Answers
Answer:
756 N.
Explanation:
So, we are given the following data or parameters or information which is going to assist us in solving this particular Question or problem effectively;
=> The bathroom scale in an elevator is not moving.
=> " The scale reads 588 N. "
=> "The elevator then moves down at an acceleration of - 2.8 m/s2."
For the second point above: 588 N = mass × gravity.
Thus, the scale that will read while the elevator moves down is given below;
(Mass × gravity) - (mass × acceleration).
(The value of scale when it is not moving) × (1 + acceleration/gravity).
=> 588 × { 1 + 2.8/9.8} = 756 N
Related Questions
4. Interpret Data The graph below shows the
motion of an elevator. Explain its motion.
Answers
Answer:
Below
Explanation:
0-1 sec descends at constant rate from 10 to 6 m
1-2 sec stops at 6m
2-3 sec descends at constant rate to 2 m
3-4 sec stops at 2 m
4-5 sec descends at another constant rate to 0 m
Compare sound and earthquake waves
Answers
When materials vibrate, waves are created that travel through the substance, and this energy is what we hear as sound. Earthquakes are earth vibrations that cause the (potential) energy held within rocks to be released (as a result of their pressure-generating relative positions). Seismic waves are produced by earthquakes.
How do sound waves and earthquakes compare?
The waves lose energy as they move through the air with sound or through the ground with shaking during an earthquake. Therefore, a band can be heard louder close to the stage than farther away, and an earthquake can be felt more strongly close to the fault than farther away.
In actuality, sound in the air cannot match how quickly earthquake waves move. In rock, the compressional or "P" wave of an earthquake moves at the In actuality, sound in the air cannot match how quickly earthquake waves move. The speed of a P wave is typically 10,000 mph. The speed of sound through air is roughly 750 mph.
To learn more about sound waves use:
https://brainly.com/question/16093793
#SPJ1
A heat engine exhausts 6000 J of heat while performing 2000 J of useful work.
Determine the efficiency of the engine
Answers
Answer:
Explanation:
The efficiency can be calculated by:
\(\eta = \frac{Q_{E}-Q_{W}}{Q_{E}}=\frac{6000-2000}{6000}=\frac{2}{3}\)
or we can say it becomes approximately 66.7%
how many newtons does a 190 lb person weigh? express your answer in newtons. activate to select the appropriate template from the following choices. operate up and down arrow for selection and press enter to choose the input value typeactivate to select the appropriates symbol from the following choices. operate up and down arrow for selection and press enter to choose the input value type w
Answers
The weight of a 190 lb person is 844.5 N.
What is the definition of 1 Newton?Newton is the SI (International System) unit of force, named after Sir Isaac Newton, a famous physicist, and mathematician. It is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared (1 N = 1 kg m/s²).
To convert pounds (lb) to Newtons (N), we need to use the conversion factor:
1 lb = 4.45 N
Therefore, a 190 lb person weighs:
190 lb × 4.45 N/lb = 844.5 N
So the weight of a 190 lb person is 844.5 N.
Learn more about Newton here:
https://brainly.com/question/20389058
#SPJ1
Let E =3i^+1j^ and F =1i^−3j^.
A. Find the magnitude of E.
B. Find the magnitude of F.
C. Find the magnitude of G =E +F.
D. Find the magnitude of H =−E −2F.
Answers
The given vectors E and F are in Cartesian form. To find their magnitudes, we can use the formula:
|v| = √(vx² + vy²)
where vx and vy are the x and y components of the vector.
What is the Cartesian algebra?Cartesian algebra, also known as coordinate algebra or analytic geometry, is a branch of mathematics that deals with the use of algebraic equations to describe geometric shapes and their properties. It is named after the French philosopher and mathematician René Descartes, who developed the Cartesian coordinate system, which provides a way to describe the position of points in space using numbers.
A. Magnitude of E:
|E| = √((3i)² + (1j)²)
= √(9i² + 1j²)
= √(9 + 1)
= √(10)
Therefore, the magnitude of E is √(10).
B. Magnitude of F:
|F| = √((1i)² + (-3j)²)
= √(1 + 9)
=√(10)
Therefore, the magnitude of F is √(10).
C. Magnitude of G = E + F:
G = E + F = (3i + 1i) + (1j - 3j)
= 4i - 2j
|G| = √((4i)² + (-2j)²)
=√(16 + 4)
= √(20)
= 2√(5)
Therefore, the magnitude of G is 2√(5).
D. Magnitude of H = -E - 2F:
H = -E - 2F = (-3i - 2i) + (-1j + 6j)
= -5i + 5j
|H| = √(-5i)² + (5j)²)
= √(25 + 25)
= √(50)
= 5√(2)
Therefore, the magnitude of H is 5√(2).
To know more about geometric shapes, visit:
https://brainly.com/question/10059415
#SPJ1
Newton's Second Law Assignment: Lab Report
Answers
Explanation:
The force of an object is equal to its mass times its acceleration
PHYSICS : MODULE 01 GALILEO GARDENS : 01.02 GRAPHING DATA
Graphing Activity
Let’s take another look at the experimental data given to you in the exploratory activity. Graph the data once again, applying the knowledge and skills you have learned.
Procedure:
Table 1 shows some data that Rafael and Cristine collected during an experiment to measure the stretch of a spring as more force was applied.
Graph the data from Table 1 on your graph paper. Do not use a graphing program.
Answers
The experimental value of the expression due to gravity through the experiment will come out to be 8.41u, the error in the value has Accord because of air friction.
What is acceleration due to gravity?Acceleration due to gravity is a form of acceleration that is exercised by the gravitational pull of the earth its value is fixed at the surface n is equal to 9.8u.
What is air friction?Aries composed of molecules and their food when an object passes through air strikes the a molecules they are molecules according to Newton's third law strike back at the object therefore reducing its speed. This force by the molecule is known as air friction.
The setup of the given experiment consists of:
A bob of mass m
A stopwatch with high accuracy
An inch tape
A speedometer
Experiment is conducted in the following manner:
First the bob will be released and from the point that it is being released we will measure the distance using the inch tape we will also calculate the time it takes for the bob to hit the ground.Using the speedometer will measure the final velocity before it is the ground.Now using Newton's first law of motion we can derive the acceleration due to gravity we know the final velocity using the speedometer the distance it has covered and the time it has taken to complete that distance.Using Newton's first law of motion
i.e. v = u + a × t
Where,
u is initial velocity
v is final velocity
a is acceleration due to gravity
t is time taken to cover distance
From the data given v = 16.82m/s
t is 2 seconds
Substituting value in Newton's first law of motion we get
Value of acceleration due to the gravity = 8.41
Therefore, The experimental value of the expression due to gravity through the experiment will come out to be 8.41u, the error in the value has Accord because of air friction.
Learn more about Newton's law of motion here:
https://brainly.com/question/974124
#SPJ1
A dog races up the stairs in a time of 1.80 seconds. If the stairs are 12 feet high, how much power in hp is the dog putting out? The weight of the dog is 48 lbs
Answers
The time taken by the dog to climb the stairs, t=1.80 s
The height of the stairs, h= 12 feet=3.66 m
The weight of the dog, m=48 lbs=21.77 kg
The work done by the dog in climbing up the stairs is,
\(W=\text{mgh}\)Where g is the acceleration due to gravity.
On substituting the known values,
\(W=21.77\times9.8\times3.66=780.85\text{ J}\)The power is given by,
\(P=\frac{W}{t}\)On substituting the known values,
\(P=\frac{780.85}{1.80}=433.80\text{ J/s}\)1 J/s = 1.34×10³ hp
Therefore,
\(433.80\text{ J/s=433.80}\times1.34\times10^3\text{ hp=581.3}\times10^3\text{ hp}\)Therefore the power put out by the dog is 581.3×10³ hp
Three cars are driving at 29.0 m/s along the road shown in the figure (Figure 1). Car B is at the bottom of the hill and car C is at the top. Suppose each car suddenly brakes hard and starts to skid. Assume μk=1.00. What is the x-component of the tangential acceleration (i.e., the acceleration parallel to the road) of car A?
Answers
Since the car masses are unknown, we are unable to calculate the numerical value of the x-component of Car A's tangential acceleration.
How do kinetic and potential energy compare?The energy that is held in any object or system as a function of its position or component arrangement is known as potential energy. The object or system is unaffected by external factors like air pressure or altitude. Kinetic energy, on the other hand, describes the power of moving particles within a system or an object.
They are being affected by the kinetic frictional force, which is caused by:
f = μk * N
Therefore,
fB = μk * N = μk * mB * g
Car C is at its highest point at the top of the hill, where the normal force acting on it is equal to the force of gravity. Therefore,
fC = μk * N = μk * mC * g
where mC is the mass of Car C.
For Car A, the x-component of the tangential acceleration is given by:
aA = (fB - fC) / mA
where mA is the mass of Car A.
We can substitute the following values and simplify by assuming that the mass of each of the three automobiles is the same:
aA = (μk * mB * g - μk * mC * g) / mA
aA = μk * g * (mB - mC) / mA
Since μk = 1.00 and g = 9.81 m/s², we can plug in the values and get:
aA = (mB - mC) * 9.81 / mA
To know more about tangential acceleration visit:-
https://brainly.com/question/14993737
#SPJ1
Graph a heating curve for water. Label (with the most specific names & numbers) the following parts of the graph, adding units where appropriate:
1) x axis
2) y axis
3) title
4) all 3 phases of matter
5) show where KE is increasing
6) show where PE is increasing
7) identify the phases changes
Answers
Answer:
Explanation:
1. x-axis: Temperature (in degrees Celsius)
2. y-axis: Heat (in Joules)
3. Title: Heating Curve for Water
4. All 3 phases of matter: solid (ice), liquid (water), gas (steam)
5. Show where KE is increasing: The line segment from A to B represents the increase in kinetic energy as the water is heated from solid to liquid state, and the line segment from C to D represents the increase in kinetic energy as the water is heated from liquid to gas state.
6. Show where PE is increasing: The line segment from A to B represents the increase in potential energy as the ice is melting into water, and the line segment from C to D represents the increase in potential energy as the liquid water is vaporizing into steam.
7. Identify the phase changes: The segment from A to B represents the melting of ice (solid to liquid), and the segment from C to D represents the vaporization of water (liquid to gas). The flat portions between B and C represent the heating of water in liquid state and the absorption of heat without any change in temperature (latent heat of fusion and latent heat of vaporization).
Which is the best description of biodiversity?
1. All animals in an ecosystem
2. The variety of the type of life within the biosphere
3. The study of life
3. The variety of plants on Earth
Answers
Answer:2
Explanation:
Which techniques can scientists use to determine the characteristics of Earth's layers? Select the two correct answers.
examine the behavior of minerals at extremely low temperatures
study how seismic waves travel through different layers
drill deep mines to obtain samples from Earth's mantle and core
conduct experiments about how minerals change under high pressure
use X-rays to obtain a view of Earth's interior layers
Answers
The techniques that scientists can use to determine the characteristics of Earth's layers include:
study how seismic waves travel through different layersuse X-rays to obtain a view of Earth's interior layersWaves were used by scientists to study the layers of the Earth. This was done through the use of seismic waves. These are the waves that are generated by nuclear test explosions.
Also, another technique to determine the characteristics of Earth's layers is the use X-rays to obtain a view of Earth's interior layers.
Read related link on:
https://brainly.com/question/14646338
Answer:
study how seismic waves travel through different layers
use X-rays to obtain a view of Earth's interior layers
:)
Explanation:
Enunciado: Una bola se lanza verticalmente de la parte superior de un edificio con una velocidad inicial de 25 m/s. La bola impacta al suelo en la base del edificio 7 segundos después de ser lanzada. (Marque la respuesta correcta)
¿Qué altura subió la bola (medida desde la parte superior del edificio)? a) 19.6 m b) 12.75 m c) 31.88 m d) 40 m e) 20 m
Answers
Responder:
Explicación:
Usaremos la ecuación de movimiento para determinar la altura de la bola medida desde la parte superior del edificio.
Usando la ecuación para obtener la altura de caída
S = ut + 1 / 2gt²
u es la velocidad inicial = 25 m / s
g es la aceleración debida a la gravedad = 9,81 m / s²
t es el tiempo = 7 segundos
S es la altura de la caída
S = 25 (7) +1/2 (9,81) × 7²
S = 175 + 4,905 (49)
S = 175 + 240,345
S = 415,35 m
Esto significa que la pelota se elevó a 415,35 m de altura
La altura vertical máxima alcanzada es de 31,88 m.
Tenemos la siguiente información de la pregunta;
Velocidad inicial = 25 m/s
Velocidad final = 0 m/s (a la altura máxima)
tiempo empleado = 3,5 minutos (el tiempo empleado para subir y bajar es igual).
Usando la ecuación;
v^2 = u^2 - 2gh
Dado que v = 0
u^2 = 2gh
h = tu^2/2g
h = (25)^2/2 *9.8
h = 31,88 m
Obtenga más información sobre las ecuaciones de movimiento: https://brainly.com/question/8898885
You put your book on the bus seat next to you. When the bus stops suddenly the book slides forward off the seat. Why?
A.) The book received a push from the seat hitting it.
B.) The force applied by the bus caused it to accelerate forward.
C.) The book's inertia carried it forward.
D.) The book could never slide forward to begin with.
Answers
Answer:
C) The book's inertia carried it forward.
When the bus stops suddenly, the book tends to remain in motion due to its inertia. The book was at rest on the seat of the bus, and when the bus stopped suddenly, the book continued moving forward with the same speed and direction it had before the bus stopped. As a result, the book slid off the seat and onto the floor.
A wrench is accidentally dropped at the top of an elevator shaft in a tall building. (a) How many meters does the wrench fall in 1.5s
Answers
Answer:
11.25m
Explanation:
\(s = ut + \frac{1}{2} a {t}^{2} \\ = 0 \times 1.5 + \frac{1}{2} \times 10 \times {1.5}^{2} \\ = 5 \times 2.25 \\ = 11.25\)
if a bird catches its prey from a height which was initially at rest then momentum is conserved for?
Bird
Prey
Both
None
Answers
For the two animals involved (bird and its prey), the momentum of both animals is conserved.
What is principle of conservation of linear momentum?
The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.
Initial momentum = final momentum
Thus, for the two animals involved (bird and its prey), the momentum of both animals is conserved.
Learn more about conservation of linear momentum here: https://brainly.com/question/7538238
#SPJ1
A supercluster is 100 million light-years across. How long would it take light to travel from one edge of the supercluster to the center of the supercluster?
Answers
Answer:
50 million years
Explanation:
light years is the distance light travels in one year given that the supercluster is 100 million light years across the the distance to the center will be half that amount therefore the answer is 50 million years
A copper (Young's modulus 1.1 x 1011 N/m2) cylinder and a brass (Young's modulus 9.0 x 1010 N/m2) cylinder are stacked end to end, as in the drawing. Each cylinder has a radius of 0.32 cm. A compressive force of F = 5000 N is applied to the right end of the brass cylinder. Find the amount by which the length of the stack decreases.
Answers
The length of the stack shortens by 4.88 x 10-6 m.
What is Young's brass modification?Brass and steel have Young's modules of 1.0 and 2 respectively, 1010N/m2. Under the same force, a brass wire of the same length and a steel wire with radii of RB and RS, respectively, are both expanded by 1 mm.
The change in length of each cylinder due to the compressive force can be found using the formula:
ΔL = (F * L) / (A * E)
First, let's find the cross-sectional area of each cylinder:
A = π * r² = π * (0.32 cm)² = 0.3217 cm²
L = Lcopper + Lbrass
L = 2 * Lcopper
Ftotal = Fbrass + (-Fcopper) = Fbrass - Fbrass = 0
Since the total force on the stack is zero, the amount by which the length of the stack decreases is the same as the amount by which the length of the brass cylinder decreases:
ΔL = (Fbrass * Lbrass) / (Abrass * Ebrass)
ΔL = (5000 N * Lbrass) / (0.3217 cm²* 9.0 x 10¹⁰ N/m²)
ΔL = (1.554 x 10⁻⁴ m/N) * Lbrass
V = π * r² * Lbrass
Lbrass = V / (π * r²)
Lbrass = 1 cm / (π * (0.32 cm)^2)
Lbrass = 3.14 cm
Finally, we can substitute this value into the equation for ΔL:
ΔL = (1.554 x 10⁻⁴ m/N) * 3.14 cm
ΔL = 4.88 x 10⁻⁶ m
To know more about length visit:-
https://brainly.com/question/30284988
#SPJ1
8. Two perpendicular forces, one of 45.0 N directed upward and the other of 60.0 N directed to the
right, act simultaneously on an object with a mass of 35.0 kg. What is the magnitude of the
resultant acceleration of the object?
a) 2.14 m/s
b) 5.25 m/s
c) 3.00 m/s
d) 1.41 m/s
Answers
Answer:
\(a=2.14\ m/s^2\)
Explanation:
Force in upward direction = 45 N
Force in right side = 60 N
Mass of the object, m = 35 kg
Net force on the object is given by :
\(F=\sqrt{45^2+60^2} \\F=75\ N\)
We know that,
F = ma
Where
a is acceleration of the object
\(a=\dfrac{F}{m}\\\\a=\dfrac{75\ N}{35\ kg}\\\\a=2.14\ m/s^2\)
So, the acceleration of the object is \(2.14\ m/s^2\).
Don’t understand how to do this question!!!
Answers
Refer to the photos. So I kind of interpreted this problem in two different ways. You'll have to let me know which one ended up being the correct way to go about the problem. But hopefully this helps you get thinking!
Calculate the efficiency of a compact fluorescent light if a power input of 20 J/s gives an output power of 9 J/s.
Answers
The efficiency of the machine is 45%
What is efficiency?Efficiency is a measure of how well a system, process, or machine uses resources to produce outputs compared to the inputs used. It indicates the extent to which time, effort, and resources are used effectively to achieve desired goals and minimize waste. The efficiency of a system can be improved by reducing inputs, increasing outputs, or a combination of both.
The efficiency is;
Output power/ Input power * 100/1
= 9/20 * 100/1
= 45%
Learn more about efficiency:https://brainly.com/question/30280642
#SPJ1
A 682-kg elevator starts from rest and moves upward for 3.10 s with constant acceleration until it reaches its cruising speed, 1.80 m/s.
(a) What is the average power of the elevator motor during this period? (Answer in horsepower)
(b) How does this amount of power compare with its power during an upward trip with constant speed? (Give the power during an upward trip with
constant speed.) (answer in horsepower)
Answers
a) the average power of the elevator motor during this period is 0.1696 hp
b) The power during an upward trip with constant speed is 16.13 horsepower.
To calculate the average power of the elevator motor during the period of acceleration, we need to find the work done by the motor and divide it by the time taken.
Given:
Mass of the elevator (m) = 682 kg
Acceleration (a) = (1.80 m/s - 0) / 3.10 s = 0.5806 m/s²
Time taken for acceleration (t) = 3.10 s
(a) First, let's calculate the displacement (d) using the formula for uniformly accelerated motion:
d = 0.5 * a * t^2
= 0.5 * 0.5806 m/s² * (3.10 s)^2
= 1.0153 m
Next, we can calculate the work done (W) by the elevator motor:
W = m * a * d
= 682 kg * 0.5806 m/s² * 1.0153 m
= 391.55 J
Now, to find the average power (P), we divide the work done by the time taken:
P = W / t
= 391.55 J / 3.10 s
= 126.36 W
To convert the power to horsepower, we can use the conversion factor: 1 horsepower (hp) = 745.7 watts.
Therefore, the average power of the elevator motor during this period is:
P = 126.36 W / 745.7
= 0.1696 hp
(b) During an upward trip with constant speed, the elevator does not accelerate, so the power required is only to counteract the force of gravity and friction. The power during an upward trip with constant speed is equal to the power required to overcome the force of gravity and friction.
The force of gravity (Fg) can be calculated using:
Fg = m * g
= 682 kg * 9.8 m/s²
= 6683.6 N
The power (P) required is given by the formula:
P = Fg * v
= 6683.6 N * 1.80 m/s
= 12030.5 W
To convert the power to horsepower:
P = 12030.5 W / 745.7
= 16.13 hp
Therefore, the power during an upward trip with constant speed is 16.13 horsepower.
Know more about work done here:
https://brainly.com/question/28356414
#SPJ8
A hot dog cooker heats hot dogs by connecting them to 120 V household electricity. A typical hot dog has a mass of 70 g and a resistance of 160 Ω.
Part A
How long will it take for the cooker to raise the temperature of the hot dog from 20∘C to 85 ∘C? The specific heat of a hot dog is approximately 2500 J/kg⋅K
Answers
It will take about 233.34 seconds for the hot dog cooker to raise the temperature of the hot dog from 20∘C to 85∘C.
What is specific heat?Specific heat is the amount of heat energy required to raise the temperature of a substance by one degree Celsius or one Kelvin per unit mass.
Here,
To solve this problem, we can use the formula for the amount of heat required to change the temperature of an object,
Q = mcΔT
First, we need to calculate the amount of heat required to raise the temperature of the hot dog from 20∘C to 85∘C:
Q = (0.07 kg)(2500 J/kg⋅K)(85∘C - 20∘C)
Q = 1058.5 J
Next, we can use the formula for electrical power,
P = IV
We can rearrange this formula to solve for the current:
I = P/V
The power required to heat the hot dog can be calculated using the formula for electrical power:
P = V²/R
Substituting the given values, we get:
P = (120 V)²/160 Ω
P = 90 W
I = 90 W/120 V
I = 0.75 A
Finally, we can use the formula for the amount of time required to transfer a certain amount of heat:
t = Q/(IΔT)
Substituting the values we calculated, we get:
t = 1058.5 J/(0.75 A)(65∘C)
t = 233.34 s
Therefore, it will take about 233.34 seconds for the hot dog cooker to raise the temperature of the hot dog from 20∘C to 85∘C.
Learn more about specific heat here:
https://brainly.com/question/11297584
#SPJ1
4. True or false. When measuring a liquid ingredient, the measuring cup should be held up so the mark on
the cup for the desired amount is at eye level.
Foods class
Answers
Adiabatic Equation of State Derive the adiabatic equation of state (2.3.19) using particle conservation (2.3.7) and energy conservation (2.3.21), by assuming that the heat flow vector q and all collision terms in these equations are zero.
p=Cn^{\gamma } Equation 19
\frac{\partial n}{\partial t}+\bigtriangledown (nu)=G-L Equation 7
\bigtriangledown (\frac{3}{2}pu)=\frac{\partial }{\partial t}(\frac{3}{2}p)\mid c Equation 22
Answers
Answer:
Explanation:
jhgfhmhvmghmm
The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?
Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.
Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!
Answers
The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.
The p-waves travel with a constant velocity of 7 km/s
The time can be calculated by using the formula
t = d / v
where
T1 = 10:05 a.m
d is the distance they take to travel from the epicenter
v is the speed of the p-waves
On average, the speed of p-waves is
v = 7 km/s
d = 5600 km (given)
Substituting the values in the formula;
t = d / v
t = 5600 ÷ 7
t = 800 seconds
Converting into minutes,
t = 800 ÷ 60
t = 13.3
≈ 13 mins
T1 - 13 mins = T2
10:05 - 13 mins = 9.52 am
It means the earthquake occurred prior 13 minutes, that is at 9.52 am.
Therefore, the earthquake occurred at 9.52 am.
Learn more about earthquakes from the given link.
https://brainly.com/question/25843505
Darrel wakes up and notices there are water droplets on his window. He is confused about why there are water droplets because it did not rain last night. Which of the following statements best explains why there are water droplets on the window?
Answers
Answer:
You didn't put any options but there are water droplets on the window due to dew-condensation.
Explanation:
I learned this in class.
Answer:
its C or D
Explanation:
The energy from the sun caused water to heat up and evaporate.
if a and b are vectors, write the mathematucal expressioons of scalar quantity
Answers
Magnitude of a vector: The magnitude of a vector a is a scalar quantity, denoted by |a|. It is given by:
|a| = sqrt(a . a)
where a . a is the dot product of a with itself.
Dot product of two vectors: The dot product of two vectors a and b is a scalar quantity, denoted by a . b. It is given by:
a . b = |a| |b| cos(theta)
where |a| and |b| are the magnitudes of vectors a and b, respectively, and theta is the angle between them.
Projection of a vector: The projection of a vector a onto another vector b is a scalar quantity, denoted by proj_b(a). It is given by:
proj_b(a) = |a| cos(theta)
where theta is the angle between vectors a and b.
Scalar triple product of three vectors: The scalar triple product of three vectors a, b, and c is a scalar quantity, denoted by (a x b) . c. It is given by:
(a x b) . c = det([a b c])
where det([a b c]) is the determinant of the matrix formed by the vectors a, b, and c.
Three vectors with magnitudes 120N, 100N and 80N are given in the diagram below. Write them using the unit vectors i, j and k. . 100N 80N 53° 40° Y 37° 120N X Trigonometric values you may use Cos37⁰ = 0.8 = sin53° sin37° 0.6 = cos53° cos40° = 0.766, sin40° = 0.643
Answers
The vectors can be expressed using unit vectors as follows:
Vector A = 96N i + 96N j + 0N k
Vector B = 76.6N i + 64.3N j + 0N k
Vector C = 64N i + 48N j + 0N k.
In the given diagram, let's consider the vectors as follows:
Vector A with magnitude 120N, Vector B with magnitude 100N, and Vector C with magnitude 80N.
To express these vectors using unit vectors i, j, and k, we need to determine their respective components in the x, y, and z directions.
For Vector A (120N), we have the following information:
Magnitude = 120N
Direction: X-axis (cosine component) with an angle of 37° and Y-axis (sine component) with an angle of 53°.
Using the trigonometric values provided:
cos37° = 0.8 and sin53° = 0.8
Therefore, the components of Vector A are:
Ax = 120N * 0.8 = 96N (in the X-direction)
Ay = 120N * 0.8 = 96N (in the Y-direction)
Az = 0N (no component in the Z-direction)
Thus, Vector A can be written as 96N i + 96N j + 0N k.
Similarly, using the trigonometric values for Vector B and Vector C, we can calculate their components:
For Vector B (100N):
Bx = 100N * cos40° = 100N * 0.766 = 76.6N
By = 100N * sin40° = 100N * 0.643 = 64.3N
Bz = 0N
Vector B can be expressed as 76.6N i + 64.3N j + 0N k.
For Vector C (80N):
Cx = 80N * cos37° = 80N * 0.8 = 64N
Cy = 80N * sin37° = 80N * 0.6 = 48N
Cz = 0N
Vector C can be written as 64N i + 48N j + 0N k.
In summary, the vectors can be expressed using unit vectors as follows:
Vector A = 96N i + 96N j + 0N k
Vector B = 76.6N i + 64.3N j + 0N k
Vector C = 64N i + 48N j + 0N k.
For more questions on Magnitude , click on:
https://brainly.com/question/30337362
#SPJ8
URGENT HELP PLS
(a) Find the frequency ratio between the two frequencies f1 = 320 Hz and
½2 = 576 Hz.
S) If we go down from / by an interval of a fourth, find the frequency ratio filfi.
(c) Find the frequency of f3.
Answers
The frequency of f3 is approximately 716 Hz.
What is frequency?The frequency of a repeated event is its number of instances per unit of time. Hertz (Hz), which stands for the number of cycles per second, is a popular unit of measurement.
a. Given two frequencies, f1 and f2, the frequency ratio is as follows:
frequency ratio= \(\frac{f2}{f1}\)
Inputting the values provided yields:
frequency ratio = \(\frac{576}{320Hz}\) =1.8.
As a result, the difference in frequency between f1 = 320 Hz and f2 = 576 Hz is 1.8.
b. Since there are 12 half-steps in an octave and a fourth is a distance of 5 half-steps, going down a fourth requires dividing the frequency by \(2^{(4/12)}\). Hence, once a fourth is subtracted, the frequency ratio between f and f1 is:
frequency ratio= \(\frac{f}{ (f1 /f2 ) }\)= \(\frac{f}{ (f1 / 1.3348) }\)
By dividing the numerator and denominator by 1.3348, we may make this more straightforward:
frequency ratio= (f × 1.33348)/f1
As a result, (f × 1.3348) / f1 is the frequency ratio between f and f1 after descending a fourth.
c. (c) To find the frequency of f3, we need to know the interval between f1 and f3. Let's assume that f3 is a fifth above f2. The frequency ratio for a fifth is given by: \(2^{(7/12)}\) = 1.49831
Therefore, the frequency of f3 is:
f3 = f1 × (\(2^{(7/12)}\)) × (\(2^{(7/12)}\)) = 320 Hz × 1.49831 ×1.49831 = 716 Hz
Therefore, the frequency of f3 is approximately 716 Hz.
To know more about frequency, visit:
brainly.com/question/14316711
#SPJ1