
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what is the thickness of the central portion of a thin conveying lens can be determined very accurately by using (a) vernier calliper (b) micro meter screw guage (c) telescope ( d) microscope
Option B The thickness of the central portion of a thin conveying lens can be determined very accurately by using a micrometer screw gauge.
What can be measured using a micrometer screw gauge?One micrometer of thickness can be measured with a micron micrometre screw gauge. A Use of Micrometer Screw Gauge as like example Upon turning the screw of the micrometer screw gauge four times, a 2 mm space is covered.
What purposes does a micrometer serve?A tool known as a micrometer is used to measure solid objects’ lengths, thicknesses, and other dimensions precisely and linearly.
What is the micrometer screw gauge’s SI unit?The SI symbol m is also known as a micron, which is an SI-derived unit of length equaling 1106 meters, where 106 is the SI standard prefix for the prefix “micro-.” A micrometer is one-millionth of a meter.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Which of the following is a physical property of sodium?
A. Melting point
B. Combustibility
C. Molecular structure
D. Reactivity
Answer:
melting point (a)
Explanation:
A car must be driven a distance of 120 km in 2.5 h. During the first 1.5 h, the average speed was 70 km/h. Calculate the average speed for the remainder of the journey.
The average speed for the remainder of the journey of the car which covers a distance of 120 km in 2.5 h is 15 km / h
v = d / t
v = Average velocity
d = Distance
t = Time
During the first 1.5 h,
v = 70 km / h
d = v * t
d = 70 * 1.5
d = 105 km
During the remainder of the journey,
d = 120 - 105
d = 15 km
t = 2.5 - 1.5
t = 1 hr
v = 15 / 1
v = 15 km / h
Therefore, the average speed for the remainder of the journey is 15 km / h
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i need help please hanks
Increasing human population have advanced the problem of the impact of humans on the environment as shown above.
How does population affect the environment?We know that the environment has to do with our natural surroundings. The environment has to do with that space that is around us from which we obtain the materials and energy that are necessary to support life.
We know that the greatest pressure that is placed on the environment and the resources that is in it comes from anthropogenic activities. These are the activities of the people that live within the environment. The extraction of resources for the provision of energy as well as construction pts great pressure on the environment
As we look at the image, we call to mind that the the explosions in the population of human beings have put more pressure on the environment and thus made it unable to support the human population.
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What are four things that a electromagnet and a generator does
Answer:
can be used to generate a magnetic effect ( magnetic field ) or magnetism can be generated by electricity , There is a relation between magnetism and electricity , where electric current has a magnetic effect , while magnet generates an electric current .The electromagnet is used in factories to move ( lift ) the heavy iron blocks as it is used for making big-sized winch ( crane ) .The electromagnet is used in making many appliances ( devices ) as the electric bell , the electric mixer , the disc drive and the television .The electromagnet is used in factories to move ( lift ) the heavy iron blocks as it is used for making big-sized winch ( crane ) .The electromagnet is used in making many appliances ( devices ) as the electric bell , the electric mixer , the disc drive and the television .
Explanation:
Error Analysis On a math test the students are given a right triangle. One of the acute angles has a measure of 33". One student says that the measure of the other acute angle is 147". What is the
measure of the other acute angle? What error might the student have made?
The measure of the other acute angle is
Error might the student have made was in angle 147 as acute angle means angle less than 57°.
What is an acute angle?An acute angle is any angle that is more than 0° and less than 90°.
Briefing:1st angle = 33 °
That sum of acute angles of a triangle should be less than 90°.
Let's assume other angle be x.
So ;
x + 33° < 90°
x <90° - 33°
x < 57°
The student had measured ∠2 wrongly because sum of acute angles of a triangle should be less than 90°.
The correct measure of other angle should be less than 57°.
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What is the minimum wave amplitude amin such that the ant will become momentarily weightless at some point as the wave passes underneath it? assume that the mass of the ant is too small to have any effect on the wave propagation.
The minimum amplitude of the wave is equal to [tex]\frac{g \mu}{T_{\mathrm{s}}}\left(\frac{\lambda}{2 \pi}\right)^2[/tex]
What are the many kinds of wave propagation?A type of radio propagation known as a surface wave is known as ground wave propagation. Low and medium frequency versions of these waves travel across the surface of the earth. Mostly, these are employed for transmission between the earth's surface and the ionosphere. The quantity of individual waves makes up these.
The expression for the velocity of the wave is as follows:
[tex]v=\sqrt{\frac{T_s}{\mu}}[/tex]
Here,
Ts is the tension and
μ is the mass per unit length.
The expression for the wave vector is as follows:
[tex]k=\frac{2 \pi}{\lambda}[/tex]
λ is the wavelength of the wave.
The expression for the angular frequency is as follows:
ω = v k
Here, v is the velocity of the wave.
The expression for the minimum amplitude is as follows:
[tex]A=\frac{g}{\omega^2}[/tex]
Here, g is the acceleration due to gravity.
putting the values of v and k in w
[tex]\begin{aligned}&\omega=v k \\&\omega=\left(\sqrt{\frac{T_s}{\mu}}\right)\left(\frac{2 \pi}{\lambda}\right)\end{aligned}[/tex]
[tex]\begin{aligned}A=& \frac{g}{\omega^2} \\A=& \frac{g}{\left(\left(\sqrt{\frac{T_s}{\mu}}\right)\left(\frac{2 \pi}{\lambda}\right)\right)^2} \\&=\frac{g}{\frac{T_s}{\mu}\left(\frac{2 \pi}{\lambda}\right)^2} \\&=\frac{g \mu}{T_s}\left(\frac{\lambda}{2 \pi}\right)^2\end{aligned}[/tex]
The minimum amplitude of the wave is equal to [tex]\frac{g \mu}{T_{\mathrm{s}}}\left(\frac{\lambda}{2 \pi}\right)^2[/tex]
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As ____ is added to the ice cube from a flame, the thermal ______ will change to ______ energy, which causes the ice molecules to move faster. The faster moving molecules will vibrate against each other.
calculate the distance and displacement in 0-10sec from velocity time graph shown above
The total distance covered is 100m and displacement is 60m
The area under curve(a1)=1/2×b×h
=1/2×6×20
=60m
The area under curve(a2)=1/2×b×h
=1/2×2×10
=20m
The area under curve(a3)=l×b
=2×10
20m
∴The total distance covered=a1+a2+a3
=(60+20+20)m
=100m
∴The displacement=a1-a2+a3
=(60-20+20)m
=60m
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Krusty Krabs Breath Mints Mr. Krabs created a secret ingredient for a breath mint that he thinks will “cure” the bad breath people get from eating crabby patties at the Krusty Krab. He asked 100 customers with a history of bad breath to try his new breath mint. He had fifty customers (Group A) eat a breath mint after they finished eating a crabby patty. The other fifty (Group B) also received a breath mint after they finished the sandwich, however, it was just a regular breath mint and did not have the secret ingredient. Both groups were told that they were getting the breath mint that would cure their bad breath. Two hours after eating the crabby patties, thirty customers in Group A and ten customers in Group B reported having better breath than they normally had after eating crabby patties.
1. Which people are in the control group?
2. What is the independent variable?
3. What is the dependent variable?
4. What should Mr. Krabs’ conclusion be?
5. Why do you think 10 people in group B reported fresher breath?
1) The control group are the people that are in group B
2) The independent variable is the administration of the breath mint
3) The dependent variable is the breath of the participants
4) The conclusion of Mr Krab should be that the breath mint is effective in treating bad breath.
5) 10 people in group B reported fresher breath because they thought that they got the breath mint.
What is an experiment?The term experiment is used to describe the way tat we could be able to spot the relationship between the dependent and the independent variable. Let us note that the independent variable is the variable that we have to manipulate in the course of an experiment while the dependent variable is the variable that would change as we change the independent variable.
We can see that there was a sort of improvement of the breath of the customers which according to the hypothesis of the experiment would be attributable to the new formula of the breath mint.
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A warehouse worker moves a box of equip-ment weighing 250 N onto the top of a sheif that is 15 m high. How much work did he do?
Answer:
work = force x displacement
force = 250N
displacement = 15m
work = 250 x 15
work = 3750J
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an object of mass m is lifted at constant velocity a vertical distance h in time t. the power supplied by the lifting force is (a) mght (b) mgh/t (c) mg/ht (d) mgt/h (e) zero
Option (b) mgh/t will be the power supplied by the lifting force.
What does Newton's first law of motion state?
According to Newton's first law of motion, if a body is at rest or moving in a straight line at a constant speed, it will continue to move at that speed or remain at rest until acted on by a force.
How are formulas of power and force interlinked?
F = mg is the formula for force where,
F = force required
m = mass of the object
g = gravitational constant
and P=Fd/t is the formula for power where,
P= power
F=force
d= distance
and t= time
Substituting the value F=mg, in P=Fd/t we get,
P=mgd/t or P=mgh/t
Hence, we can conclude,
F = mg is the equation that expresses the force required to raise an item at a constant speed. P = Fd/t = mgh/t is then used to calculate the power.
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Stephen learned that any two objects exert a gravitational force on each other. If the distance between two objects triples, the gravitational force between them will change by a factor of what?.
The gravitational force between them will change by a factor 1/9.
We need to know about gravitational force to solve this problem. The gravitational force is the force caused by two masses objects. The magnitude of gravitational force can be determined as
F = G.m1.m2 / R²
where F is the gravitational force, G is the gravitational constant (6.674 × 10¯¹¹ Nm²/kg²), m1 and m2 are the mass of the object and R is the radius.
From the question above, we know that
R2 = 3R1
By substituting the following parameters, we get
F2/F1 = G.m1.m2 / R2² / G.m1.m2 / R1²
F2/F1 = G.m1.m2 / (3R1)² / G.m1.m2 / R1²
F2/F1 = 1/9
Hence, the gravitational force between them will change by a factor 1/9.
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How much does the force of gravity change between two objects if their masses remain the same but their distance of separation doubles?
The force of gravity will become one fourth of the original force when the masses of the objects remain the same but their distance of separation doubles.
Force of gravity is an attraction force which holds the object towards the ground surface.
The gravitational force depends directly on the masses of two objects and indirectly on the square of the distance between them.
This means that the gravitational force increases with mass but decreases with increasing distance between objects.Mathematically, [tex]F = \frac{Gm1m2}{r^{2} }[/tex]Let
m₁ and m₂ be the two different masses
r₁ be the initial distance between the the two masses
r₂ be the distance when their separation doubles.
i.e. r₂ = 2r₁
So, according to the formula,
F₁ = [tex]\frac{Gm1m2}{r1^{2} }[/tex]
F₂ = [tex]\frac{Gm1m2}{r2^{2} }[/tex]
since masses are same:
[tex]\frac{F1}{F2} = \frac{r2^{2} }{r1^{2} }[/tex]
[tex]\frac{F1}{F2} = \frac{4r1}{r1}[/tex]
F₁ = 4F₂
F₂ = [tex]\frac{1}{4}[/tex]F₁
The resultant force is one fourth of the original force.
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A pot plant falls off the balcony of an apartment. The balcony is 20 m above the ground and the pot plant has a mass of 2 kg. After falling a distance of 2 m from the balcony, the pot plant has a velocity of 6,26 m·s-1 . Ignore the effect of air resistance. 5.1
Calculate the gravitational potential energy of the pot plant before it begins to fall. 5.2 Calculate the total mechanical energy of the pot plant after it has fallen two meters. 5.3 Is this a closed system?
Explain your answer. 5.4 Calculate the speed with which the pot plant hits the ground.
The gravitational potential energy of the pot plant before it begins to fall is 392 J.
The total mechanical energy of the pot plant after it has fallen two meters is 78.39 J.
The speed with which the pot plant hits the ground is 19.8 m/s.
What is the gravitational potential energy?
The gravitational potential energy of the pot plant before it begins to fall is calculated as follows;
P.E = mgh
where;
m is mass of the potg is acceleration due to gravityh is height of the initial height of the potP.E = (2 kg) (9.8 m/s²) (20)
P.E = 392 J
The total mechanical energy of the pot plant after it has fallen two meters is calculated as follows.
M.E = K.E + P.E
where;
K.E is kinetic energyP.E is potential energyM.E = ¹/₂mv² + mgh
M.E = ¹/₂(2 kg)(6.26 m/s)² + (2 kg)(9.8 m/s²)(2 m)
M.E = 78.39 J
The speed with which the pot plant hits the ground is calculated by applying the principle of conservation of energy as follows;
K.E(bottom) = P.E(up)
¹/₂mv² = mgh
v² = 2gh
v = √2gh
where;
h is the initial height of the potv = √(2 x 9.8 x 20)
v = 19.8 m/s
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at a certain point on a heated metal plate, the greatest rate of temperature increase, 6 degrees celsius per meter, is toward the northeast. if an object at this point moves directly north, at what rate is the temperature increasing?
tempreture
√12 is degrees Celsius per meter.
What is tempreture?
tempreture is the degree of hotness or coldness of any kind of objects.
Sol-
The highest rate of tempreture increase is given as 6degrees as per the question
Imagine this high rate as a diagonal vector pointing in the northeast direction.
This vector has an x component (horizontal, or east) and a y component (vertical, or north).
The highest rate (maximum) is found as the magnitude of these two components.
It is the square root of (x^2)+(y^2).
6= √((x^2)+(y^2))
-> Take the square of both sides to remove the square root on the right side of the equation.
36 = (x^2)+(y^2)
-->The x^2 and y^2 values each must equal 8 in order to get: 12
(x^2) = 12
x = √12
(y^2) = 12
y = √12
If the object moves directly north, it is therefore moving only in the y-direction.
Thus, it is increasing tempreture at a rate of √12 degrees Celsius per meter.
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The 2012 Mia Electric Car has one of the slowest accelerations of all cars, taking
30.0s to accelerate from 0 mi/hr to 60.0 mi/hr. How long does the on ramp to the 1-25 need to be to allow the Mia to accelerate to 80.0 mi/hr before merging onto the
highway south of town? Give your answer in feet.
The time taken for the car to accelerate to the given speed is 10 seconds.
What is the acceleration of the car?
The acceleration of the car is the change in the velocity of the car with time.
a = Δv/Δt
where;
Δv is change in velocity of the carΔt is change in time of motion of the carThe initial velocity of the car = 0 mi/hr = 0 m/s
The final velocity of the car = 60 mi/hr = 26.82 m/s
The acceleration of the electric car = (26.82 m/s - 0 m/s) / 30 s = 0.89 m/s²
When the final velocity of the car = 80 mi/hr = 35.76 m/s, the time taken to reach the speed is calculated as follows;
v = u + at
where;
v is the final velocity of the caru is the initial velocityt is time of motiona is accelerationt = (v - u)/a
t = (35.76 - 26.82) / 0.89
t = 10 s
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