Calcule la magnitud del área de un triángulo cuyos lados están dados por los vectores A, B y A+B. Donde el vector A= 3i+10j-k y B= -i+2j+11k
Answers
The vectors A and B span a parallelogram. The area of this parallelogram is equal to the magnitude of the cross product, A × B. Cut this area in half and you get the area of the triangle of interest.
Recall that for any two vectors x and y, we have
||x × y|| = ||x|| ||y|| sin(θ)
where θ is the angle between the two vectors; also, recall that
x • y = ||x|| ||y|| cos(θ)
Use the dot-product identity to find the angle between A and B. Compute the dot product and magnitudes:
A • B = (3i + 10j - k) • (-i + 2j + 11k) = -3 + 20 - 11 = 6
||A|| = √(3² + 10² + (-1)²) = √110
||B|| = √((-1)² + 2² + 11²) = √126 = 3√14
Solve for the angle:
cos(θ) = 6/(√110 • 3√14) = 1/√385
θ = arccos(1/√385)
Now using the cross-product identity, we have
||A × B|| = √110 • 3√14 sin(arccos(1/√385)) = 3√1540 • √(384/385) = 48√6
and this is the area of the parallelogram. The area of the triangle in question is half of this, 24√6.
Alternatively, you can compute the cross product directly.
Recall that for any two vectors x and y,
x × x = 0
x × y = - (y × x)
and that the cross product is defined by the following rules:
i × j = k
j × k = i
k × i = j
Then the cross product is
A × B = (3i + 10j - k) × (-i + 2j + 11k)
A × B = -3 (i × i) - 10 (j × i) + (k × i)
… … … … … + 6 (i × j) + 20 (j × j) - 2 (k × j)
… … … … … + 33 (i × k) + 110 (j × k) - 11 (k × k)
A × B = 10k + j + 6k + 2i - 33j + 110i
A × B = 112i - 32j + 16k
Compute its magnitude:
||A × B|| = √(112² + (-32)² + 16²) = √288 = 48√6
and cut it in half to get the area of the triangle; again, you end up with 24√6.
Related Questions
Which statement best describes the major disadvantage of geothermal energy?
a) The heat in Earth's mantle is neither consistent nor reliable.
b) This type of energy can only be harnessed in specific locations.
c) Earthquakes occur wherever geothermal energy is mined.
d) Energy outputs from this type of plant are hard to predict.
Answers
The statement that best describes the major disadvantage of geothermal energy is:
b) This type of energy can only be harnessed in specific locations.
Geothermal energy is a renewable and sustainable source of power that utilizes the heat from the Earth's core to generate electricity. Geothermal energy relies on accessing the heat from the Earth's mantle, which is most easily done in areas with high volcanic activity or geothermal hotspots.
This limitation means that geothermal energy cannot be utilized everywhere, making it less widespread compared to other renewable energy sources. Geothermal energy requires specific geological conditions, such as the presence of hot rocks or water reservoirs near the Earth's surface, which limit its availability to certain areas.
Additionally, drilling and mining activities associated with geothermal energy can cause minor seismic activity, although this is usually not a significant problem. Despite these limitations, geothermal energy is an important alternative to fossil fuels and can provide a reliable source of clean energy for areas that have access to it.
So, the correct statement here is b) This type of energy can only be harnessed in specific locations.
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. A man of mass 80 kg stands in a lift, what is the reaction from the floor of the lift if the lift;A. moves upwards with steady speed. moves upwards with acceleration 0.5m/sC. moves downward with acceleration 0.4m/s(g - 9.8m/s')
Answers
The reaction of the floor is as follows:
R = 784 NR = 816 NWhat is the reaction from the floor for a man in a lift?The reaction of the floor on the man is equal to the weight of the man and the upward force.
Reaction, R = mg + maA) When the lift moves upwards with steady speed.
R = 80 * 9.8 + * 80 * 0
R = 784 N
B) When the lift moves upwards with acceleration 0.4m/s
R = 80 * 9.8 + * 80 * 0.4
R = 816 N
In conclusion, the reaction of the floor changes as the body accelerates upwards.
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The percent of body weight composed of fat co.pared to the percent that is composed of tissue, bone and muscle is know as what?
A. Body composition
B. Muscular Endurance
C. Flexibility
D. Max heart rate
Answers
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Answers
Answer:
Two lasers are shining on a double slit, with slit separation d. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patterns on a screen a distance 4.60 mm away from the slits.
A) Which laser has its first maximum closer to the central maximum?
B) What is the distance between the first maxima (on the same side of the central maximum) of the two patterns?
Answers
Answer:
A. Laser 1 has its first maximum closer to the central maximum.
B. 0.077 mm
Explanation:
A) Which laser has its first maximum closer to the central maximum?
Since for a double slit interference, sinθ = mλ/d where θ is the angle between the central axis and the maximum point, m = order of fringe, λ = wavelength of light and d = width of slit.
Also tanθ = y/D where θ is the angle between the central axis and the maximum point, y = distance between maximum point and central axis and D = distance between slit and screen = 4.60 mm.
Since θ is small, sinθ ≅ θ and tanθ ≅ θ
So, sinθ ≅ tanθ
mλ/d = y/D
So, y = mλD/d for the first maximum, m = 1.
So, y = (1)λD/d
y = λD/d
For the Laser 1, λ = d/20
So, y = λD/d
y = (d/20)D/d
y = D/20
y = 4.60 mm/20
y = 0.23 mm
For the Laser 2, λ' = d/15
So, y' = λ'D/d
y' = (d/15)D/d
y' = D/15
y' = 4.60 mm/15
y' = 0.307 mm
Since y = 0.23 mm < y' = 0.307 mm, Laser 1 has its first maximum closer to the central maximum.
B) What is the distance between the first maxima (on the same side of the central maximum) of the two patterns?
The distance between the first maxima (on the same side of the central maximum) of the two patterns is Δy = y' - y = 0.307 mm - 0.23 mm = 0.077 mm
imagine two like charges in close contact. if one of the charges becomes oppositely charged, what happens to the electrostatic force?
Answers
If one of the charges becomes oppositely charged, the electrostatic force between the charges will change from a repulsive force to an attractive force.
This change occurs because opposite charges attract each other, while like charges repel each other. When one of the charges becomes oppositely charged, the electrostatic force between the charges changes direction and becomes attractive.
The strength of the electrostatic force between the charges will depend on the magnitude of the charges and the distance between them.
It is important to note that when one of the charges becomes oppositely charged, the net charge of the system may be different than before. If the charges have equal magnitudes before the change, the net charge of the system will be zero.
However, if one of the charges has a greater magnitude, the net charge of the system will be nonzero, and the electrostatic force between the charges may be stronger or weaker than before depending on the new net charge.
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A wire of radius 6mm and length 400 is melted into a sphere, calculate the radius of the sphere in centimeters
Answers
The radius of the sphere in centimeters is 50 cm
The wire has a certain volume that can be calculated as follows:
V_wire = πr²l
where r is the radius of the wire and l is its length.
If the wire is melted and formed into a sphere, it will still have the same volume as before, which can now be expressed as:
V_sphere = (4/3)πr³
where r is the radius of the sphere.
Since the wire and the sphere have the same volume, we can equate the two expressions for volume:
πr²l = (4/3)πr³
Simplifying this equation by dividing both sides by πr² and then multiplying both sides by 3/4, we get:
r = (3/4)l/r
Substituting the given values, we get:
r = (3/4)(0.4 m)/(0.006 m) ≈ 50 cm
Therefore, the radius of the sphere is approximately 50 centimeters.
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a converging lens with a focal length of 60 cm and a diverging lens with a focal length of -44 cm are 284 cm apart. a 3.7-cm-tall object is 80 cm in front of the converging lens.
Answers
To determine the final position and size of the image formed by the combination of the converging and diverging lenses, we can use the lens formula and the lens-maker's formula. Here are the steps to solve the problem:
Determine the position and size of the image formed by the converging lens:
Given: Focal length of the converging lens (f₁) = 60 cm
Object height (h₁) = 3.7 cm
Object distance (u₁) = -80 cm (negative sign indicates the object is in front of the lens)
Using the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Substituting the given values:
1/60 = 1/v - 1/(-80)
Solving for v₁, the image distance formed by the converging lens:
1/v₁ = 1/60 - 1/80
1/v₁ = (4 - 3)/240
1/v₁ = 1/240
v₁ = 240 cm
The image distance (v₁) is positive, indicating that the image formed by the converging lens is real and on the opposite side of the lens from the object.
To determine the magnification (M₁) of the converging lens, we can use the formula: M₁ = -v₁/u₁
M₁ = -240/(-80)
M₁ = 3
The magnification (M₁) is positive, indicating that the image formed by the converging lens is upright.
Determine the position and size of the image formed by the diverging lens:
Given:
Focal length of the diverging lens (f₂) = -44 cm
Object distance (u₂) = 240 cm (distance between the two lenses)
Using the lens formula for the diverging lens:
1/f = 1/v - 1/u
Substituting the given values:
1/-44 = 1/v₂ - 1/240
Solving for v₂, the image distance formed by the diverging lens:
1/v₂ = -1/44 + 1/240
1/v₂ = (-6 + 1)/240
1/v₂ = -5/240
v₂ = -48 cm
The image distance (v₂) is negative, indicating that the image formed by the diverging lens is virtual and on the same side of the lens as the object.
To determine the magnification (M₂) of the diverging lens, we can use the formula: M₂ = -v₂/u₂
M₂ = -(-48)/240
M₂ = 1/5
The magnification (M₂) is positive, indicating that the image formed by the diverging lens is upright.
Determine the final position and size of the combined image:
To find the final position of the combined image, we add the image distances of the converging and diverging lenses:
v = v₁ + v₂
v = 240 + (-48)
v = 192 cm
To find the magnification of the combined lenses, we multiply the magnifications of the individual lenses:
M = M₁ * M₂
M = 3 * 1/5
M = 3/5
The final image distance (v) is positive, indicating that the combined
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What is the function of the Integumentary System?
Answers
Answer:
The skin and accessory structures perform a variety of essential functions, such as protecting the body from invasion by microorganisms, chemicals, and other environmental factors; preventing dehydration; acting as a sensory organ; modulating body temperature and electrolyte balance; and synthesizing vitamin D.
Explanation:
Ray has two metal bars. He knows metal bar 1 is a magnet. How could he use metal bar 1 to find out if metal bar 2 is a magnet?
Answers
Ray could use metal bar 1 in a variety of ways to detect if metal bar 2 is a magnet.
Detecting a magnet with a magnetRay can use metal bar 1 (the magnet) to find out if metal bar 2 is also a magnet by performing the following steps:
Hold metal bar 1 near one end of metal bar 2 without touching it.Slowly move metal bar 1 along the length of metal bar 2.If metal bar 2 is also a magnet, it will attract or repel metal bar 1 as he moves it along its length.If metal bar 2 is not a magnet, there will be no attraction or repulsion between the two bars.Alternatively, Ray could also suspend metal bar 2 from a string and bring metal bar 1 near it. If metal bar 2 is a magnet, it will be attracted to metal bar 1 and start to swing towards it. If metal bar 2 is not a magnet, it will remain still.
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1.
Major advances in technology can influence just about every aspect of
life, including
SELECT ALL THAT APPLY
a medicine
b transportation
C communication
d food production
Check it
Answers
Answer:
c
Explanation:
47) The moment of inertia of a 0.98-kg bicycle wheel rotating about its center is 0.13 kg · m2. What is the radius of this wheel, assuming the weight of the spokes can be ignored?
Answers
Answer:
0.36 m
Explanation:
The moment of inertial of a wheel can be calculated as
\(I=mr^2\)Where r is the radius of the wheel and m is its mass.
Solving the equation for r, we get
\(r=\sqrt[]{\frac{I}{m}}\)So, replacing I by 0.13 kg m2 and m by 0.98 kg, we get
\(r=\sqrt[]{\frac{0.13\operatorname{kg}\cdot m^2}{0.98\operatorname{kg}}}=0.36\text{ m}\)Therefore, the radius of the wheel is 0.36 m
(a) is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) is it possible for the electric force on a charge moving in an electric field to be zero? (c) is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?
Answers
a)It is possible for the magnetic force on a charge moving in a magnetic field to be zero. The force acting on the charge is zero when a charge is moving in the same or opposite direction of the magnetic field. When a is charge moving parallel in the same direction of the magnetic field, then the magnetic force is zero.
b)It is not possible for the electric force on a charge moving in an electric field to be zero. If there's a charged particle in a magnetic field, it's impossible for this force to become zero.
c)It is not possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero. The magnetic force can be zero but the electric force cannot be zero because it is not affected by the motion of the particles.
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When an engine works, energy is transferred from one form to another form in four stages. The energy wasted in each stage is 10%. Calculate the efficiency of the engine.
(I WILL GIVE BRAINLIEST PLS HELP)
Answers
The efficiency of the engine is 60%.
What is the efficiency of engine?The efficiency of a heat engine describes the amount of input energy converted into useful work.
It also entails the amount of useful work done by the engine. The greater the amount of useful work done by the engine, the greater the efficiency of the engine.
The efficiency of an engine ranges from 0 to 100%.
If there four stages in the energy conversion cycle, and 10% energy is wasted in each cycle, the total energy wasted in the four cycles is calculated as;
Total wasted energy = 4 x 10% = 40%
Efficiency of the engine = Useful energy = 100% - 40% = 60%
Thus, the efficiency of the engine is the useful work done by the engine.
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express the internal shear in terms of x for 0≤x≤6ft, where x is in ft.
Answers
The internal shear in terms of x for \($0 \leq x \leq 6 \mathrm{ft}$\), where x is in ft. will be\(V_x & =A_y-400 \times x =1900-400 x\)
A free-body diagram is a graphical representation used in physics and engineering to show the applied forces, moments, and consequent reactions on a body in a specific situation. It shows a body or group of connected bodies together with all the applied forces, times, and responses that the bodies experience.
Potential energy and equilibrium are related in that the body's potential energy is lower in such an equilibrium.
In this case, the state generates a force that does not resist the displacement when a little distance displaces the body.
Draw the free-body diagram as shown below.
Consider the moment equilibrium condition about B.
\($$\begin{aligned}& M_B=0 \\& A_y \times 9-400 \times 6 \times\left(\frac{6}{2}+3\right)-900 \times 3=0 \\& A_y=1900 \mathrm{lb}\end{aligned}$$\)
Write the internal shear force equation for \($0 \leq x \leq 6 \mathrm{ft}$\).
\(V_x & =A_y-400 \times x =1900-400 x\)
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The complete question should be:
Express the internal shear in terms of x for \($0 \leq x \leq 6 \mathrm{ft}$\), where x is in ft.
Express your answer in terms of x. Express your answer using three significant figures.
Which of the following energies defines energy stored inside a spring?
A. Gravitational Potential
B. Elastic potential
C. Kinetic
Answers
Answer:
Elastic potential energy
What is the relationship between the sizes
of the planets and their distances from the sun?
Answers
Answer:
The inner, rocky planets are smaller than the outer, gaseous planets
Explanation:
The relationship between the sizes of the planets and their distances from the Sun is: The smaller planets are closer to the sun while the bigger planets are farther from the sun.
A solar system can be defined as a collection of both the inner and outer planetary bodies alongside the Moon in orbit (travel) around the Sun, in slightly elliptical orbits.
Basically, the nine (9) planets of the solar system orbiting (traveling) in order of their distance around the Sun are;
Mercury.Venus.Earth.Mars.Jupiter.Uranus.Neptune.Pluto.Venus.Saturn.Basically, the relationship between the sizes of the planets and their distances from the Sun is that the smaller planets are closer to the sun while the bigger planets are farther from the sun.
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the position of a particle is m. determine its velocity and acceleration as a function of time. ( 0 3 ) m/s ( 4 0 0 ) m/s2 what are its velocity and acceleration at time ?
Answers
At time t = 0, the velocity and acceleration of an object are represented by the equations a. (t) = 8 hati + 0 hatj - 0 hatk, and a. (0) = 8 hati + 0 hatj - 0 hatk.
The particle position is given as
\underset{r}{\rightarrow}(t) = 4 t2\hat{i} + 2.4 \hat{j} - 5.6 t \hat{k}
velocity is given as the derivative of position relative to time
1 (t) = dx(t)/dt
1 (t) = (d/dt) (4 t2\hat{i} + 2.4 \hat{j} - 5.6 t \hat{k})
1 (t) = (8t) \hat{i} + 0 \hat{j} - 5.6 \hat{k}
acceleration is given as the derivative of velocity relative to time
a. (t) = d1 (t)/dt
a. (t) = (d/dt) ((8t) \hat{i} + 0 \hat{j} - 5.6 \hat{k})
a. (t) = 8 \hat{i} + 0 \hat{j} - 0 \hat{k}
velocity is given as
1 (t) = (8t) \hat{i} + 0 \hat{j} - 5.6 \hat{k}
at t = 0
1 (0) = (8(0)) \hat{i} + 0 \hat{j} - 5.6 \hat{k}
1 (0) = 0\hat{i} + 0 \hat{j} - 5.6 \hat{k}
acceleration is given as
a. (t) = 8 \hat{i} + 0 \hat{j} - 0 \hat{k}
at t = 0
a. (0) = 8 \hat{i} + 0 \hat{j} - 0 \hat{k}
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Q2. True or False? A force is a push or a pull that acts on
an object due to the interaction with another object.
Answers
Answer:
True
Explanation:
----------------
a baseball bat collides with a 0.145 kg baseball moving with an initial velocity of 35 m/s to the left. if the collision lasts 0.005 seconds and the final velocity of the ball is 25 m/s to the right, what was the force of the bat on the ball?
Answers
According to Newton's third law of motion, the ball imparts an equal and opposite force on the bat. i.e 290 N
Given that,
The mass of the ball = .145 kg
initial velocity of 35 m/s
collision lasts 0.005 seconds
final velocity of the ball is 25 m/s
We have momentum = mass x velocity.
a) Initial momentum = 0.145*35 = 5.075 kg-m/s
b) Final momentum = 0.145*25 = 3.625 kg-m/s
c) Change in momentum = 5.075 - 3.625 = 1.45 kg-m/s
Impulse = Force x time = change in momentum
F = change in momentum/time = 1.45/0.005 = 290 N
d) By Newton's third law of motion, the ball imparts an
equal and opposite force on the bat.
therefore, Force = 290 N.
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A bus starting from a speed of 24 m/s slows to 6 m/s in a time of 3 s. The acceleration of the bus in meters per second squared is *
Answers
The acceleration of the bus for the given velocities and time of motion is 6 m/s².
The given parameters;
Initial speed of the bus, u = 24 m/sFinal sped of the bus, v = 6 m/sTime of motion of the bus, t = 3 sAcceleration is defined as the time rate of change of velocity.
Acceleration can be uniform if the change in velocity occurs at equal time interval.
The acceleration of the bus for the given velocities and time of motion is calculated as;
\(a = \frac{v-u}{t} \\\\a = \frac{24-6}{3} \\\\a = 6 \ m/s^2\)
Thus, the acceleration of the bus for the given velocities and time of motion is 6 m/s².
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the unit of force, Newton is a derived unit. (give reasons)
Answers
Answer:
\( \boxed{ \sf{see \: below}}\)
Explanation
The unit of force, Newton is a derived unit because it depends on three fundamental units. i.e kilogram , meter and second.
Hope I helped!
Best regards! :D
HELP PLEASE! DUE TONIGHT! If the wind speed in the top figure increased, what would happen to the plane’s ground speed?
Answers
Answer: Flying into the wind provides more lift, but reduces the plane's “ground speed”, the speed of the plane relative to the ground hope this helps
How much energy is given to each coulomb of charge that flows through a 1. 5-v battery?.
Answers
Answer:
1.5 jouls for 1 coulomb
Explanation:
energy(U)=charge(q)*potential(V)
so U for 1 coulomb U=1*1.5=1.5 jouls
and for 1 electron U=(1.6*10^(-19))*1.5= 2.4*10^(-19) jouls
A 2 kg object with a weight of 20 N is being pulled up by a rope with a tension of 12N what is the acceleration of the object
Answers
Answer:
The object accelerates downward at 4 m/s² since the tension on the rope is less than weight of the object.
Explanation:
Given;
mass of the object, m = 2 kg
weigh of the object, W = 20 N
tension on the rope, T = 12 N
The acceleration of the object is calculated by applying Newton's second law of motion as follows;
T = F + W
T = ma + W
ma = T - W
\(a = \frac{T-W}{m} \\\\a = \frac{12 - 20}{2} \\\\a = -4 \ m/s^2\) (the negative sign indicates deceleration of the object)
The object accelerates downward at 4 m/s² since the tension on the rope is less than weight of the object.
How long does it take sound to travel 3525 meters (speed of sound is 330 m/s)?
Answers
3525 / 330 = amount of seconds
Amount if seconds = 11.75
Hope this helped :)
How much time is it required for a athlete to lift a 1200 Kg weights up 14m from the ground if he can only produce 9 Kw of power.
Answers
Given,
The mass is m=1200kg
Height is h=14 m
Power is P=9kW
We know
Energy per unit time is power.
Thus,
P=mgh/t
where t is the time.
Thus,
\(\begin{gathered} 9\times10^3=\frac{1200\times9.81\times14}{t} \\ \Rightarrow t=18.312 \end{gathered}\)The time is 18.312 sec.
Managerial objectives are essential. What are these
objectives for and how does the SMART concept help the process?
Answers
Managerial objectives are essential for guiding and directing the efforts of an organization towards specific goals. These objectives serve as a roadmap to achieve desired outcomes and provide a framework for decision-making and resource allocation. They help in setting clear expectations, aligning efforts, and evaluating performance.
The SMART concept is a helpful framework for setting effective managerial objectives. SMART stands for Specific, Measurable, Achievable, Relevant, and Time-bound. By applying these criteria to objectives, they become more focused, well-defined, and actionable.
1. Specific: Objectives should be clear and specific, leaving no room for ambiguity or misinterpretation. They should answer the questions of what, why, who, and how.
2. Measurable: Objectives should be quantifiable or have some criteria for measuring progress and success. This enables tracking and evaluation of performance.
3. Achievable: Objectives should be realistic and attainable within the given resources, capabilities, and constraints of the organization.
4. Relevant: Objectives should align with the overall strategic direction and priorities of the organization. They should contribute directly to the desired outcomes and address key challenges or opportunities.
5. Time-bound: Objectives should have a defined timeframe or deadline for completion. This creates a sense of urgency and helps in prioritizing activities.
By applying the SMART concept, managerial objectives become more effective in providing clarity, focus, and measurability. They enhance accountability, enable better planning and resource allocation, and improve decision-making by providing a clear framework for evaluation and adjustment.
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Placing a soccer ball on the top shelf increases the...
Kinetic energy
Chemical energy
Gravitational potential energy
Elastic potential energy
Answers
Answer:
Gravitational potential energy
Explanation:
PE = m*g*h
m = mass
g = 9.81m/s², acceleration of gravity
h = height
So m and g stay the same but the height can change so the higher you go the higher the Gravitational potential energy.
Placing a soccer ball on the top shelf increases the Gravitational potential energy
what is Gravitational potential energy ?In a gravitational field the energy possessed by an object due to a change in its position called as gravitational potential energy, it is an energy that is related to gravitational force or to gravity.
When a mass of the body (m) is moved from infinity to a point inside the gravitational influence of a source mass (M) in absence of acceleration and the amount of work done in displacing it into the source field is stored in the form of potential energy denoted with the symbol Ug.
when external force is applied, then the position of the body changes potential energy is equal to the amount of work done on the body by the forces.
The gravitational influence on a body at infinity is zero, then the potential energy is zero, PE = m*g*h where m = mass, g = 9.81m/s², acceleration of gravity, h = height
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When you pump a bicycle tire, what is happening to the particles inside the tire?
A:Nothing, because pumping in more air does not affect the particles inside.
B:They are moving closer together and contracting, filling the tire and making it more firm.
C:They are moving farther and farther apart, which is what expands the tire.
D:They are moving faster and faster, making the tire feel more full.
Answers
collisions of particles with the inside walls of the tire cause the pressure that is exerted by the enclosed gas. because of the increasing the number of air particles increases the number of collisions, which then increased the pressure of the tire.
Answer:B
Explanation: Just did it