Answer:
The average kinetic energy
The amount of heat a substance has or the average kinetic energy of particles in a substance
The largest stars we know of have masses of a little over 1035 kilograms, while the lowest mass stars have masses of about 1032 kilograms. How many times more massive are the most massive stars than the lowest mass stars?
Group of answer choices
a thousand times more massive.
a hundred times more massive.
ten times more massive.
ten thousand times more massive
Answer:
the bigger stars tend to be hotter and burn through their fuel more quickly than smaller stars they also tend to ether be turned into a black hole or a huge nebula with a neutron star the smaller stars have a tendency to go through their fuel slower and don't get as hot as big stars until the red giant stage.
Explanation:
Indiana Jones is in a temple searching for artifacts. He finds a gold sphere with a radius of 2 cm sitting on a pressure sensitive plate. To avoid triggering the pressure plate, he must replace the gold with something of equal mass. The density of gold is 19.3.103 kg/m3, and the volume of a sphere is V = 4/3 Ar3. Indy has a bag of sand with a density of 1,602 kg/m3.
(A) What volume of sand must he replace the gold sphere with? If the sand was a sphere, what radius would it have?
Answer:
Volume of Sand = 0.4 m³
Radius of Sand Sphere = 0.46 m
Explanation:
First we need to find the volume of gold sphere:
Vg = (4/3)πr³
where,
Vg = Volume of gold sphere = ?
r = radius of gold sphere = 2 cm = 0.02 m
Therefore,
Vg = (4/3)π(0.2 m)³
Vg = 0.0335 m³
Now, we find mass of the gold:
ρg = mg/Vg
where,
ρg = density of gold = 19300 kg/m³
mg = mass of gold = ?
Vg = Volume of gold sphere = 0.0335 m³
Therefore,
mg = (19300 kg/m³)(0.0335 m³)
mg = 646.75 kg
Now, the volume of sand required for equivalent mass of gold, will be given by:
ρs = mg/Vs
where,
ρs = density of sand = 1602 kg/m³
mg = mass of gold = 646.75 kg
Vs = Volume of sand = ?
Therefore,
1602 kg/m³ = 646.75 kg/Vs
Vs = (646.75 kg)/(1602 kg/m³)
Vs = 0.4 m³
Now, for the radius of sand sphere to give a volume of 0.4 m³, can be determined from the formula:
Vs = (4/3)πr³
0.4 m³ = (4/3)πr³
r³ = 3(0.4 m³)/4π
r³ = 0.095 m³
r = ∛(0.095 m³)
r = 0.46 m
Mary and Carl's car broke down so they are pushing the car. Mary is pushing the car at
9N and Carl is pushing the car at 11N.
The resultant force while pushing the car would be 20 N.
What is Newton's second law?Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
As given in the problem Mary and Carl's car broke down so they are pushing the car. Mary is pushing the car at 9N and Carl is pushing the car at 11N.
As both Mary and Carl apply the force in the same direction while pushing the broke car
Resultant force= 9 N + 11 N
= 20 N
Thus, the resultant force comes out to be 20N.
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The question seems incomplete, the complete question is,
Mary and Carl's car broke down so they are pushing the car. Mary is pushing the car at 9N and Carl is pushing the car at 11N. Find out the resultant force while pushing the car
with a mass if 74 kg, is a moving with a velocity of 11m/s, what is the kinetic energy ?
Answer:
4477 JExplanation:
The kinetic energy of an object can be found by using the formula
\(k = \frac{1}{2} m {v}^{2} \\ \)
m is the mass
v is the velocity
From the question we have
\(k = \frac{1}{2} \times 74 \times {11}^{2} \\ = 37 \times 121\)
We have the final answer as
4477 JHope this helps you
In which of the following forms of energy might you find specially placed tiles on the floor? O A. passive solar O B. geothermal O c. wind power O D. biomass
Answer:
A, Passive Solar.
Explanation:
Object 1 with mass 1=3.25 kg
is held in place on an inclined plane that makes an angle
of 40.0∘
with the horizontal. The coefficient of kinetic friction between the plane and the object is 0.535.
Object 2 with mass 2=4.75 kg
is connected to object 1 with a massless string over a massless, frictionless pulley. The objects are then released.
Calculate the magnitude
of the initial acceleration.
Calculate the magnitude
of the tension in the string once the objects are released.
The magnitude of the initial acceleration of the object is 4.2 m/s².
The tension in the string once the object starts moving is 13.65 N.
What is the magnitude of the initial acceleration?The magnitude of the initial acceleration of the object is calculated by applying Newton's second law of motion as follows;
F(net) = ma
m₂g - μm₁g cosθ = a(m₁ + m₂)
where;
m₁ and m₂ are the masses of the blocksg is acceleration due to gravityμ is coefficient of frictionθ is the angle of inclinationa is the acceleration(4.75 x 9.8) - (0.535 x 3.25 x 9.8 x cos40) = a(3.25 + 4.75)
33.5 = 8a
a = 33.5/8
a = 4.2 m/s²
The tension in the string once the object starts moving is calculated as;
T = m₁a
T = 3.25 x 4.2
T = 13.65 N
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Samir is waiting for a slow reaction to finish. What is the best way to make the reaction go faster?
Question 12 options:
Put it in the fridge where it is cold
Cover it with a blanket so it's dark
Warm it up on the stove
There is nothing you can do to change the speed of the reaction
In general, option c - warming it up on the stove - is often an effective method to increase the reaction rate.
Increasing the temperature of a reaction generally leads to faster reaction rates. This is because higher temperatures provide more thermal energy to the reactant particles, causing them to move faster and collide more frequently. The increased collision frequency and energy lead to more successful collisions and a higher likelihood of effective molecular interactions, which speeds up the reaction. On the other hand, options a and b - putting it in the fridge where it is cold or covering it with a blanket to make it dark - are unlikely to have a significant effect on the reaction rate. While temperature can influence reaction rates, cooling the reaction or making it dark typically reduces the kinetic energy of the particles, resulting in slower reaction rates. Option d - there is nothing you can do to change the speed of the reaction - is not accurate. The reaction rate can be influenced by various factors such as temperature, concentration, catalysts, and surface area, among others. By manipulating these factors, it is often possible to control and change the speed of a reaction. Hence option c, is correct
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clarity the term fair discrimination
Answer:
The discrimination which is based on affirmative action, inherent requirement of a particular job, productivity and compulsory discrimination by law are termed as fair discrimination.
hope it helps :)
Explanation:
Standing on a skateboard and shoot a paintball gun at your friend
Answer:
ok
Explanation:
Answer:
shooting
Explanation:
i hope you're joking
A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm,find the emf of the cell.
A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm, the electromotive force (emf) of the cell is approximately 14.5 volts.
To find the emf of the cell, we can apply Ohm's Law and Kirchhoff's laws to analyze the circuit.
Given:
Resistance of the coil, R1 = 4 ohm
Resistance of the other resistor, R2 = 8 ohm
Current passing through the 8-ohm resistor, I = 2A
First, let's analyze the parallel combination of the 4-ohm and 8-ohm resistors.
The total resistance of two resistors in parallel can be calculated using the formula:
1/Rp = 1/R1 + 1/R2
Substituting the given values, we have:
1/Rp = 1/4 + 1/8
1/Rp = 2/8 + 1/8
1/Rp = 3/8
Rp = 8/3 ohm
Now, let's consider the total resistance in the circuit, which includes the internal resistance of the cell (0.5 ohm) and the parallel combination of the resistors (8/3 ohm).
R_total = R_internal + Rp
R_total = 0.5 + 8/3
R_total = 1.833 ohm
Now, we can find the emf of the cell using Ohm's Law:
emf = I * R_total
emf = 2 * 1.833
emf ≈ 3.667 volts
Therefore, the emf of the cell is approximately 3.667 volts.
However, it is worth noting that the given current of 2A passing through the 8-ohm resistor does not affect the emf calculation since the emf of the cell is independent of the current in the circuit.
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A cat that weighs 4 kilograms is moving at a velocity of 1 m/s. What is the kinetic energy?
The kinetic energy of the cat is 2 joules (J).
The kinetic energy of an object can be calculated using the formula KE = 1/2 * mass * velocity^2.
The kinetic energy of an object can be calculated using the formula:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
In this case, the mass of the cat is 4 kilograms, and its velocity is 1 m/s. Plugging these values into the formula:
KE = 0.5 * 4 kg * (1 m/s)^2
Simplifying the equation:
KE = 0.5 * 4 kg * 1 m^2/s^2
KE = 0.5 * 4 kg * 1
KE = 2 kg
Therefore, the kinetic energy of the cat is 2 joules (J).
Kinetic energy is the energy possessed by an object due to its motion. In this case, the cat's kinetic energy is determined by its mass and velocity. The formula for kinetic energy demonstrates that it is directly proportional to the mass and square of the velocity. As the mass increases, the kinetic energy also increases. Similarly, as the velocity increases, the kinetic energy increases exponentially.
In this example, the cat's kinetic energy is relatively low due to its mass and velocity values. If the cat were moving at a higher velocity or had a greater mass, the kinetic energy would be significantly higher. Kinetic energy is an important concept in understanding the energy associated with moving objects and is utilized in various fields such as physics, engineering, and sports science.
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An object with a mass of 7 kg accelerates 8 m/s2 when an unknown force is applied to it. What is the amount of the force?
The amount of force applied to the 7kg object that caused it to accelerate at 8m/s² is 56 newtons.
What is the force applied to the object?A force is simply a push or a pull of an object resulting from the object's interaction with another object.
From newton's second law;
Force = mass × acceleration
Given the data in the question;
Mass of the object = 7kgAcceleration = 8m/s²Applied force = ?Plug the given values into the formula to determine the applied force.
Force = mass × acceleration
Force = 7kg × 8m/s²
Force = 56kgm/s²
Force = 56 N
Therefore, the applied force is 56 newtons.
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A boat on a river is moving with a steady speed. The engine is running.
What would happen if the engine was turned off?
If the engine of a boat on a river is turned off while the boat is moving with a steady speed, several things would happen Loss of propulsion,Drifting,Loss of steering control and Potential hazards.
Loss of propulsion: Without the engine running, the boat would lose its power source for propulsion. The boat would gradually slow down and eventually come to a stop unless other external forces, such as currents or wind, continue to move it.
Drifting: Once the boat comes to a stop, it would start to drift with the current of the river or be affected by wind forces. The direction and speed of the drift would depend on the strength and direction of the current or wind.
Loss of steering control: When the engine is turned off, the boat's steering mechanism, such as a rudder, would also lose power. Without the ability to steer, the boat would follow the course determined by the river's current or the wind direction.
Potential hazards: Depending on the surroundings and the current conditions, there could be potential hazards for a boat that is no longer under power. These hazards might include other vessels, obstacles, shallow areas, or strong currents. The boat's crew would need to take appropriate actions to ensure the safety of the boat and its occupants.
It's important to note that the specific behavior of the boat after the engine is turned off can vary depending on factors such as the size and design of the boat, the strength and direction of the current, and the presence of wind or other external forces.
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A ball is thrown from the top of a 15.0 m tall building. The ball is initially released with a speed of 25.0 m/s in the direction 30.0 degrees above the horizontal. 2.00 seconds after it was released, the ball is traveling with a speed of 22.8 m/s in the direction 18.2 degrees below the horizontal. Using a coordinate system where x points in the direction the ball was released and y points up, what is the y component of the ball's motion after 2.00 seconds
Answer: the final velocity and final velocity velocity can also be written as we It went to one route A. V. Of X. Care plus movie. Why is here? This is a vision number two. And this is a revision number one food equation and one into to get we want to and wrote. We now takes scared plus we not scared away helpless to And by and the horizontal and the vertical component which are we know scare X is equal to we not cost it and we're not scared by going to we not scientific putting these value. Immigration number three. We get we will too. Are we not scared? I got scared to to less. We not scare Science square theater plus two. Why? So this we equal to he went to work and rude. We're not scared people to got scared he to less science security theater Last two. A. Y. Sure we get we s we're not scared into I. Plus to A Y. So we is able to. And road we now scared. Plus two. Am I. So this is a vision number four. And we are given me an artist 14 m purse again. And why he has given us. Uh huh. three m. So we can we find out by putting this value innovation number for the disk 14 scared. Uh huh. Plus To into -9.8 into three. We get to be It will do 11.7. Me did last
Explanation:
Which element below would not be predicted to form bonds with other atoms?CarbonSodiumArgonFluorine
Argon
as it is an inert elemnt
15. A 1200 kg car has a velocity of 15 m/s at ground level (h=0, PE = 0).
What is the maximum height it can go up?
a.
b. What is the velocity of the car if it goes up a hill 3 meters high?
a. To determine the maximum height the car can go up, we need to use conservation of energy. At ground level, the car has kinetic energy equal to 1/2 mv^2, where m is the mass of the car and v is its velocity.
As the car moves up, its kinetic energy will be converted into potential energy, which is equal to mgh, where h is the height above ground level and g is the acceleration due to gravity (9.8 m/s^2). At the maximum height, all of the car's kinetic energy will have been converted into potential energy, so we can set these two expressions equal to each other and solve for h:
1/2 mv^2 = mgh
h = (1/2 v^2)/g
h = (1/2) (15 m/s)^2 / 9.8 m/s^2
h = 11.5 meters
Therefore, the maximum height the car can go up is 11.5 meters.
b. To determine the velocity of the car if it goes up a hill 3 meters high, we can use conservation of energy again. This time, the car will have both potential energy (due to its height above ground level) and kinetic energy. At the bottom of the hill, the car has kinetic energy equal to 1/2 mv^2, where m is the mass of the car and v is its velocity. As the car goes up the hill, its kinetic energy will be converted into potential energy, which is equal to mgh, where h is the height of the hill (3 meters) and g is the acceleration due to gravity (9.8 m/s^2). At the top of the hill, all of the car's kinetic energy will have been converted into potential energy, so we can set these two expressions equal to each other and solve for v:
1/2 mv^2 = mgh
v = sqrt(2gh)
v = sqrt(2 * 9.8 m/s^2 * 3 meters)
v = 7.7 m/s
Therefore, the velocity of the car if it goes up a hill 3 meters high is 7.7 m/s.
a. To find the maximum height the car can go up, we'll use the conservation of mechanical energy principle. At the maximum height, the car's kinetic energy (KE) will be converted to gravitational potential energy (PE). The formula for KE is (1/2)mv^2 and for PE is mgh.
At ground level, KE = (1/2)(1200 kg)(15 m/s)^2 = 135000 J, and PE = 0.
At the maximum height, KE = 0 and PE = mgh. So, we can set up the equation:
135000 J = (1200 kg)(9.81 m/s^2)(h)
Solving for h, we get:
h = 135000 J / (1200 kg * 9.81 m/s^2) ≈ 11.48 m
So, the maximum height the car can go up is approximately 11.48 meters.
b. To find the velocity of the car when it goes up a hill 3 meters high, we can use the conservation of mechanical energy principle again:
Initial KE + Initial PE = Final KE + Final PE
(1/2)mv^2_initial + 0 = (1/2)mv^2_final + mgh
(1/2)(1200 kg)(15 m/s)^2 = (1/2)(1200 kg)v^2_final + (1200 kg)(9.81 m/s^2)(3 m)
Solving for v_final, we get:
v_final ≈ 13.43 m/s
So, the velocity of the car when it goes up a hill 3 meters high is approximately 13.43 m/s.
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The rotational analogue of force is moment of force, also called torque.
a) The turning effect of force is maximum when the angle between R and F is.--------
b) A wheel starting from rest acquires an angular velocity of 10 rad/s in two seconds. The moment
of inertia of the wheel is 0.4 kg m 2 . Calculate the torque acting on it.
c) The possibility of falling backward with the ladder is more when you are high up on the ladder
than when you just begin to climb. Explain why.
Answer:
the inertia would be the force equal mass times the acceleration
10 thieworhet
Explanation:
A dog is walking back home and its motion is modeled by the graph above. What position was the dog at 3 seconds after it started walking home?
The velocity time graph of an object mass 50 g is shown in figure study graph and answer
1)calculate force acting on object in time interval 0-3 seconds
2)calculate the force acting on the object in the time interval 6-10 seconds
3)Is there any time interval in which no force acts on object.Justify
1) The force acting on the object during the time interval 0-3 seconds is 1/3 N.
2) The force acting on the object during the time interval 6-10 seconds is -0.5 N.
3) There is no time interval in which no force acts on the object.
(i) Force acting on the object in time interval 0-3 seconds. Force acting on the object is equal to the product of its mass and acceleration, i.e.,F = ma.
In the given velocity-time graph, the acceleration of the object can be determined by determining the slope of the velocity-time graph from 0 to 3 seconds.
Slope = (change in velocity) / (change in time)= (20-0) / (3-0) = 20/3 m/s^2
Acceleration, a = slope= 20/3 m/s^2
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × 20/3= 1/3 N.
Therefore, the force acting on the object during the time interval 0-3 seconds is 1/3 N.
(ii) Force acting on the object in time interval 6-10 seconds. Similar to the first question, the force acting on the object in time interval 6-10 seconds can be determined by determining the acceleration of the object during this time interval.
The slope of the velocity-time graph from 6 seconds to 10 seconds can be determined as follows:
Slope = (change in velocity) / (change in time)= (-20-20) / (10-6) = -40/4= -10 m/s^2 (negative sign indicates that the object is decelerating)
Mass of the object, m = 50 g = 0.05 kg
∴ Force acting on the object, F = ma= 0.05 × (-10)= -0.5 N.
Therefore, the force acting on the object during the time interval 6-10 seconds is -0.5 N.
(iii) Time interval in which no force acts on the object. There is no time interval in which no force acts on the object. This is because, as per Newton's first law of motion, an object will continue to remain in a state of rest or uniform motion along a straight line unless acted upon by an external unbalanced force.In other words, if the object is moving with a constant velocity, there must be a force acting on the object to maintain its motion.
Therefore, there is no time interval in which no force acts on the object.
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A car traveling at 3500 m/s is to stop on a 35-meter long shoulder of the road. What minimum deceleration is required?
The minimum deceleration required to stop the car in 35 meters is 40000 m/s^2.
What is deceleration?Deceleration is defined as the decrease in speed as the body moves away from the starting point.
The minimum deceleration required can be calculated using the equation of motion:
d = v^2 / (2 * a)
where d is the distance, v is the initial velocity, and a is the acceleration.
Rearranging the equation to solve for a:
a = v^2 / (2 * d) = (3500 m/s)^2 / (2 * 35 m) = 40000 m/s^2
In conclusion, , the minimum deceleration required to stop the car in 35 meters is 40000 m/s^2.
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draw each of the following vectors then find its x and y component. a. a = 3.5 m/s^2, negative x directionb. v = 440 m/s, 30° below the positive x-axisc. r = 12 m, 40° above the positive x-axis
Drawing the vectors, we have:
Now, calculating the components of each vector:
\(\begin{gathered} a_x=a\cdot\cos (180\degree)=3.5\cdot(-1)=-3.5 \\ a_y=a\cdot\sin (180\degree)=3.5\cdot0=0 \\ \\ v_x=v\cdot\cos (-30\degree)=440\cdot0.866=381 \\ v_y=v\cdot\sin (-30\degree)=440\cdot(-\frac{1}{2})=-220 \\ \\ r_x=r\cdot\cos (40\degree)=12\cdot0.766=9.19 \\ r_y=r\cdot\sin (40\degree)=12\cdot0.6428=7.71 \end{gathered}\)A 220g mass is on a frictionless horizontal surface at the end of a spring that has a force constant of 7.0N/m The mass is displaced 5 2m from its equilibrium position and then released to undergo simple harmonic motion.
At what displacement from the equilibrium position is the potential energy equal to kinetic energy?
Answer:
Explanation:
Your numbers seem wonky, so I'll just assume that the initial displacement is a distance A (Amplitude) from the equilibrium position. Spring constant = k
Initial potential energy is
PE = ½kA²
As potential energy and kinetic energy are constantly exchanging in SHM,
the position x where half of the original spring potential exists is found where
½kx² = ½(½kA²)
x² = ½A²
x = (√0.5)A
x ≈ 0.707A
just plug in your actual starting position A
With A = 5.2 cm
x = 3.67695... 3.7 cm
Which of the following is not one of the rules that must be followed regarding animal research? A. Animal research must have a clear scientific purpose. B. Animal research can acquire its animals illegally. C. Animal research must provide humane care and housing. D. Animal research must ensure the least amount of suffering possible. Please select the best answer from the choices provided A B C D
On research on animals they must given proper care and housing. And the purpose of the research must have a scientific reason. Thus option B is correct.
What is animal research?Animal research includes various scientific investigation on animals such as testing various doses of some drugs, effect of various chemicals, level of toxicity of some compounds etc.
According to the research ethics, no animals can be used to conduct any unscientific works. There must be a scientific purpose which is very important to conduct any animal research.
If any animals irrespective of its nature,it must be provided proper care, food and housing. No harmful things must be there which make them more suffering. Hence, option B is correct.
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9. When air or water is cools it...
A.) Sinks
B.) Becomes less dense
Answer:
when air or water cools it sinks
Two
cars, A and B , are travelling in the same
direction
although
Car B is 186 metres behind A. The
speed car B is 24.4 m/s and the speed of car A is 18.6 m/ s. How much time does it take for car B to catch up with car A?
Answer:
SA = 18.6 * t + 186 total distance traveled by A in time t
SB = 24.4 t total distance car B must travel to catch car A
SA - SB = 0 = 18.6 t + 186 = 24.4 t
(24.4 - 18.6) t = 186
t = 186 m / 5.8 m/s = 32 s
Check 18.6 * 32 + 186 = 781 m
24.4 * 32 = 781 m
If the coefficient of kinetic friction between a 29 kg crate and the floor is 0.38, what horizontal force is required to move the crate at a steady speed across the floor?
Let F be the magnitude of the force needed to keep the box sliding at constant speed, and f the magnitude of kinetic friction. Then by Newton's second law, the net horizontal force on the crate is
F - f = 0
so that
F = f
f is proportional to the magnitude of the normal force n,
f = 0.38n
The net vertical force is
n - mg = 0
which tells us that
n = mg = (29 kg) (9.8 m/s²) ≈ 284 N
Then the required force must have magnitude
F = f = 0.38 (284 N) ≈ 110 N
a spring is hanging from the ceiling. attaching a 560 gg physics book to the spring causes it to stretch 25 cmcm in order to come to equilibrium.part awhat is the spring constant?express your answer with the appropriate units.view available hint(s)for part aactivate to select the appropriates 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 typekk
The value of the spring constant is 8704 N/m.
The spring constant (k) can be found using Hooke's law, which states that the force required to stretch or compress a spring is proportional to the distance it is stretched or compressed.
Mathematically, it can be expressed as:
F = -kx
where F is the force applied to the spring,
k is the spring constant, and
x is the distance the spring is stretched or compressed.
Since the force applied to the spring is equal to the weight of the book, we can write:
F = mg = -kx
where m is the mass of the book and
g is the acceleration due to gravity.
Substituting the given values, we get:
560 g * 9.8 m/s^2 = -k * 0.25 m
Dividing both sides by -0.25 m and solving for k,
we will get it as:
k = (560 g * 9.8 m/s^2) / 0.25 m
k= 8704 N/m
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A hot air balloon 30 m above the ground is tethered by three cables as shown by DA, DB and DC. The coordinates of the the points A, B and C with respect to the origin are (-20,0,0), (30,0,20) and (0,0,20), respectively,
If the hot air balloon is pulling upwards with a force of 900 N, what is the tension in each three cables.
The grid lines on the ground plane are spaced 10 m apart. Note: Height is along the y axis.
a)Find position vector for DA , DB , DC
b) Find unit vector for DA , DB , DC
c) Using Laws of Equilibrium find force in each cable.
The force in each cable depends on the orientation of the cable relative
to the force of the balloon and to each other.
Responses:
a) The position vectors are;
Position vector, DA, \(r_{DA}\) = -20·i - 30·j + 0·k
DB, \(r_{DB}\) = 30·i - 30·j + 20·k
DC, \(r_{DC}\) = 0·i - 30·j + 20·k
\(b) \hspace{0.15 cm} Unit \ vectors \ are, u_{DA} = \underline{ \dfrac{-2 \cdot \sqrt{13} \cdot i}{13} - \dfrac{ 3 \cdot \sqrt{13} \cdot j }{13 }}\)
\(u_{DB} = \underline{\dfrac{3 \cdot \sqrt{13} }{13} \cdot i + \dfrac{2 \cdot \sqrt{13} }{13} \cdot k}\)\(u_{DC} = \underline{ -\dfrac{3 \cdot \sqrt{13} }{13} \cdot j + \dfrac{2 \cdot \sqrt{13} }{13} \cdot k}\)c) The approximate values of the force in each cable are;
DA: 3245 NDB: 2163.3 NDC: -2163.3 NWhich method is used to calculate forces in vector form?a) The position vector is a vector that locates a point relative to another point.
The position vector,
\(r_{DA} = \mathbf{ r_A - r_D}\)
Whereby the coordinate of the point D is taken as (0, 30, 0), we have;
\(r_{DA}\) = -20·i + 0·j + 0·k - (0·i + 30·j + 0·k) = -20·i - 30·j + 0·kSimilarly, we have;
\(r_{DB}\) = 30·i + 0·j + 20·k - (0·i + 30·j + 0·k) = 30·i - 30·j + 20·k
\(r_{DC}\) = 0·i + 0·j + 20·k - (0·i + 30·j + 0·k) = 0·i - 30·j + 20·k
b) The unit vectors are therefore;
\(u_{DA} = \mathbf{ \dfrac{r_{DA}}{|r_{DA} |}}\)
Which gives;
\(u_{DA} = \dfrac{-20 \cdot i - 30 \cdot j + 0 \cdot k}{\sqrt{(-20)^2 + (-30)^2 + 0} } = \dfrac{-2 \cdot i - 3 \cdot j }{\sqrt{13} } = \dfrac{\left(-2 \cdot i - 3 \cdot j \right) \times \sqrt{13} }{13 }\)
\(u_{DA} = \mathbf{ \dfrac{-20 \cdot i - 30 \cdot j + 0 \cdot k}{\sqrt{(-20)^2 + (-30)^2 + 0} }}} = \dfrac{-2 \cdot i - 3 \cdot j }{\sqrt{13} } = \underline{\dfrac{-2 \cdot \sqrt{13} \cdot i}{13} - \dfrac{ 3 \cdot \sqrt{13} \cdot j }{13 }}\)
\(u_{DB} = \dfrac{30 \cdot i + 0 \cdot j + 20 \cdot k}{\sqrt{(30)^2 + (20)^2 + 0} } = \mathbf{\dfrac{3 \cdot i +2 \cdot k }{\sqrt{13} } } = \underline{\dfrac{3 \cdot \sqrt{13} }{13} \cdot i + \dfrac{2 \cdot \sqrt{13} }{13} \cdot k}\)
\(u_{DC} = \mathbf{\dfrac{-30 \cdot j + 20 \cdot k}{\sqrt{(30)^2 + (20)^2 } } }= \underline{-\dfrac{3 \cdot \sqrt{13} }{13} \cdot j + \dfrac{2 \cdot \sqrt{13} }{13} \cdot k}\)
c) The force in each cable are found as follows;
\(\vec F_{DA} = \mathbf{ \dfrac{-2 \cdot \sqrt{13} }{13}\cdot i \cdot F_{DA}- \dfrac{ 3 \cdot \sqrt{13} }{13 } \cdot j\cdot F_{DA}}\)
\(\vec F_{DB} = \mathbf{ \dfrac{3 \cdot \sqrt{13} }{13} \cdot i \cdot F_{DB}+ \dfrac{2 \cdot \sqrt{13} }{13} \cdot k\cdot F_{DB}}\)
\(\vec F_{DC} = \mathbf{ -\dfrac{3 \cdot \sqrt{13} }{13} \cdot j \cdot F_{DC}+ \dfrac{2 \cdot \sqrt{13} }{13} \cdot k\cdot F_{DC}}\)
Sum of forces, ∑F = 0, gives;
\(\mathbf{ \dfrac{-2 \cdot \sqrt{13} }{13}\cdot i \cdot F_{DA} +\dfrac{3 \cdot \sqrt{13} }{13} \cdot i \cdot F_{DB}} = 0\)
\(\mathbf{ - \dfrac{ 3 \cdot \sqrt{13} }{13 } \cdot j\cdot F_{DA} -\dfrac{3 \cdot \sqrt{13} }{13} \cdot j \cdot F_{DC} + 900} = 0\)
\(\mathbf{ \dfrac{2 \cdot \sqrt{13} }{13} \cdot k\cdot F_{DB} + \dfrac{2 \cdot \sqrt{13} }{13} \cdot k\cdot F_{DC}} = 0\)
Solving the above simultaneous equation with a graphing calculator gives;
The force in the cable DA, \(F_{DA}\) ≈ 3245 NThe force in the cable DB, \(F_{DB}\) ≈ 2163.3 NThe force in the cable DC, \(F_{DC}\) ≈ -2163.3 NLearn more about vectors here:
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Explain the advantages and disadvantages of having a racecar with a small mass in reference to Newton’s 1st law of motion. Use the term inertia in your answer.
Answer:
Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This tendency to resist changes in a state of motion is inertia.
Explanation:
Which expenses do you think will change based on how much you drive
Increased driving can lead to higher vehicle maintenance and repair expenses, increased fuel costs, potential increases in auto insurance premiums, and additional parking fees, all of which should be considered when estimating the overall impact on your expenses.
The expenses that are likely to change based on how much you drive can be broadly categorized into two main areas: vehicle-related expenses and fuel-related expenses.
1. Vehicle-related expenses: The more you drive, the more wear and tear your vehicle will experience, leading to increased maintenance and repair costs. Regular oil changes, tire replacements, brake pad replacements, and other routine maintenance tasks will be required more frequently.
2. Fuel-related expenses: It's intuitive that the more you drive, the more fuel you'll consume, resulting in higher fuel expenses. Fuel prices can vary, but regardless of fluctuations, increased mileage will directly impact your fuel budget. Fuel-efficient vehicles may mitigate some of these costs, but the overall impact on your expenses will still be noticeable.
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