Answer:
You take the light from a star, planet or galaxy and pass it through a spectroscope, which is a bit like a prism letting you split the light into its component colours. "It lets you see the chemicals being absorbed or emitted by the light source. From this you can work out all sorts of things," says Watson
How to find the angle in a projectile motion when displacement and heigh are the same
projectile's vertical speed v yv y v, start , y, drops prior to reaching its maximum height since its acceleration is in the opposite direction. Since the object's height is rising, the initial direction of the velocity is upward
.
At the projectile's highest point, vertical velocity zeroes out. After reaching the highest point, the vertical speed increases due of the same-direction acceleration. As the object's height lowers, the vertical velocity has a downward direction.
In projectile The beginning vertical velocity determines the maximum height. Increasing the launch angle raises the maximum height because steeper launch angles have a larger vertical velocity component.
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A 615 N student standing on a scale in an elevator notices that the scale reads 645 N. From this information, the student knows that the elevator must be moving
a) downwards
b) upwards
c) you cannot tell if it is moving upward or downward.
I thought the answer would be B but it says it is C
A 615 N student standing on a scale in an elevator notices that the scale reads 645 N. From this information, the student cannot tell that if the elevator is moving upward or downward. The correct answer is option C.
The reason for this is that the scale reading depends not only on the weight of the student but also on the acceleration of the elevator. If the elevator is accelerating upwards, the scale will read more than the actual weight of the student.
Similarly, if the elevator is accelerating downwards, the scale will read less than the actual weight of the student.
In this case, we know that the scale reads 645 N, which is 30 N more than the actual weight of the student (615 N).
However, we don't know whether the elevator is accelerating upwards or downwards. It could be accelerating upwards with an acceleration of 3 m/s^2 (in which case the apparent weight would be 645 N), or it could be accelerating downwards with an acceleration of 3 m/s^2 (in which case the apparent weight would be 585 N).
Therefore, based on the information given, we cannot determine whether the elevator is moving upwards or downwards. The correct option is c.
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A proton starts from rest, and moves 1 meter through a constant electric field. The potential difference between its starting and ending points is 500 V. How fast is the proton moving at the end? How large is the electric field? How long does it take the proton to complete its journey? [Late clarification: since the field is accelerating the particle from rest, you can assume that the direction of the particle's motion is parallel to the field.]
Answer:
E = - 500 V / m, v = 30.95 10⁴ m / s and t = 6.46 10⁻⁶ s
Explanation:
For this problem we use the relation
ΔU = - E s
E = -ΔU / s
E = - 500/1
E = - 500 V / m
Now we can look for the proton approach
F = q E
let's use Newton's second law
F = m a
a = F / m
a = q E / m
Now let's use kinematics relations, where the proton starts from the rest
v₀ = 0
v² = v₀² + 2 a x
v = √2 q E / m x
v = √ (2 1.6 10⁻¹⁹ 500 / 1.67 10⁻²⁷ 1)
v = √ (958.08 108)
v = 30.95 10⁴ m / s
for time let's use the equation
x = v₀ t + ½ to t2
t = √2x / a
t = √ (2x m / qE)
t = √ (2 1 1.67 10⁻²⁷ / (1.6 10⁻¹⁹ 500))
t = √ (0.004175 10⁻⁸)
t = 0.0646 10⁻⁴ s
t = 6.46 10⁻⁶ s
Equation of path of projectile is y=x(1-x)
The equation of the path of a projectile is y = x(1 - x). Projectile motion is the movement of an object in a parabolic trajectory as a result of being propelled or released under the influence of gravity. A projectile, in simple terms, is any object that is launched into the air, such as a bullet, a baseball, or a rock. It's important to note that the parabolic trajectory is due to the force of gravity acting on the object.
To better understand projectile motion, we must first examine the horizontal and vertical components of motion. The horizontal component of motion is constant, indicating that there is no acceleration in that direction. The vertical component, on the other hand, has acceleration because of gravity. The parabolic trajectory is the result of these two components of motion.As the projectile is launched, it travels a certain distance horizontally before beginning to descend as a result of gravity's influence, resulting in a parabolic path.The general formula for the trajectory of a projectile in two dimensions is given by:y = xtanθ - (gx²) / 2(v₀cosθ)²Where:y is the vertical distance covered by the projectilex is the horizontal distance covered by the projectileθ is the angle of projectiong is the acceleration due to gravityv₀ is the initial velocity of the projectile In the case of the given equation, y = x(1 - x), the path of the projectile will be a parabolic trajectory with a vertex at x = 0.5 and y = 0.25. The equation represents the projectile's vertical distance, y, as a function of its horizontal distance, x. It is crucial to note that the projectile's initial velocity and angle of projection are not considered in this equation.For such more question on acceleration
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earth energy budget is the relationship between how much energy the earth _______ and energy the earth _________
earth energy budget is the relationship between how much energy the earth receive from the sun and energy the earth radiates out.
What is energy?Energy is described as the quantitative property that is displaced to a body or to a physical system, recognizable in the performance of work and in the form of heat and light.
The term earth's energy budget is also described as the balance between of the amount of energy, that gets to the earth. from the Sun and the energy that leaves Earth and returns to the universe.
The earth's energy budget was mainly three types as shown:
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Water flows steadily from an open tank as shown in the figure. (Figure 1)The elevation of point 1 is 10.0 m , and the elevation of points 2 and 3 is 2.00 m . The cross-sectional area at point 2 is 4.80×10−2 m2 ; at point 3, where the water is discharged, it is 1.60×10−2 m2 . The cross-sectional area of the tank is very large compared with the cross-sectional area of the pipe. What is the gauge pressure p_gauge at point 2?
The gauge pressure at point 2 is 98100 Pa or 9.81 x\(10^4\) Pa, which is equivalent to 6.97 x\(10^4\) Pa when rounded to two significant figures.
Step 1: Identification of the given data:
- Elevation at point 1 (h1) = 10.0 m
- Elevation at points 2 and 3 (h2 = h3) = 2.00 m
- Cross-sectional area at point 2 (A2) = 0.0480 \(m^2\)
- Cross-sectional area at point 3 (A3) = 0.0160 \(m^2\)
Step 2: Determination of the discharge rate:
As mentioned earlier, the discharge rate (Q) is given by Q = A2 * v2, and since the velocity at point 2 (v2) is negligible, the discharge rate will be 0.
Therefore, the discharge rate is 0 cubic meters per second.
Step 3: Determination of the gauge pressure at point 2:
To find the gauge pressure at point 2, we'll use Bernoulli's equation:
P1 + (1/2)ρ\(v1^2\) + ρgh1 = P2 + (1/2)ρ\(v2^2\) + ρgh2
Since the velocity at point 2 (v2) is negligible, the term (1/2)ρ\(v2^2\) can be ignored.
The equation simplifies to:
Patm + ρgh1 = P2 + ρgh2
We want to find the gauge pressure at point 2, so we'll subtract the atmospheric pressure (Patm) from P2:
\(P_g_a_u_g_e\) = P2 - Patm
Now let's substitute the given values into the equation:
\(P_g_a_u_g_e\) = (Patm + ρgh1) - Patm
\(P_g_a_u_g_e\) = ρgh1
Plugging in the values:
\(P_g_a_u_g_e\) = (1000 kg/m^3) * (9.81 \(m/s^2\)) * (10.0 m)
\(P_g_a_u_g_e\) = 98100 Pa
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what is the total time that the bullet is in contact with the board?
Answer:
an acceleration of the boy as it passes through the board and be the total time the boy is in contact with the board solution
The tires of a car make 90 revolutions as the car reduces its speed uniformly from 88.0 km/hkm/h to 56.0 km/hkm/h. The tires have a diameter of 0.84 mm.
1. What was the angular acceleration of the tires?
2. If the car continues to decelerate at this rate, how much more time is required for it to stop?
3. If the car continues to decelerate at this rate, how far does it go? Find the total distance.
Answer:
1) α = 2.2 rad / s² , 2) t = 7.068 s , 3) in this interval s = 23.096 m
total distance s = 57.4 m
Explanation:
For this exercise we use the angular kinematic relations, before starting the problem we reduce all the magnitude to the SI system
v₀ = 88 km / h (1000 m / 1km) 1h / 3600s) = 24.44 m / s
v = 56.0 km / h = 15.55 m / s
θ = 90 rev (2pi rad / 1 rev) = 565,487 rad
d = 0.84 m
r = d / 2
r = 0.84 / 2
r = 0.42 m
1) ask for angular acceleration
w² = w₀² - 2 α Δθ
α = (w₀² -w²) / 2 Δθ
To find the angular velocities we use the acceleration between the linear and angular velocity
v = w r
w = v / r
w₀ = 24.44 / 0.42
w₀ = 58.20 rad / s
w = 15.55 / 0.42
w = 30.037 rad / s
we calculate
α = (58.20² - 30.037²) / (2 565.487)
α = 2.2 rad / s²
2) how much longer does it take to stop
w₂ = 15.55 rad / s
w = 0
w = w₂ - α t
t = (w₂ -0) / α
t = 15.55 / 2.2
t = 7.068 s
3) the distance that the car travels from the beginning of the movement, we can find it by looking for the number of revolutions until it stops and then using the relationship between the angular and linear variable
w² = w₀² - 2 α θ
at the end of the movement speed is zero
0 = w₀² - 2 α θ
θ = w₀² / 2 α
θ = 24.44² / (2 2.2)
θ = 135.80 rad
If the angles are measured in radians, we can apply the relation
θ = s / R
s = R ttea
s = 0.42 135
s = 57.4 m
this is the distance from when the movement starts
the distance for the final part of the movement is
w = 15.55 rad / s
θ = w² / 2 α
θ = 15.55 2 / (2 2.2)
θ = 54.99 rad
the distance in this interval is
s = 0.42 54.99
s = 23.096 m
Which statement correctly compares sound and light waves?Both light and sound waves need matter to carry energy from one place to another.Neither light nor sound waves need matter to carry energy from one place to another.Light waves carry energy parallel to the motion of the wave, while sound waves carry energy perpendicular to it.Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
What is energy parallel?Energy parallel is a type of energy efficiency strategy that seeks to reduce the amount of energy used in a building or facility by utilizing multiple energy sources instead of relying solely on one. This type of energy efficiency strategy works by drawing energy from multiple sources, such as solar, geothermal, wind, and water energy, and combining them to power a single building or facility. By utilizing multiple energy sources, energy parallel helps to reduce the overall amount of energy used in a building or facility, thus improving its overall energy efficiency. Additionally, this type of energy efficiency strategy helps to reduce the amount of energy that is wasted or lost by utilizing energy sources that are renewable and more sustainable.
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Two cars collide head-on and stick together.
Car A, with a mass of 2000 kg, was initially
moving at a velocity of 10 m/s to the east. Car
B, with an unknown mass, was initially at rest.
After the collision, both cars move together at
a velocity of 5 m/s to the west. What is the
mass of Car B?
OF
The mass of Car B is -6000 kg.
To solve this problem, we can apply the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
Therefore, we can write the equation for the conservation of momentum as:
(mass of Car A * velocity of Car A) + (mass of Car B * velocity of Car B) = (mass of Car A + mass of Car B) * velocity after collision
Let's substitute the given values into the equation:
(2000 kg * 10 m/s) + (mass of Car B * 0 m/s) = (2000 kg + mass of Car B) * (-5 m/s)
Simplifying the equation:
20000 kg*m/s = -5 m/s * (2000 kg + mass of Car B)
Dividing both sides by -5 m/s:
-4000 kg = 2000 kg + mass of Car B
Subtracting 2000 kg from both sides:
mass of Car B = -4000 kg - 2000 kg
mass of Car B = -6000 kg
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High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers have calculated the maximum horsepower for the engine to be 630HP
. Twenty five engines are randomly selected for horsepower testing. The sample has an average maximum HP of 650
with a standard deviation of 60HP
. Assume the population is normally distributed.
Step 1 of 2 : Calculate a confidence interval for the average maximum HP for the experimental engine. Use a significance level of α=0.01
. Round your answers to two decimal places.
The 99% confidence interval for the average maximum HP for the experimental engine is (610.12, 689.88).
To calculate the confidence interval for the experimental engines' average maximum HP, we can use the following formula:
To find the z-score for α=0.01, we can refer to a standard normal distribution table or use a calculator. The z-score is approximately 2.58.
Substituting the given values into the formula, we get:
CI = 650 ± 2.58*(60/√25) CI = 650 ± 30.96
Rounding to two decimal places, the confidence interval for the experimental engines' average maximum HP is:
CI = [619.04 HP, 680.96 HP]
Therefore, we can say with 99% confidence that the true average maximum HP for the experimental engines falls between 619.04 HP and 680.96 HP. Thus, we can conclude that the experimental engines' average maximum HP is likely to be within this range. However, note that this range does not include the manufacturer's claimed maximum HP of 630 HP, which may indicate that the engines are performing below expectations.
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What is a pendulum?
A.)A pendulum is a grandfather clock.
B.)A pendulum is a mass suspended on the bottom of a string.
C.)A pendulum is several weights tied together and arranged in a circle.
D.) A pendulum is the time it takes for a bob to swing back and forth one time.
B) A pendulum is a mass suspended on the bottom of a string.
A pendulum is a simple mechanical device that consists of a mass (known as the bob) suspended from a fixed point by a string, wire, or rod. When the bob is pulled to one side and released, it swings back and forth under the influence of gravity, forming a regular pattern of motion. The time it takes for the pendulum to complete one full swing (i.e., from one extreme position to the other and back again) is known as its period. The period of a pendulum is affected by the length of the string and the strength of gravity. The longer the string, the longer the period, and the stronger the gravity, the shorter the period.Pendulums have a wide range of practical applications, such as timekeeping, as seen in grandfather clocks. They are also used in scientific experiments to measure time intervals and gravitational acceleration.
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10. Convert the following:
a. 37.4 mL into ML
b. 689 km/hr into m/s
c. 34.5 m² into mm²
A. When we convert 37.4 mL to ML, the result obtained is 3.74×10¯⁸ ML
B. When we convert 689 km/hr to m/s, the result obtained is 191.39 m/s
C. When we convert 34.5 m² to mm², the result obtained is 3.45×10⁷ mm²
A. How to convert millimeters (mL) to megaliter (ML)Volume (mL) = 37.4 mLVolume (ML) =?1 mL = 1×10¯⁹ ML
Therefore,
37.4 mL = 37.4 × 1×10¯⁹
37.4 mL = 3.74×10¯⁸ ML
Thus, 37.4 mLis equivalent to 3.74×10¯⁸ ML
B. How to convert 689 km/hr to m/sConversion scale
3.6 Km/hr = 1 m/s
Therefore,
689 km/hr = 689 / 3.6
689 km/hr = 191.39 m/s
Thus, 689 km/hr is equivalent to 191.39 m/s
C. How to convert 34.5 m² to mm²Conversion scale
1 m² = 1×10⁶ mm²
Therefore,
34.5 m² = 34.5 × 1×10⁶
34.5 m² = 3.45×10⁷ mm²
Thus, 34.5 m² is equivalent to 3.45×10⁷ mm²
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Please help me Thanks!
l will help and if you get it correctly I will say you are welcome
A ball weighing 60 N is swinging like a pendulum at the end of a 6.0 m rope. As the ball swings through its lowest point, its speed is measured at 5.0 m/s. What is the tension in the rope at this point?
A. 58.6 N
B. 85.4 N
C. 90.2 N
D. 97.3 N
Answer:
85.4 N
Explanation:
Weight of the ball, W = 60 N
W = mg, m is mass
m = W/g
m = 60/9.8 = 6.12 kg
Length of a rope, r = 6 m
Speed, v = 5 m/s
We need to find the tension in the rope at this point. Tension is equal to the centripetal force It is given by :
\(F=\dfrac{mv^2}{r}+mg\\\\F=\dfrac{6.12\times (5)^2}{6}+60\\\\=85.5\ N\)
So, the correct option is (b) " 85.4 N".
Problem
THE FLIGHT OF A BALL A ball is launched at 5.5 m/s at 76° above
the horizontal. It starts and lands at the same distance from the
ground. What are the maximum height above its launch level and the
flight time of the ball?
1. The maximum height above its launch level is 1.45 m
2. The time of flight of the ball is 1.1 s
1. How do I determine the maximum height?
From the question given above, the following data were obtained:
Initial velocity (u) = 5.5 m/sAngle of projection (θ) = 76 °Acceleration due to gravity (g) = 9.8 m/s²Maximum height (H) =?The maximum height can be obatianed as follow:
H = u²Sine²θ / 2g
H = [5.5² × (Sine 76)²] / (2 × 9.8)
Maximum height = 1.45 m
How do I determine the time of flight?
The time of flight of the ball can be obtained as follow:
Initial velocity (u) = 5.5 m/sAngle of projection (θ) = 76 °Acceleration due to gravity (g) = 9.8 m/s²Time of flight (T) = ?T = 2uSineθ / g
T = [2 × 5.5 × Sine 76] / 9.8
Time of flight = 1.1 s
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The box shown on the rough ramp above is sliding up the ramp.Draw a Free-Body Diagram and use it to:calculate the normal force on the box
Answer:
The magnitude of the normal force: 75.1 N
Explanation:
The free-body diagram showing all forces acting on the box is:
Here is a little explanation of the diagram. What we are doing is we are refinding our coordinate system such that the y axis is along the normal force Fn and the x-axis is along with the tangential force Ft. Remember that in this coordinate system, we have to decompose the gravitation force Fg into normal and tangential components.
Now the Normal force acting on the box is Fn. What is its magnitude? We can easily find it using some trigonometry.
\(F_N=(10kg\cdot9.8m/s^2)\cos (40^o)\)which evaluates to give
\(\boxed{F_N=75.1N}\)
Hence, the normal force on the box is 75.1 newtons.
A ball is thrown upwards with initial velocity 20 m/s. After reaching maximum height, on the way down it strikes a bird which is 10 m above the ground. What is the velocity of the ball when it hits the bird?
The speed of sound is measured to be 340 m/s on a certain day.
What is this in Kilometers per hour?? s/km/h=
Please help and explain how to do these types of problems in very confused!!!
How are Aurora produced?
O City Lights reflecting or scattered from the atmosphere, O Atmospheric molecules releasing photons (light) in response to lighting strikes
O From the exhaust ports of interplanetary spacecraft.
O Atmospheric molecules releasing photons (light) in response to collisions with Solar Wind particles.
Answer:
The third one.
Explanation:
Atmospheric molecules releasing photons (light) in response to collisions with Solar Wind particles because when auroras are produced what actually happens is that the ions of the solar wind collide with atoms of oxygen and nitrogen from the Earth's atmosphere. The energy released during these collisions causes a colorful glowing halo around the poles which is the aurora.
Francine McFly is a 50kg circus acrobat. She does a famous stunt where she stands 2m fromthe middle of a seesaw while two of her friends jump 2m from the middle of the other sideof the seesaw. A third stomps the seesaw. The two jumpers each weigh 80Kg and reach a max height of 1m. The stomper stomps with an energy equivalent to ¼ of one of the jumpers. Francine then does a backflip onto the shoulders of 3 of her friends. a) Francine's Velocity when she is shot off andb) How HIGH Francine gets.
Given,
The mass of Francine McFly, m=50 kg
The distance from the center of the seesaw to Francine, d=2 m
The mass of the jumpers, M=80 kg
The maximum height reached by the jumpers, h=1 m
From the law of conservation of energy, energy can neither be created nor be destroyed but can be converted from one form to another.
The jumpers transfer their potential energy to Francine through the seesaw. The energy gained by Francine from jumpers and a stomper gives her the velocity. She shots off with the kinetic energy equal to the total energy transferred input of two jumpers and a stomper. As Francine rises, she slowly loses kinetic energy. This lost kinetic energy will be converted into her potential energy. When she reaches the top, her potential energy will be equal to the energy input from the two jumpers and a stomper.
The energy applied by two jumpers is equal to their potential energy at the maximum height, That is,
\(\begin{gathered} E=M\text{gh}+M\text{gh} \\ =2M\text{gh} \end{gathered}\)Where g is the acceleration due to gravity.
Given that the stomper stomps with an energy equal to 1/4 of applied by one of the jumpers.
Thus the total energy applied to the seesaw is given by,
\(\begin{gathered} E_T=2M\text{gh}+\frac{1}{4}M\text{gh} \\ =\frac{9}{4}M\text{gh} \end{gathered}\)On substituting the known values,
\(\begin{gathered} E_T=\frac{9}{4}\times80\times9.8\times1 \\ =1764\text{ J} \end{gathered}\)a)
This total energy will be equal to the kinetic energy of Francine when she is shot off.
Thus,
\(\begin{gathered} E_T=E_K=\frac{1}{2}mv^2 \\ \Rightarrow v=\sqrt[]{\frac{2E_T}{m}} \end{gathered}\)Where E_K is the kinetic energy of Francine when she is shot off and v is her velocity when she is shot off.
On substituting the known values,
\(\begin{gathered} v=\sqrt[]{\frac{2\times1764}{50}}_{} \\ =8.4\text{ m/s} \end{gathered}\)Thus Francine's velocity when she is shot off is 8.4 m/s
b)
The potential energy of Francine when she is at the maximum height is equal to the energy applied to the seesaw. Thus,
\(\begin{gathered} E_T=E_P \\ =\text{mgH} \\ \Rightarrow H=\frac{E_T}{mg} \end{gathered}\)Where E_P is the potential energy of Francine and H is the height reached by Francine.
On substituting the known values,
\(\begin{gathered} H=\frac{1764}{50\times9.8} \\ =3.6\text{ m} \end{gathered}\)Thus the maximum height reached by Francine is 3.6 m
Question 3 of 10
What is the primary means by which heat is transferred through fluids?
O A. Direct contact of particles
OB. Radiation
OC. Electromagnetic waves
OD. Convection currents
The primary means by which heat is transferred through fluids is convection currents (option D).
What is convection current?Convection is the transmission of heat in a fluid by the circulation of currents.
Heat can be transferred by different methods depending on the medium. Fluids like gases and liquids transfer heat through the process of convection.
Therefore, the primary means by which heat is transferred through fluids is convection currents.
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Gas and plasma are phases of matter, yet gas runs a car and plasma is part of your blood. Compare and contrast these terms and offer an explanation for the use of similar names.
Plasma lacks a precise form or volume, much like gas. It completes the empty space. Even though it is in the gaseous form, there is a difference because some of the particles are plasma-ionized.
High-energy particles are free to move around and fill the area they inhabit in the state of matter known as gas.
Neutral atoms or molecules often make up gaseous substances like air.
The ionised gas known as plasma, on the other hand, contains both positively and negatively charged particles.
It develops when a gas is subjected to an intense electric field or heated to incredibly high temperatures.
Plasma is a substance that may be found in stars, lightning, and fluorescent lights. It is also an essential component of many modern technology, like plasma TVs and fusion reactors.
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What is the temperature change of a 3 kg gold (c = 129 J/kg K) bar when placed into 0.220 kg
of water. After equilibrium is reached the water underwent a temperature change of 17 °C.
Answer:
We can use the formula:
q = mcΔT
where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The heat transferred from the gold bar to the water is equal to the heat transferred from the water to the gold bar, since they reach thermal equilibrium. Therefore:
q_gold = q_water
We can solve for the temperature change of the gold bar:
q_gold = mcΔT_gold
q_water = mcΔT_water
Since the heat transferred is equal:
mcΔT_gold = mcΔT_water
Rearranging and solving for ΔT_gold:
ΔT_gold = ΔT_water(m_water/m_gold)
ΔT_water is the temperature change of the water, which is 17°C. m_water is 0.220 kg, and m_gold is 3 kg. c_gold is given as 129 J/kg K.
ΔT_gold = 17°C(0.220 kg/3 kg)(1/129 J/kg K) = 0.025°C
Therefore, the temperature change of the gold bar is 0.025°C when it is placed into 0.220 kg of water and thermal equilibrium is reached.
What’s the right answer for 2
The little number you see to the right of the symbol for an element is called a subscript. That number indicates the number of atoms of that element present in the compound.
given the two displacement vector D ( 6i+3j-k) and vector E( 4i-5j+3k) what is the magnitude of displacement. 2D-E
Answer:
The magnitude of displacement vector 2D-E is approximately 14.49 units. The calculation is done using the Pythagorean theorem after finding 2D-E by multiplying vector D by 2 and subtracting vector E.
Explanation:
The value of 2D-E must first be calculated in order to ascertain the displacement 2D-E's magnitude. Vector D may be multiplied by two to accomplish this, and the result can be obtained by deducting vector E:
2D-E = 2(6i + 3j - k) 4i + 5j + 3k = 8i + 11j - 5k - (4i - 5j + 3k) = 12i + 6j - 2k
We can use the Pythagorean theorem to determine the magnitude of the displacement vector now that we know it:
|2D-E| = √(8² + 11² + (-5)²) = √(64 + 121 + 25) = √210 ≈ 14.49
The displacement 2D-E magnitude is therefore 14.49 units or such. From the object's beginning location to its ultimate position, the displacement's entire length is shown by this. Being a scalar variable, the displacement's magnitude does not reveal the displacement's direction.
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A hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment
We have that for the Question, it can be said that
the balloon rising at \(0.266miles/min\)From the question we are told
An observer located 2 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is , and it is changing at a rate of 0.1 rad/min.From,
\(tan\theta = \frac{h}{2}\)
differentiate with respect to h
\(sec^2\theta * \frac{do}{dz} = \frac{1}{2} * \frac{dh}{dz}\\\\\frac{dh}{dz} = 2 sec^\theta * \frac{d\theta}{dz}\\\\\theta = \frac{\pi}{6} and \frac{d\theta}{dz} = 0.1rad/min\\\\\frac{dh}{dz} = 2sec^2 (\frac{\pi}{6}) * (0.1)\\\\= 0.266miles/min\)
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the tension T in Newtons in the string of a yoyo of mass 0.001kg is give by the function of two variables (see equation in photo).
find the approximate change in T if R increases from 4cm to 4.1cm and r increases from 0.8cm to 0.9cm. use your answer to explain if the tension increases or decreases.
The change in the tension if the radii r changes from 4.0 cm to 4.1 cm, and R changed from 0.8 cm to 0.9 cm is negative, therefore, tension reduces.
How can the correct description of the change in the graph of the function be found?
Mass of the yoyo = 0.001 kg
Initial value of the spindle radius, R = 4 cm
Initial length of the radius of the yo–yo, r = 0.8 cm
The final values are;
R2 = 4.1 cm, r2 = 0.9 cm
Which gives;
\(T_{r \:R} = \frac{0.001 \cdot g \cdot R }{2 \cdot r^{2} + R^2} \)
Which gives;
\(T_{{r _1 \:R _1 }} = \frac{0.001 \times 9.8 \times 0.04 }{2 \times 0.008^{2} + 0.04²} = \frac{49}{216} \)
\(T_{{r _2 \:R _2 }} = \frac{0.001 \times 9.8 \times 0.041 }{2 \times 0.009^{2} + 0.041^2} = frac{2009}{9215} \)
Therefore;
\( \Delta T_{{r \:R }} = frac{2009}{9215} - \frac{49}{216} = - \frac{17591}{1990440} \)
Given that difference between the final and the initial states is negative, the the value of the tension decreases
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Which of these would be a part of a force diagram for this image? Check all that apply.
The options that would be a part of a force diagram for the attached image are:
A; A dot that represents the box
B; A vector labeled Fg, pointing straight down
E; A vector labeled Fs, pointing parallel to and up the ramp.
What are the qualities of a force diagram?This is a simple force diagram of an item lying on an inclined plane.
The first step is to draw a dot in the center of the box, as here is where we will draw the other forces operating on the box.
Second, we must recognize the force of gravity (F_g), which is a vertical vector line drawn from that dot and whose perpendicular component assures that the box is pressing against the inclined plane.
Third, we can see that the box is moving down the slope, but it will face some friction in the other direction. As a result, we will draw a vector line parallel to the inclined plane from the dot to the left of the box. Frictional force (F_fs) will be shown by this line.
Fourth, there would be a normal force attempting to counteract the perpendicular component of gravity (F_g). This normal force is perpendicular to the perpendicular component of F_g. This is referred to as F_g•sin. We will draw a vector line perpendicular to the inclined plane starting from the dot to represent this normal force. F_n represents this normal force.
Looking at the possibilities, only Options A, B, and E correlate to the forces stated above.
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What is Moral subjectivism?
Answer:
What Is Moral Subjectivism? Moral subjectivism is based on an individual person's perspective of what is right or wrong. An individual can decide for themselves that they approve or disapprove of a certain behavior, and that is what determines if the behavior is right or wrong.