A typical 16-line poem that described centripetal force can be found below.
Centripetal forceIn circular motion, a force we call,
Centripetal, it keeps things in thrall.
Directed towards the center of the path,
Without it, objects would face a wrath.
Angular velocity is key,
The rate of change of the angle we see.
And the radius of the circle too,
Both play a role in what we must do.
The mass of the object cannot be ignored,
It factors in with gravity's cord.
As the force pulls towards the center,
Centripetal force is what we enter.
It is the sum of all the forces in play,
Equal to mass times velocity squared, we say.
And if the force is too weak or too strong,
Off the circular path, the object goes wrong.
Thus, centripetal force is what we need,
To keep objects moving at the speed,
In a circular path, they're meant to be,
A force that keeps them in harmony.
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When does alzheimers disease occur
Answer:
For most people with Alzheimer's — those who have the late-onset variety — symptoms first appear in their mid-60s or later. When the disease develops before age 65, it's considered early-onset Alzheimer's, which can begin as early as a person's 30s, although this is rare.
Help with parts a through part f.
The equation = RC, where R is the resistance and C is the capacitance, yields the time constant of the circuit. We obtain the value = RC = (5.5 k)(4.5 F) = 24.75 ms = 0.02475 s by substituting the above variables.
What is circuit, exactly?In electronics, a circuit is a completely circular channel through which electricity flows. A current source, conductors, and a load make up a straightforward circuit.
The equation = RC, where R is the resistance and C is the capacitance, yields the time constant of the circuit. Inputting the values provided yields:
τ = RC = (5.5 kΩ)(4.5 µF) = 24.75 ms = 0.02475 s
The voltage drop Vc across the capacitor is equal to the voltage of the battery, i.e., Vc = VB = 180 V.
After a very long time, the voltage across the capacitor is equal to the voltage of the battery, i.e., V = VB = 180 V. Substituting the given values, we get:
Q = CV = (4.5 µF)(180 V) = 810 µC = 8.1 × 10⁻⁴ C
The current I in the circuit is equal to the current in the resistor, which is given by Ohm's law as I = V/R, where V is the voltage of the battery. Substituting the given values, we get:
I = V/R = (180 V)/(5.5 kΩ) = 32.73 mA = 3.273 × 10⁻² A
To find the time t when the current through the resistor is one-third of its maximum value, we can set I = (1/3)(VB/R) and solve for t:
(1/3)(VB/R) = (VB/R)e(-t/τ)
e(-t/τ) = 1/3
-t/τ = ln(1/3)
t = τln(3) ≈ 0.867τ
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A 4.0-N puck is travelling at 3.0m/s. It strikes an 8.0-N puck, which is stationary. The two
pucks stick together. Their common final speed is:
Answer: 2.858(m/s)
Explanation: F= mg→ m1= 4.0/9.8 = 0.408(kg)
m2= 8 /9.8 = 0.816(kg)
m1v1 = (m1+m2)v2→ v2= m1v1(m1+m2) = 0.408+3/(0.408+0.816)= 2.8589m/s)
400-kg go-cart begins at rest and obtains a velocity of 20 m/s east after 10 seconds. a.) What is the object’s initial momentum?
The object's initial momentum is 0 kg*m/s.
The go-cart starts from rest, so its initial velocity (u) is zero. The final velocity (v) is 20 m/s. The mass of the go-cart is 400 kg.
The formula for momentum (p) is:
p = m * v
where m is mass and v is velocity.
Using the given values, we can calculate the momentum at the final velocity:
p = 400 kg * 20 m/s = 8000 kg*m/s
However, we are asked for the initial momentum, which we can find using the conservation of momentum principle. Since no external forces act on the go-cart, the total momentum of the system remains constant.
At the initial moment when the go-cart is at rest, its velocity (u) is zero and hence its momentum is also zero. Therefore, the initial momentum of the system is 0 kg*m/s.
What is momentum?
Momentum is a fundamental concept in physics that describes the amount of motion an object has. It is defined as the product of an object's mass and velocity.
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how many hydrogen-bonds does this molecule have?
how many acceptors does it have?
How many h-bonds can this molecule form with another identical
How many h-bonds can it form with water?
Acetic anhydride has two hydrogen bond acceptor atoms and one hydrogen bond donor atom.
It can form two hydrogen bonds with another identical molecule and two hydrogen bonds with water.
O
//
H3C-C-O-C-CH3
\\
O
Acetic anhydride has two hydrogen bond acceptor atoms
Acetic anhydride can form two hydrogen bonds with another identical molecule and two hydrogen bonds with water
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I need this tomorrow 50 points.
Answer: 849.15NM/S
Explanation: the power associated with forse F IS GIVEN BYP= F'.V' ,
WHERE V' IS THE VELOCITY OF THE PROJECT OF THE OBJECT ON WHICH THE FORCE ACTS . THUS,
P= F'.V. = COSФ
P = (135N) (7.4M/S)COS31° = 849.15NM/S
if a space rover has a mass of 3900 kg, then what is its weight on earth
Answer:
38 220
Explanation:
Weight =Mg
W=Mg
W = (3900)(9.8)
W = 38 220
You have to
design a circuit that has an interface to the outside world made
up of 5 wires:
a. One wire connects to ground.
b. One wire connects to a single supply voltage, Vsupply. (See Design Constraints below).
c. One wire connects to a control signal. During testing, this signal is only allowed to have values 0 or +5V.
d. The remaining two wires v1 and v2 are what the switch is supposed to connect. If Vcontrol = 0V
then the switch should be closed and ideally v1=v2 . If Vcontrol = +5V then the switch is open
and ideally i1=i2=0 where i1 and i2 are the currents into each of the two wires v1 and v2 .
Design Constraints
1. You are limited to the use of a single dc power supply. Vsupply ≤ +5V .
2. You are allowed the use of MOSFETs, diodes, resistors, and capacitors that are available in your
component kits.
3. You have a single control voltage. The function of the control voltage is as described above for
each type of switch.
Answer:
the unit of m×g×h×10 is no 3
Accuracy: 100%
A student wants to estimate the gravitational force between an asteroid and a planet other than Earth.
Which of the following information would be most likely needed to make this calculation?
Select ALL that apply.
Elimination Tool
Select all that apply
A
B
C
D
E
G
F
The mass of the asteroid.
The mass of Earth.
The mass of the planet.
The radius of Earth.
The distance between the asteroid and the planet.
The constant g 9.80 m/s².
The constant G-6.67 x 10-¹¹ Nx m²/kg.
Answer:
Explanation:The information that would be most likely needed to make the calculation of the gravitational force between an asteroid and a planet other than Earth are:
The mass of the asteroid (A)
The mass of the planet (C)
The distance between the asteroid and the planet (E)
The constant G-6.67 x 10^-11 Nm²/kg (G)
Therefore, the options that apply are A, C, E, and G.
A car initially traveling 10 m/s stops in a distance of 6 m. In another instance, the same car applying the same constant force is traveling 20 m/s. What is the required distance to come to a stop now?
The required distance to come to a stop now is 30 meters.
Steps
To solve this problem, we can use the equation:
v^2 = u^2 + 2as
where:
v is the final velocity (zero in this case)
u is the initial velocity (10 m/s in the first instance and 20 m/s in the second instance)
a is the acceleration (which is constant in this case)
s is the distance traveled (6 m in the first instance and we need to find it for the second instance)
Solving for s, we get:
s = (v^2 - u^2) / (2a)
For the first instance:
u = 10 m/s
v = 0 m/s
s = 6 m
a = (v^2 - u^2) / (2s) = (0 - 10^2) / (2 x 6) = -16.67 m/s^2 (negative sign indicates deceleration)
Now, using the same constant force, we can find the required distance s for the second instance:
u = 20 m/s
a = -16.67 m/s^2
v = 0 m/s (since the car stops)
s = (v^2 - u^2) / (2a) = (0 - 20^2) / (2 x -16.67) = 30 m
Therefore, the required distance to come to a stop now is 30 meters.
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Use nodal analysis to find V1 and V2 in the circuit shown in Fig. 6.
Kirchhoff's current law is applied in nodal analysis. There will be 'n-1' simultaneous equations to solve when there are 'n' nodes in a given electrical circuit. 'n-1' must be solved in order to retrieve all of the node voltages.
Hence, we can solve for V1 and V2:
V1=Vi(R2+R3−k)k(1−nR3)−R2−R3.
V2=Vi(k−R2−R3(1+nR2))k(nR3−1)+R2+R3.
What is the significance of nodal analysis?Nodal analysis is a fundamental approach used to investigate voltage and current distribution in a circuit and is one of the simulations included in SPICE simulators. This method successfully integrates Kirchhoff's and Ohm's laws into a single matrix equation.
The distinction between mesh and nodal analysis is that nodal analysis uses Kirchhoff's current law to calculate the voltages at each node in an equation. Mesh analysis, on the other hand, is an application of Kirchhoff's voltage law, which is used to calculate current.
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Cognitive psychology focuses on which of the following areas?
Personal responsibility and individual awareness
Behavior and attitudes
Physical capabilities and self-esteem
Perception and memory retention
The internal brain processes required to make sense of the environment and choose the best course of action are the subject of cognitive psychology.
Which six subfields make up cognitive psychology?Complex attention, executive function, learning and memory, language, perceptual-motor control, and social cognition are the six major cognitive function domains identified by the DSM-5.
What distinguishing characteristics characterise the cognitive psychology approach?The cognitive approach's main characteristics are: a conviction that psychology should be treated as a pure science and that research methods should be based on science. The main focus is on thinking and related mental functions like language, perception, memory, and forgetting.
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A scuba diver is in a freshwater lake with water of density 1000 kg/m3. To have neutral buoyancy, she has to wear a weight belt that has a mass of 8 kg.
a. If she and the rest of her gear had a total mass of 65 kg before putting on the weight belt, what is her total volume, in liters, after putting it on? 1 m3 = 1000 liters. (1 point)
b. If she takes a very deep breath, her body's volume increases by 3 L. What is the change in the buoyant force on her body? (1 point)
c. If her next dive is going to be in a saltwater lake (ρ = 1025 kg/m3), what mass of weight belt should she wear to have neutral buoyancy? (1 point)
When the gas in a swim freshwater lake allows its density to match that of the water around it, the fish is said to be in water level (Pflugrath et al., 2012). The maximal neutral buoyant depth (MNBD) is a limit below which fish will have become lot of negative if they swim. Your overall dive depth should be roughly being one your neutral buoyancy depth, but not less than ten metres (32ft).
Hence, as a solid item is embedded in a liquid, its volume increases, more fluid weight is displaced, increasing the hydrostatic pressure. The buoyant force is at its greatest when a solid item is fully submerged in a fluid.
The formula B = V g, where and V are indeed the entity's volume and capacity, correspondingly, and g is the velocity brought on by gravity, is used to calculate the buoyancy required for just an object. 1000 kg/m3 is the density of water. Thus, the required force is 1000 kg/m3 times 1 L times 9.81 m/s2 equals 9.81 N.
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4. Kepler-22b is an extrasolar planet orbiting within the habitable zone of the Sun-like star. It has a mass that is 36 times the mass of Earth and a radius that is 2.4 times that of Earth. What is the acceleration due to gravity on Kepler-22b?
answers:
a. 3g/100
b. g/33
c. 3g/10
d. 9g/20
The acceleration due to gravity on Kepler-22b would be 10.9 m/s^2.
Acceleration due to gravityThe acceleration due to gravity on a planet can be calculated using the formula:
g = GM/r^2
where G is the gravitational constant, M is the mass of the planet, r is the radius of the planet.
For Kepler-22b, we are given that its mass is 36 times that of Earth, so its mass is:
M = 36M_E
where M_E is the mass of Earth. We are also given that its radius is 2.4 times that of Earth, so its radius is:
r = 2.4R_E
where R_E is the radius of Earth.
Substituting these values into the formula for g, we get:
g = GM/r^2
g = G(36M_E)/(2.4R_E)^2
g = G(36M_E)/(5.76R_E^2)
g = (36/5.76)G(M_E/R_E^2)
g = 6.25G(M_E/R_E^2)
The value of g for Earth is approximately 9.81 m/s^2. Substituting this value for G, M_E, and R_E, we get:
g = 6.25(6.674×10^-11 N·m^2/kg^2)(5.97×10^24 kg)/(6.38×10^6 m)^2
g = 10.9 m/s^2
Therefore, the acceleration due to gravity on Kepler-22b is approximately 10.9 m/s^2.
So the answer is not one of the options given.
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Cold water ~
has the highest density at what temperature.. ?
Answer:
The maximum density of water occurs at around 4° Celsius. The density of ice is less than liquid water, so it floats. Upon freezing, the ice density decreases by about 9%.
Explanation:
thanks for the question
How does understanding what occurs at the various tectonic plate boundaries support our understanding of the past and current movement of rocks at earth's surface?
Answer:
Understanding what occurs at the various tectonic plate boundaries supports our understanding of the past and current movement of rocks at Earth's surface because the movement of the plates is responsible for shaping the planet's surface features, such as mountain ranges, ocean basins, and volcanoes. Different types of plate boundaries produce different geological features and events. For example, convergent plate boundaries, where two plates move towards each other, result in subduction zones, where one plate is forced beneath another, and can cause volcanic activity and earthquakes. Divergent plate boundaries, where two plates move away from each other, can cause seafloor spreading, mid-ocean ridges, and rift valleys. Transform plate boundaries, where two plates move past each other, can cause earthquakes. By studying the processes and features associated with these plate boundaries, scientists can gain insight into how the Earth's surface has changed over time and how it continues to change today.
Explanation:
If a tennis racquet is briefly in contact with a 0.058 kg tennis ball initially traveling at -9.0 m/s* and then (after contact) the tennis ball moves with a velocity of 9.0 m/s.* If the time the racquet is in contact witht the ball is 0.004 seconds, what is the average force of the racquet on the ball? *Negative velocities mean towards the left and positive velocities mean towards the right.
The average force of the racquet on the ball, given that the time the racquet is in contact with the ball is 0.004 seconds, is 261 N
How do i determine the average force of the racquet?The following data were obtained from the question:
Mass of tennis (m) = 0.058 KgInitial velocity (u) = -9 m/sFinal velocity (v) = 9 m/sTime (t) = 0.004 secondsAverage force (F) =?We can easily obtain the average force of the racquet on the ball as follow?
F = m(v - u) / t
F = [0.058 ×(9 - -9)] / 0.004
F = [0.058 ×(9 + 9)] / 0.004
F = [0.058 × 18] / 0.004
F = 1.044 / 0.004
F = 261 N
Thus, we can conclude from the above calculation that the average force on the ball is 261 N
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HELPPP MEEEEE
HOMEWORK
Answer:i believe the answer is d: a motion force
Explanation:
The energy (E) of photon depends upon its wavelngth 'λ' , Planck's constant ' h ' and velocity
' c'. Derive the formula for energy using dimensional analysis.
Planck's frequency (h) and indeed the light's velocity (c) are used to connect a photon's energy (E) to its wavelength (), frequency (v), and wavelength. E = hν = hc/λ.
What is energy, exactly?We frequently use the word "energy" in our everyday speech. Energy has an unique physical meaning even if the term is frequently used figuratively. Energy is defined in physics as something's capacity to perform work. Many types of energy are possible. All energy is kinetic in some way.
The energy is lacking.Energy is present everywhere and comes in a variety of shapes and sizes. Objects at rest have potential energy that, if released, will cause them to move. All moving things contain kinetic energy.
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if an astronaut weighs 981 N on earth and only 160 N on the moon, then what is his mass on the moon
Answer:
mass=kg
Explanation:
M=(160)(9.8)
M=1568
the following diagrams depict inelastic collisions between objects of different mass. For each case, determine the post-collision velocity (v) of the two coupled objects. Express v in terms of v
The colliding objects stick together after the collision, or some kinetic energy is lost to the environment.
What is an inelastic collision?The question is incomplete but I will discuss the concept of inelastic collision generally.
An inelastic collision is a type of collision in which kinetic energy is not conserved. In other words, in an inelastic collision, some of the kinetic energy of the colliding objects is transformed into other forms of energy, such as heat, sound, or deformation of the objects.
In an inelastic collision, the colliding objects stick together after the collision, or some kinetic energy is lost to the environment. This means that the final kinetic energy of the objects is less than the initial kinetic energy, and that the objects move with a lower velocity after the collision than they did before.
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helllp science ixl U.1
Answer:
All of the above.
Explanation:
Terms
- Chlorophyll is the green coloring matter of leaves and plants, essential to the production of carbohydrates by photosynthesis, and occurring in a bluish-black form, C55H72MgN4O5 (chlorophyll a), and a dark-green form, C55H70MgN4O6 (chlorophyll b).
- Photosynthesis is the complex process by which carbon dioxide, water, and certain inorganic salts are converted into carbohydrates by green plants, algae, and certain bacteria, using energy from the sun and chlorophyll.
- Carbon dioxide is a colorless, odorless, incombustible gas, CO2, present in the atmosphere and formed during respiration, usually obtained from coal, coke, or natural gas by combustion, from carbohydrates by fermentation, by reaction with limestone or other carbonates, or naturally from springs: used extensively in industry as dry ice, or carbon dioxide snow, in carbonated beverages, fire extinguishers, etc.
- Water is a transparent, odorless, tasteless liquid, a compound of hydrogen and oxygen, H2O, freezing at 32°F or 0°C and boiling at 212°F or 100°C, that in more or less impure state constitutes rain, oceans, lakes, rivers, etc.: it contains 11.188 percent hydrogen and 88.812 oxygen, by weight.
- Plants cells are the cells present in green plants, photosynthetic eukaryotes of the kingdom Plantae. Their distinctive features include primary cell walls containing cellulose, hemiculloses and pectin, the presence of plastids with the capability to perform photosynthesis and store starch, a large vacuole that regulates turgor pressure, the absence of flagella or centrioles, except in the gametes, and a unique method of cell division involving the formation of a cell plate or phragmoplast that separates the new daughter cells.
- Celluar respiration is the oxidation of organic compounds that occur within cells, producing energy for cellular processes.
- Chemical energy is the net potential energy liberated or absorbed during the course of a chemical reaction.
-------------------------------------------------------------------------------------------------
First: True
The process by which Chlorophyll is able to trap energy from Sun is called Photosynthesis, because this trapped light (Electromagnetic) energy is converted into chemical energy and stored in Glucose synthesized from carbon dioxide and water as per following reaction
6CO2 + 6H2O = -—-Light Energy---> C6H12O6+ 6O2
-------------------------------------------------------------------------------------------------------
Second: True
Plants absorb water (H2O) and carbon dioxide (CO2) from the earth and atmosphere during photosynthesis. Water is oxidized, which means it loses electrons, while carbon dioxide is reduced, which means it gets electrons, inside the plant cell. Water is converted into oxygen and carbon dioxide into glucose as a result.
----------------------------------------------------------------------------------------------------
Third: True
During the photosynthetic process in a plant cell, chloroplast produces sugar by transforming light energy into chemical energy held in glucose. The process of cellular respiration in mitochondria converts sugar into energy that plant cells can use to survive and develop.
----------------------------------------------------------------------------------------------------
Fourth: True
In the light reactions, one molecule of the pigment chlorophyll absorbs one photon and loses one electron. This electron is passed to a modified form of chlorophyll called pheophytin, which passes the electron to a quinonemolecule, allowing the start of a flow of electrons down an electron transport chain that leads to the ultimate reduction of NADP to NADPH. In addition, this creates a proton gradient across the chloroplast membrane; its dissipation is used by ATP synthase for the concomitant synthesis of ATP. The chlorophyll molecule regains the lost electron from a water molecule through a process called photolysis, which releases a dioxygen (O2) molecule. The overall equation for the light-dependent reactions under the conditions of non-cyclic electron flow in green plants is:
2 H2O + 2 NADP+ + 3 ADP + 3 Pi + light → 2 NADPH + 2 H++ 3ATP+ O2
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A rocket at rest on the ground with initial mass 20,000 kg, 80% of which is fuel, burns 200kg/s as it flies
directly upwards. The exhaust gas exits the rocket at a relative speed of 1.80 km/s. Find (a) the thrust of
the rocket, (b) how long it takes to exhaust its fuel, and (c) the rocket’s speed at the end of its engine burn.
Assume g is constant and neglect air resistance.
Answer:
(a) The thrust of the rocket can be found using the formula:
Thrust = (mass flow rate) x (exhaust velocity)
The mass flow rate is the rate at which mass is expelled from the rocket, which is equal to the burn rate times the mass fraction of fuel:
mass flow rate = burn rate x (mass of rocket) x (mass fraction of fuel)
mass flow rate = 200 kg/s x 20,000 kg x 0.8
mass flow rate = 32,000 kg/s
The exhaust velocity is given as 1.80 km/s. Therefore, the thrust of the rocket is:
Thrust = 32,000 kg/s x 1.80 km/s
Thrust = 57,600 kN
(b) The time it takes to exhaust the fuel can be found using the formula:
time = (mass of fuel) / (burn rate)
The mass of fuel is 80% of the initial mass of the rocket:
mass of fuel = 0.8 x 20,000 kg
mass of fuel = 16,000 kg
Therefore, the time it takes to exhaust the fuel is:
time = 16,000 kg / 200 kg/s
time = 80 seconds
(c) The rocket's speed at the end of its engine burn can be found using the rocket equation:
Δv = (exhaust velocity) x ln[(initial mass) / (final mass)]
The final mass is the mass of the rocket after it has burned all of its fuel, which is:
final mass = (mass of rocket) - (mass of fuel)
final mass = 20,000 kg - 16,000 kg
final mass = 4,000 kg
The initial mass is 20,000 kg. Therefore, the change in velocity is:
Δv = 1.80 km/s x ln[(20,000 kg) / (4,000 kg)]
Δv = 1.80 km/s x ln(5)
Δv = 3.89 km/s
Since the rocket was initially at rest, its final speed is equal to the change in velocity:
final speed = 3.89 km/s
Therefore, the rocket's speed at the end of its engine burn is 3.89 km/s.
laws of reflection help us to predict the path of reflected ray with refrence to incident ray. How?
Answer:
The laws of reflection govern how incident light rays are reflected on reflecting surfaces such as mirrors, smooth metal surfaces, and clear water. The laws of reflection are as follows: The incident ray reflected ray, and normal to the mirror’s surface are all in the same plane. The incidence angle equals the reflection angle.
Explanation:
What are the stresses?
Stress refers to a state of mental or emotional strain resulting from adverse or demanding circumstances. It can also refer to the physical forces that act on an object, causing deformation or strain.
What are the effects of stress?In terms of mental or emotional stress, it can result from a variety of factors such as work-related pressure, financial problems, relationship issues, health concerns, and other life events that require us to adapt and cope with changing circumstances.
Physical stress refers to the force or pressure applied to an object, which can cause it to deform, strain, or break. This type of stress can arise from a variety of sources such as gravity, external forces, or internal forces caused by changes in temperature, pressure, or other physical conditions.
Examples of physical stress include tension in a bridge caused by the weight of traffic passing over it, strain in a metal bar due to changes in temperature, or compression of a spring due to a force applied to it. In all cases, the object is subjected to forces that cause it to deform or change shape, leading to stresses that can impact its strength, durability, and performance.
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The displacement vectors
A
and
B
shown in the figure below both have magnitudes of 1.95 m. The direction of vector
A
is
= 29.0°.
A graph shows two displacement vectors A and B plotted on an x y plane. Vector A is a straight diagonal line that starts from the zero point and extends into the first quadrant at an angle with the horizontal. Vector B starts from the zero point and extends up along the y-axis.
(a) Find
A + B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(b) Find
A − B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(c) Find
B − A
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(d) Find
A − 2B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
The magnitude οf A + B is 1.95 m and its directiοn is 31.3° clοckwise frοm the pοsitive x-axis when the displacement vectοrs A and B is shοwn in the figure belοw bοth have magnitudes οf 1.95 m. The directiοn οf vectοr A is = 29.0°.
Hοw tο determine the magnitude and directiοn οf A + B?Tο determine the magnitude and directiοn οf A + B, we can measure the length οf the resulting vectοr and the angle it makes with the pοsitive x-axis, respectively.
Alternatively, we can use trigοnοmetry tο find the cοmpοnents οf vectοrs A and B and then add them up tο find the cοmpοnents οf A + B. Then, we can use inverse trigοnοmetric functiοns tο find the magnitude and directiοn οf the resulting vectοr.
Let's use the secοnd methοd tο sοlve this prοblem.
We are given that the magnitudes οf vectοrs A and B are 1.95 m each. The directiοn οf vectοr A is 29.0° cοunterclοckwise frοm the pοsitive x-axis. Let's call the angle between vectοr B and the pοsitive x-axis θ.
Using trigοnοmetry, we can find the x and y cοmpοnents οf vectοrs A and B as fοllοws:
Ax = 1.95 cοs 29.0° = 1.695 m
Ay = 1.95 sin 29.0° = 0.939 m
Bx = 1.95 cοs θ
By = 1.95 sin θ
Tο find θ, we need tο use the fact that the magnitude οf vectοr A + B is alsο 1.95 m. This means that:
[tex](Ax + Bx)^2 + (Ay + By)^2 = (1.95)^2[/tex]
Substituting the values of Ax and Ay, we get:
(1.695 + 1.95 cos θ)² + (0.939 + 1.95 sin θ)² = (1.95)²
Simplifying and solving for cos θ and sin θ, we get:
cos θ = -0.359
sin θ = -1.695
Since sin θ is negative, we know that vector B is pointing downwards.
Now, we can use inverse trigonometric functions to find the magnitude and direction of vector A + B:
[tex]|A + B| = sqrt((Ax + Bx)^2 + (Ay + By)^2) = 1.95 m[/tex]
θ = atan2(Ay + By, Ax + Bx) = atan2(-0.756, 1.336) = -31.3°
Therefore, the magnitude of A + B is 1.95 m and its direction is 31.3° clockwise from the positive x-axis.
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NASA is currently working on sending humans to Mars by the 2030s. When astronauts arrive on Mars, NASA intends to already have their food supply there. The food will be sent by an unmanned spacecraft. It will then be stored, unrefrigerated, for five to seven years. List at least two likely constraints and two likely criteria for this engineering design problem.
Constraints:
Limited space on the unmanned spacecraft for carrying food supplies.
The food must be durable enough to withstand the harsh conditions of space travel and long-term storage on Mars.
Criteria:
Nutritional value: The food must provide adequate nutrition to support the physical and mental health of astronauts during their mission on Mars.
Taste and variety: The food should be appetizing and varied to help maintain astronauts' morale and well-being during their extended stay on Mars.
What is the benefit of unmanned spacecraft?Cost-effectiveness: Unmanned spacecraft are generally less expensive to build, launch, and operate than manned spacecraft. This is because they do not require life support systems, crew accommodations, or other specialized equipment needed to sustain human life in space.
Safety: Sending unmanned spacecraft eliminates the risks associated with human spaceflight, such as exposure to radiation, accidents, and medical emergencies.
Scientific research: Unmanned spacecraft can be designed to carry a variety of scientific instruments and sensors to collect data and perform experiments in space, without the limitations of human endurance and safety.
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A book sitting on a shelf have 740 J of potential energy, at a height of 1.8
m. What is the mass of the book?
13053.6 J
13053.6 m
41.950 kg
41.950 J
1 point
What is silicon and what is it used for?
5. A geologist from Pogera gold mine cut out a block of ore for laboratory analysis. The sides of the ore are 8.8 dm, 92.4 mm, 0.007 dam. Work out the volume of the ore in; i. Cubic metre. (show all working out to deserve a full mark). 3 marks
Therefore, the volume of the ore is 0.0069 cubic meters.
What is volume?Volume is a measure of the amount of space that an object or substance occupies. It is a fundamental physical quantity that describes the three-dimensional size of an object or space. The SI unit of volume is the cubic meter (m³), but other units such as liters, gallons, and cubic centimeters (cm³) are also commonly used. Volume can be calculated for regular shapes, such as cubes or cylinders, using mathematical formulas, but for irregular shapes, more complex methods, such as displacement, may be needed.
Here,
To calculate the volume of the ore, we need to convert all the measurements to the same unit. We can choose to convert everything to meters since that's the base unit for volume (cubic meters).
8.8 dm = 0.88 m (1 dm = 0.1 m)
92.4 mm = 0.0924 m (1 mm = 0.001 m)
0.007 dam = 0.07 m (1 dam = 10 m)
Now we can use the formula for volume of a rectangular block:
Volume = length x width x height
Volume = 0.88 m x 0.0924 m x 0.07 m
Volume = 0.0069 cubic meters
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