the driver of a car sounds a horn while traveling away from a stationary person. compared to the sound of the horn heard by the driver, the sound heard by the stationary person has?
The stationary person will have a lower frequency and a longer wavelength compared to the sound heard by the driver.
This phenomenon is known as the Doppler effect. The Doppler effect takes place when there is relative motion between a sound source and an observer. Here, as the car moves away from the stationary person, the distance between the car and the person increases over time. When the sound waves emitted by the car are stretched out, leading to a decrease in frequency and an increase in wavelength.
Since frequency is related to pitch, the sound heard by the stationary person will be lower in pitch compared to the sound heard by the driver. Also,the longer wavelength may also result in a perceived decrease in volume or intensity of sound, though this is dependent on other factors such as the power of the sound source.
Hence, when a car horn is sounded while the car is moving away from a stationary person, the person will hear a lower-pitched sound with a longer wavelength compared to what the driver hears.
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The table shows information about four students who are running around a track. Which statement is supported by the information in the chart?
Autumn has more kinetic energy than Chiang.
Mohammed has less kinetic energy than Autumn.
Lexy has more kinetic energy than Mohammed.
Chiang has less kinetic energy than Lexy.
Answer:
Correct option: Mohammed has less kinetic energy than Autumn.
Explanation:
Kinetic Energy
Is the energy an object has due to its motion. If the object has a mass m and travels at a speed v, then the kinetic energy K is:
\(\displaystyle K=\frac{1}{2}mv^2\)
The information about four students includes their mass and velocity as follows:
Autumn has a mass of m1=50 kg and a velocity (magnitude) of v1=4 m/s, thus their kinetic energy is:
\(\displaystyle K_1=\frac{1}{2}50\cdot 4^2\)
\(K_1=400\ J\)
Mohammed has a mass of m2=57 kg and a velocity (magnitude) of v2=3 m/s, thus their kinetic energy is:
\(\displaystyle K_2=\frac{1}{2}57\cdot 3^2\)
\(K_2=256.5\ J\)
Lexy has a mass of m3=53 kg and a velocity (magnitude) of v3=2 m/s, thus their kinetic energy is:
\(\displaystyle K_3=\frac{1}{2}53\cdot 2^2\)
\(K_3=106\ J\)
Chiang has a mass of m4=64 kg and a velocity (magnitude) of v4=5 m/s, thus their kinetic energy is:
\(\displaystyle K_4=\frac{1}{2}64\cdot 5^2\)
\(K_4=800\ J\)
Sorted from lower kinetic energy to higher:
Lexy, Mohammed, Autumn, Chiang. Thus:
Autumn has more kinetic energy than Chiang. False
Mohammed has less kinetic energy than Autumn. True
Lexy has more kinetic energy than Mohammed. False
Chiang has less kinetic energy than Lexy. False
Correct option: Mohammed has less kinetic energy than Autumn.
Answer:
its b
Explanation:
got in right on edge
94. Determine the magnitude of the acceleration of the rock down the inclined plane if the rope breaks?A) zero m/s2B) 4.9 m/s2C) 5.7 m/s2D) 8.5 m/s2E) 9.8 m/s2
The correct option provided is option C) 5.7 m/s^2
How to find acceleration?When the rope is holding the rock, the tension force in the rope opposes the weight of the rock and the net force acting on the rock is zero. When the rope breaks, the tension force becomes zero and the weight of the rock is the only force acting on it.
The weight of the rock can be resolved into two components, one parallel to the inclined plane and one perpendicular to it. The component parallel to the inclined plane will cause the rock to accelerate down the plane.
The magnitude of the component of the weight parallel to the inclined plane is given by Wsinθ, where W is the weight of the rock and θ is the angle of the inclined plane with respect to the horizontal.
a = (Wsinθ)/m
where m is the mass of the rock.
Substituting the values, we get:
a = (10 kg) * sin(30°)/10 kg = 5 m/s^2
Therefore, the magnitude of the acceleration of the rock down the inclined plane if the rope breaks is 5 m/s^2.
The closest option provided is option C) 5.7 m/s^2.
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If the volume of a container of gas remains constant, what will happen to the pressure of a gas if you increase the temperature?
Answer:
This example of the effect of volume on the pressure of a given amount of a confined gas is true in general. Decreasing the volume of a contained gas will increase its pressure, and increasing its volume will decrease its pressure.
Explanation:
Hope it helps
The Atwood’s machine shown consists of two blocks of mass m1 and m2 that are connected by a light string that passes over a pulley of negligible friction and negligible mass. The block of mass m1 is a distance h1 above the ground, and the block of mass m2 is a distance h2 above the ground. m2 is larger than m1. The two-block system is released from rest. Which of the following claims correctly describes the outcome after the blocks are released from rest but before the block of m2 reaches the ground?
When the two-block Atwood's machine system is released from rest, the block of mass m1 accelerates downwards due to the force of gravity and the block of mass m2 accelerates upwards. This is because the mass of m2 is greater than the mass of m1, meaning m2 is the heavier object and thus the object that accelerates upwards. This is a result of Newton's Third Law of Motion, which states that for every action there is an equal and opposite reaction. As the block of m2 accelerates upwards, the block of m1 accelerates downwards, allowing the two blocks to move in opposite directions.
In addition, the acceleration of the two blocks is determined by the difference in masses, with the larger mass (m2) having the smaller acceleration. This is due to Newton's Second Law of Motion, which states that the acceleration of an object is equal to the force acting on it divided by its mass. As m2 has the larger mass, it has a smaller acceleration.
Before the block of m2 reaches the ground, the acceleration of both blocks will be constant. This is because there is no friction between the two blocks, meaning the force acting on them will remain constant. The two blocks will continue to move in opposite directions, and the heavier mass will continue to accelerate at a slower rate than the lighter mass.
In conclusion, when the Atwood's machine is released from rest but before the block of mass m2 reaches the ground, the two blocks will move in opposite directions with constant acceleration. The larger mass will have the smaller acceleration due to Newton's Second Law of Motion.
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a sonar system can use sound waves wih a frequency of 120kHz or 200kHz. A. what is the wavelength of each of these waves when they are sent through sea water?
B. What are their wavelengths in freshwater?
C. The ship operating these sonar systems is in sea water with a depth of 3km.
How long will it take an echo to return to the ship after a ‘ping’
(A) The wavelength of each of these waves when they are sent through sea water is 0.0126 m and 0.0076 m respectively.
(B) The wavelength of each of these waves when they are sent through freshwater is 0.012 m and 0.0074 m respectively.
(C) The time taken for the echo to return to the ship is 3.97 seconds.
What is the wavelength of the sound wave in sea water?
The wavelength of the sound wave in sea water depends on the speed of sound in seawater and frequency of the wave.
The speed of sound in seawater, v = 1,510 m/s
λ = v/f
when the frequency, f = 120 kHz
λ = 1510 / 120,000
λ = 0.0126 m
when the frequency, f = 200 kHz
λ = 1510 / 200,000
λ = 0.0076 m
The speed of sound in freshwater, v = 1481 m/s
when the frequency, f = 120 kHz
λ = 1481 / 120,000
λ = 0.012 m
when the frequency, f = 200 kHz
λ = 1481 / 200,000
λ = 0.0074 m
The time taken for the echo to return is calculated as follows
v = 2d/t
t = 2d/v
t = (2 x 3,000 m) / (1510 m/s)
t = 3.97 s
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what is the net force of a 6 kg object that goes from a velocity of 0.5 m/s to a velocity of 3 m/s over the course of 1.5 seconds? PLEASE ANSWER ASAP I HAVE 10 MINUTES PLEASEEEEEE
Answer:
∑F = 10.2 N
Explanation:
We have:
Initial velocity: 0.5 m/s
Final velocity: 3 m/s
Time: 1.5 s
We have all of the components needed to calculate acceleration. Let's do that, shall we?
a = vf-vo/t
a = 2.5/1.5
a = 1.7 \(m\)/\(s^{2}\)
Now, look at the Net Force equation:
∑F = ma
Plug in the variables, to get:
∑F = (6)(1.7)
∑F = 10.2 N (You can round this according to significant digits)
A 560 Hz tuning fork and a piano key are struck together, and four beats are heard. When a 572 Hz tuning fork and the same piano key are struck, eight beats are heard. What is the frequency of the piano key?
564 Hz
556 Hz
572 Hz
560 Hz
Answer:
556
Explanation:
suppose u is a solution of utt − c2uxx = 0, and that at a particular time t, the graph of u as a function of x is convex (uxx > 0). is the acceleration utt of the string up or down?
Hi! I'd be happy to help you with your question. We are given that u is a solution of the wave equation: utt - c^2 * uxx = 0 At a particular time t, the graph of u as a function of x is convex, which means: uxx > 0 We need to determine if the acceleration utt of the string is up or down. To do this, we can use the wave equation and the information about uxx. Rearrange the wave equation: utt = c^2 * uxx Since c^2 is always positive (c is the speed of the wave, which is a positive quantity) and we know that uxx > 0 (convex function), we can conclude: utt = c^2 * uxx > 0 This means that the acceleration utt of the string is positive, which indicates that the acceleration is up.
Let me know several term that is importent for you. First is equation, An equation is a mathematical statement in the form of a symbol that states that two things are exactly the same. Equations are written with an equal sign, as follows: x + 3 = 5, which states that the value x = 2. 2x + 3 = 5, which states that the value x = 1. The statement above is an equation. Second acceleration, acceleration is the change in velocity in a given unit of time. The acceleration of an object is caused by a force acting on the object, as explained in Newton's second law. The SI unit for acceleration is meters per second squared. this most affects the style change whether up or up, but still consider several other factors.
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The weight of a person is 51kg. The force of gravity is 9.8 m/s2. The area of one snowshoe is 0.2m2. Calculate the pressure applied when standing on (A) one snowshoe and (B) both snowshoes. List your final answers in kilo Pascals.
A person's weight is 51kg. The gravitational force is 9.8 m/s². One snowshoe has a surface area of 0.2m2. The pressure applied when standing on (A) one snowshoe and (B) both snowshoes is 2.499 kPa.
The pressure applied by a person standing on the snowshoe is given by the formula:
Pressure = Force / Area
where Force is the weight of the person and Area is the area of one snowshoe.
(A) When standing on one snowshoe:
The force exerted by the person on one snowshoe is equal to the weight of the person:
Force = 51 kg x 9.8 m/s² = 499.8 N
Therefore, the pressure applied by the person on one snowshoe is:
Pressure = Force / Area = 499.8 N / 0.2 m² = 2499 Pa = 2.499 kPa (to three decimal places)
(B) When standing on both snowshoes:
The force exerted by the person on both snowshoes is twice the weight of the person:
Force = 2 x 51 kg x 9.8 m/s² = 999.6 N
Therefore, the pressure applied by the person on both snowshoes is:
Pressure = Force / Area = 999.6 N / (2 x 0.2 m²) = 2499 Pa = 2.499 kPa (to three decimal places)
Hence, the pressure applied by the person when standing on one snowshoe or both snowshoes is the same, and it is equal to 2.499 kPa (to three decimal places).
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A 100gm GOLF BALL MOVING WITH A VELOCITY OF 20m/s COLLIDES WITH A 8kg STEEL BALL AT REST. IF THE COLLISION IS ELASTIC, COMPUTE THE VELOCITIES BOTH THE BALLS AFTER COLLISION
Answer:
Golf ball (\(0.1\; {\rm kg}\)): approximately \((-19.506)\; {\rm m\cdot s^{-1}}\) (backwards).
Steel ball (\(8\; {\rm kg}\)): approximately \(0.49383\; {\rm m\cdot s^{-1}}\) (forward.)
Explanation:
Apply unit conversion and ensure that the unit of all mass are in kilograms: \(100\; {\rm g} = 0.1\; {\rm kg}\).
In an elastic collision, both momentum \(p = m\, v\) and kinetic energy \(\text{KE} = (1/2)\, m\, v^{2}\) are conserved. Momentum of the two balls before the collision are:
\(0.1\; {\rm kg} \times 20\; {\rm m\cdot s^{-1}} = 2\; {\rm kg \cdot m \cdot s^{-1}}\) for the golf ball, and \(8\; {\rm kg} \times 0\; {\rm m\cdot s^{-1}} = 0\; {\rm kg \cdot m\cdot s^{-1}}\) for the steel ball initially at rest.Hence, the total momentum of the two balls was \(2\; {\rm kg \cdot m\cdot s^{-1}}\) before the collision and (by conservation) will still be \(2\; {\rm kg \cdot m\cdot s^{-1}}\!\) after the collision.
Kinetic energy of the two balls before the collision are:
\((1/2)\times 0.1\; {\rm kg} \times (20\; {\rm m\cdot s^{-1}})^{2} = 200\; {\rm kg \cdot m^{2} \cdot s^{-2}}\) for the golf ball, and\((1/2) \times 8\; {\rm kg} \times (0\; {\rm m\cdot s^{-1}})^{2} = 0\; {\rm kg \cdot m\cdot s^{-1}}\) for the steel ball initially at rest.Thus, the total kinetic energy of the two balls will be \(200\; {\rm kg \cdot m^{2} \cdot s^{-2}}\) before and after the collision.
Let \(m_{a}\) and \(v_{a}\) denote the mass and velocity of the golf ball after collision; \(m_{a} = 0.1\; {\rm kg}\).
Let \(m_{b}\) and \(v_{b}\) denote the mass and velocity of the steel ball after collision; \(m_{b} = 8\; {\rm kg}\).
Total momentum after the collision shall be \(2\; {\rm kg \cdot m\cdot s^{-1}}\!\). Thus:
\(m_{a}\, v_{a} + m_{b}\, v_{b} = 2\; {\rm kg \cdot m\cdot s^{-1}}\).
Total kinetic energy after the collision shall be \(200\; {\rm kg \cdot m^{2} \cdot s^{-2}}\). Thus:
\(\displaystyle \frac{1}{2} \, m_{a}\, v_{a} + \frac{1}{2}m_{b}\, v_{b} = 200\; {\rm kg \cdot m^{2}\cdot s^{-2}}\).
Assume that the unit of \(v_{a}\) and \(v_{b}\) are both "meters per second" (\({\rm m\cdot s^{-1}}\).) Combine and solve this system of two equations and two variables:
\(\left\lbrace\begin{aligned}&0.1\, v_{a} + 8\; v_{b} = 2 \\ &\frac{1}{2}\, {v_{a}}^{2} + 4\, {v_{b}}^{2} = 200\end{aligned}\right.\).
Rewrite the first equation to obtain \(v_{a} = 20 - 80\, v_{b}\). Substitute this equation into the second one to eliminate \(v_{a}\):
\(\displaystyle \frac{1}{2}\, (20 - 80\, v_{b})^{2} + 4\, v_{b}^{2} = 200\).
Solve this equation for \(v_{b}\):
\(324\, {v_{b}}^{2} - 160\, v_{b} = 0\).
There are two solutions to this quadratic equation: \((40 / 81)\) and \(0\). Note that the velocity of the steel ball must be non-zero right after the collision. Hence, \(v_{b} \ne 0\). Therefore, the only possible value for \(v_{b}\) will be \((40 / 81)\!\), which is approximately \(0.49383\; {\rm m\cdot s^{-1}}\).
Substitute \(v_{b} = (40 / 81)\) back into the first equation of the system and solve for \(v_{a}\): \(v_{a} = 20 - 80\, v_{b} \approx (-19.506)\; {\rm m\cdot s^{-1}}\). Note that the velocity of the golf ball \(v_{a}\!\) is negative since the golf ball is travelling backwards, opposite to its initial direction of motion.
In other words, the velocity right after collision will be approximately \((-19.506)\; {\rm m\cdot s^{-1}}\) (backwards) for the golf ball and approximately \(0.49383\; {\rm m\cdot s^{-1}}\) (forwards) for the steel ball.
a child is pulling an empty cart attached by a rope that is parallel to the ground. the cart is moving with constant velocity, and its mass is 1.5 kg. suppose a mass of 7.5 kg is added to the sled, and its velocity stays the same. by what factor does the tension in the rope change?
The tension in the rope is changed by 75 N
Tension is the force that is transmitted through a body which can be a rope or a wire which is pulled from both sides. Whenever there is a rope being pulled from one side then according to Newton's third law, equal force is exerted by the rope on the other side. This transmission of forces is known as tension in that rope.
Given,
Mass 1 = m₁ = 1.5 kg
Mass 2 = m₂ = 7.5 kg + 1.5 kg = 9 kg
g = 10 m/s² = acceleration due to gravity
Tension in the rope when mass 1.5 kg is attached to the string,
T₁ = m₁g = 1.5 * 10 = 15 kg
Tension in the rope when mass 1.5 kg is attached to the string,
T₂ = m₂g = 9*10 = 90 kg
The change that tension undergoes
T₂ - T₁ = 90 - 15 = 75
Therefore, the factor by which the tension in the rope changes is 75 N
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difference between universal law of gravitation and acceleration due to gravity
Explanation:
The acceleration on an object due to the gravity of any massive body is represented by g (small g). The force of attraction between any two unit masses separated by unit distance is called universal gravitational constant denoted by G(capital g). The relation between G and g is not proportional. That means they are independent entities.
G and g
In physics, G and g can be related mathematically as –
\(g=\frac{GM}{R^{2}}\)
Where,
1=g is the acceleration due to the gravity of any massive body measured in m/s2.
2=G is the universal gravitational constant measured in Nm2/kg2.
3=R is the radius of the massive body measured in km.
4=M is the mass of the massive body measured in Kg.
PLS HELP!!! I WILL GIVE BRAINLIEST! NO LINKS, NO STEALING POINTS, ONLY CORRECT ANSWERS!!
Which two atoms are Isotopes of each other?
Answer:
C is the answer
............................
why does the moon have more impact craters than the earth?
Answer:
Why does the Moon have so many craters compared to the Earth? Unlike the Earth, the Moon has no atmosphere to protect itself from impacting bodies. It also has very little geologic activity (like volcanoes) or weathering (from wind or rain) so craters remain intact from billions of years.
PLEASEEE HELP!!!!! I HAVE BEEN STRUGGLING FOR 2 DAYS
If i workout 90 minutes on earth, if I am on a rocket traveling 0.80c, according to the timer on the rocket, how long should I exercise?
Answer:
You should still workout 90 min.
The proper time is measured by a single clock in a single place.
The proper time on earth is 90 min.
The clock on the rocket is also in a single place in the frame of the rocket so you still need to workout for 90 min.
A 250. g object is attached to a spring. The object is pushed 10.0 cm against the spring, then released. Using a stopwatch, it is determined that the system experiences 12 cycles every 20 seconds. What is the spring constant
The spring constant is 0.943 N/m. The spring pushes the object back towards its original position and this energy is converted into kinetic energy.
The system in this scenario consists of the 250. g object and the spring it is attached to. When the object is pushed against the spring, it compresses and stores potential energy. When released, the spring pushes the object back towards its original position and this energy is converted into kinetic energy.
The fact that the system experiences 12 cycles every 20 seconds tells us that the object oscillates back and forth 12 times in 20 seconds. One full oscillation is equal to the object moving from its starting position, to the maximum displacement from that position, back to the starting position, and then to the maximum displacement in the opposite direction, before returning again to the starting position.
To find the spring constant, we can use the equation for the period of oscillation of a mass-spring system:
T = 2π * sqrt(m/k)
where T is the period of oscillation, m is the mass of the object, and k is the spring constant.
We know that T = 20 s / 12 = 1.67 s (since there are 12 cycles in 20 seconds). We also know that m = 250. g = 0.25 kg.
Plugging these values into the equation, we can solve for k:
1.67 s = 2π * sqrt(0.25 kg/k)
1.67 s / (2π) = sqrt(0.25 kg/k)
0.265 s^2/kg = 0.25 kg/k
k = 0.25 kg / 0.265 s^2
k = 0.943 N/m
Therefore, the spring constant is 0.943 N/m.
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A car is stationary. It accelerates at 0.8 ms^2
for 10 s and then at 0.4 ms^2
for a further 10 s. Use
the equations of motion to deduce the car’s final displacement. You will have to split the journey
into two parts, since the acceleration changes after 10 s.
Answer:
the car’s final displacement is 60 m
Explanation:
Given;
initail velocity of the car, u = 0
acceleration of the car, a = 0.8 m/s²
time of motion, t = 10 s
The first displacement of the car:
\(x_1 = ut + \frac{1}{2} at^2\\\\x_1 = 0 + \frac{1}{2} (0.8)(10)^2\\\\x_1 = 40 \ m\)
The second displacement of the car;
acceleration, a = 0.4 m/s², time of motion, t = 10 s
\(x_2 = ut + \frac{1}{2} at^2\\\\x_2 = 0 + \frac{1}{2} (0.4)(10)^2\\\\x_2 = 20 \ m\)
The final displacement of the car;
x = x₁ + x₂
x = 40 m + 20 m
x = 60 m
Therefore, the car’s final displacement is 60 m
In three trials, a block is pushed by a horizontal applied force across a floor that is not frictionless. The magnitudes F of the applied force and the results of the pushing on the block's speed are given in the table Trial A: F-5. 0N and the block's speed decreases Trial B: F-7. 0N and the block's speed remains constant Trial C:F-8. 0N and the block's speed increases F MI-M ff In all three trials, the block is pushed through the same distance d. Rank the three trials according to the change in the thermal energy of the block and floor that occurs in that distance d, least first. (a) B
The ranking of three trials according to the change in thermal energy of the block and floor that occurs in the distance d, least first is "B."
According to the law of conservation of energy, the total energy of an isolated system remains constant. In other words, energy can neither be created nor destroyed; it can only be transformed or transferred from one form to another. Based on the data given, the ranking of three trials according to the change in thermal energy of the block and floor that occurs in the distance d, least first is given below:Trial B: F - 7.0N and the block's speed remains constantTrial A: F - 5.0N and the block's speed decreasesTrial C: F - 8.0N and the block's speed increases.
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bow long does it take earth to rotate once on its axis
Answer:
23 hours, 56 minutes
Martije has made a slight error in naming a compound monocarbon tetrabromide. What compound is she most likely naming, and what is its correct name? C1B4 (monocarbon tetrabromide) C1Br4 (monocarbon tetrabromide) CB4 (carbon tetrabromide) CBr4 (carbon tetrabromide)
Answer: \(CBr_4\) : carbon tetrabromide
Explanation:
\(CBr_4\) is a covalent compound because in this compound the sharing of electrons takes place between carbon and bromine. Both the elements are non-metals. Hence, it will form covalent bond.
The naming of covalent compound is given by:
1. The less electronegative element is written first.
2. The more electronegative element is written second. Then a suffix is added with it. The suffix added is '-ide'.
3. If atoms of an element is greater than 1, then prefixes are added which are 'mono' for 1 atom, 'di' for 2 atoms, 'tri' for 3 atoms and so on.
Hence, the correct name for \(CBr_4\) is carbon tetrabromide.
Answer:
Carbon tetrabromide ~ CBr4
Chlorine monofluoride~ ClF
Explanation:
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on a map The continents have shapes that almost fits together like pieces of jigsaw puzzle how does modern science explain
Scientists believe that a long time ago the seven continents might have been connected, but they think the plates shifted apart at some point.
An object is acted upon by two forces 3N and 5N inclined at 60 degree to each other. if the object is moved through a distance of 6m by the resultant force, the workdone is
Answer:
48 J
Explanation:
Work Done = Force X Distance moved in a stated direction
Work Done = 3N + 5N X 6m
Work Done = 48 J
Two forces 3N and 5N acting on an object are inclined at 60 degrees to each other. If the resultant force moves the object a distance of 6m, the work done is 35.92 Joules (J).
In physics, work is defined as the transfer of energy that occurs when a force is applied to an object and the object is displaced in the direction of the force. Mathematically, work done is the product of the force applied and the distance moved in the direction of the force.
Work is a scalar quantity and is measured in joules (J) in the International System of Units (SI). When a force is applied to an object and there is no displacement, no work is done. Similarly, if there is displacement but no force acting on the object, no work is done.
Here in the Question,
To find the work done, we need to first find the resultant force.
Using vector addition, we can find the magnitude and direction of the resultant force:
cos(60) = adjacent/hypotenuse
adjacent = cos(60) x 5N = 2.5N
sin(60) = opposite/hypotenuse
opposite = sin(60) x 5N = 4.33N
The horizontal component of the 3N force is 3N cos(60) = 1.5N
The vertical component of the 3N force is 3N sin(60) = 2.6N
The horizontal component of the 5N force is 5N cos(30) = 4.33N
The vertical component of the 5N force is 5N sin(30) = 2.5N
The horizontal component of the resultant force is 4.33N + 1.5N = 5.83N
The vertical component of the resultant force is 2.5N + 2.6N = 5.1N
The magnitude of the resultant force is given by the Pythagorean theorem:
Resultant force = sqrt(5.83^2 + 5.1^2) = 7.59N
The direction of the resultant force is given by:
tan(theta) = opposite/adjacent
theta = tan^-1(5.1/5.83) = 43.1 degrees
The work done is given by:
work = force x distance x cos(theta)
work = 7.59N x 6m x cos(43.1) = 35.92 Joules (J)
Therefore, the work done is 35.92 Joules (J).
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Two vectors 10cm and 8cm form an angle of 60 degrees. find the magnitude of difference and the angle with respect to the larger vector.
The magnitude of difference and angle is 86.48°.
How to calculate magnitude?To find the magnitude of the difference between two vectors, subtract the magnitude of the smaller vector from the magnitude of the larger vector. The magnitude of the larger vector is 10 cm and the magnitude of the smaller vector is 8 cm, so the magnitude of the difference is 10 - 8 = 2 cm.
To find the angle with respect to the larger vector, use the dot product. Let's denote the larger vector as A and the smaller vector as B. The dot product of A and B is given by: A•B = |A||B|cos(Θ)
Where Θ is the angle between the two vectors. From the problem, the angle between the two vectors is 60 degrees, so substitute that value into the equation:
A•B = 10 x 8 x cos(60)
A•B = 10 x 8 x 0.5
A•B = 40
Now, find the angle Θ between the difference vector (A - B) and the larger vector (A) by using the dot product formula:
(A - B)•A = |A - B||A|cos(Θ)
Simplify this expression by substituting the known values:
(A - B)•A = 2 x 10 x cos(Θ)
Divide both sides by 20 to isolate cos(Θ):
cos(Θ) = (A - B)•A / (2 x 10)
cos(Θ) = (A - B)•A / 20
cos(Θ) = (A•A - B•A) / 20
cos(Θ) = (A•A - (A•B / |A|)) / 20
cos(Θ) = (A•A - (40 / 10)) / 20
cos(Θ) = (A•A - 4) / 20
cos(Θ) = (100 - 4) / 20
cos(Θ) = 96 / 20
cos(Θ) = 4.8
Finally, we can use the inverse cosine function to find the angle Θ:
Θ = acos(cos(Θ))
Θ = acos(4.8)
The angle Θ is approximately 86.48°, which is with respect to the larger vector.
In summary, the magnitude of the difference between the two vectors is 2 cm and the angle with respect to the larger vector is approximately 86.48°.
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A 8 kg basketball is dropped from a height of 10 m. Calculate the Gravitational
Potential Energy of the ball.
Answer: 0.8
Explanation: i just had it on k12 test
The Gravitational Potential Energy of the basketball as it drops from the given height is 784J
Given the data in the question;
Mass of basket; \(m = 8kg\)Distance or Height from which its dropped from; \(h = 10m\)Gravitational Potential Energy of the ball; \(P.E = ?\)Gravitational Potential Energy is the energy a matter or object possesses due to its position in gravitational field. It can be determine using the following formula:
\(U = m\ * \ g\ * \ h\)
Where m is the mass of the object, g is the gravitational field and h is the height.
And we know that for Earth's gravitational field or the acceleration due to gravity; \(g = 9.8m/s^2\)
We substitute our values into the equation
\(U = 8kg\ * \ 9.8m/s^2\ * \ 10m\\\\U = 784 J\)
Therefore, The Gravitational Potential Energy of the basketball as it drops from the given height is 784J
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18. on a clear, dry day an air mass has a temperature of 20 degrees celsius and a dewpoint temperature of 10 degrees celsius. according to the earth science reference tables, about how high must this air mass rise before a cloud can form?
A 10-degree Celsius dew point depression corresponds to an altitude of approximately 1000 meters.
According to the Earth Science Reference Tables, an air mass with a temperature of 20 degrees Celsius and a dew point temperature of 10 degrees Celsius must rise by about 1000 meters before a cloud can form.
This is because the difference between the temperature and dew point temperature is known as the dew point depression. Clouds are formed when air ascends and undergoes cooling until it reaches the temperature at which water vapor begins to condense, known as the dew point temperature.
The dew point depression in this case is 10 degrees Celsius. If an air mass rises, it will cool, and as the air cools, it will approach its dew point temperature. Once the air reaches its dew point temperature, water vapor in the air will begin to condense into visible droplets. This is how clouds form.
Therefore, the difference between the temperature and dew point temperature gives us an idea of how high an air mass must rise before a cloud can form. For every 1000 feet an air mass rises, it cools about 3.5 degrees Fahrenheit.
Therefore, a 10-degree Celsius dew point depression corresponds to an altitude of approximately 1000 meters.
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Types of Spectra 5) Stars like our Sun have low-density, gaseous atmospheres surrounding their hot, dense cores. If you were looking at the spectra of light coming from the Sun (or any star), which of the three types of spectrum would be observed? Explain your reasoning.
The spectrum observed from the Sun (or any star) would exhibit an absorption spectrum. This is because the outer gaseous atmosphere of the star absorbs specific wavelengths of light, resulting in dark absorption lines in the spectrum.
In the cooler, lower-density outer atmosphere, where white light from the star travels, some atoms or molecules in the atmosphere absorb photons with particular energy. In the spectrum, these absorptions show up as black lines at specific wavelengths. The specific set of absorption lines that each element or molecule generates results in a distinctive pattern that can be used to identify the elements that are present in the star's atmosphere.
The absorption spectrum offers insightful data on the chemical make-up and physical characteristics of the star. Astronomers can ascertain the elements present, their abundances, and other characteristics like the temperature, pressure, and velocity of the star's atmosphere by examining the absorption lines.
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Can a 20 N force and 40 N force ever produce a resultant with magnitude of 27 N?
Sure ,Let's find angle between forces
Vectors be A and B and resultant be R\(\\ \sf\longmapsto R^2=A^2+B^2+2ABcos\theta\)
\(\\ \sf\longmapsto 27^2=20^2+40^2+2(20)(40)cos\theta\)
\(\\ \sf\longmapsto 729=400+1600+1600cos\theta\)
\(\\ \sf\longmapsto 729=2000+1600cos\theta\)
\(\\ \sf\longmapsto 1600cos\theta=-271\)
\(\\ \sf\longmapsto cos\theta=-0.169\)
\(\\ \sf\longmapsto \theta=cos^{-1}(-0.169)\)
\(\\ \sf\longmapsto \theta=80.2°\)
What is the nature of material after elastic limit
Answer:
In stress strain curve of ductile materials, up to proportionality limit stress and strain are proportional to each other and also elastic in nature. After that proportionality disappears and only elasticity remains. That limit is called elastic limit.
Explanation:
which SI units of measure describle acceleration
The meter per seconds per second (m/s²) is the SI unit of measurement used to describe an acceleration unit.
What is a acceleration explain?A rate at which position and velocity of velocity change over time is referred to as acceleration. When anything starts moving faster or slower, it's referred to as accelerating. The rate at which an object's velocity with regard to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of a net force on the object determines the direction of its acceleration.
How do you calculate acceleration?Acceleration refers to the rate at which velocity changes over a predetermined amount of time. By divide a change in velocity even by change in time, acceleration is calculated. The acceleration of the object is equal to the net force exerted on it divided only by mass, or a = F m, in accordance with Newton's second rule of motion. When the mass of an item as well as the net force acting on are known, the acceleration of that object can be determined using this equation for acceleration.
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