When initially containing 13.5 moles of sulfur dioxide and 11.2 moles of oxygen, the remaining moles of O2 are 4.45 moles.
What is reaction?All forces occur in pairs, as described by the third of Newton's laws of motion in classical mechanics, so that if one object exerts a force on another, the second object exerts an equal and opposite reaction force on the first. A reaction force is the result of an opposite-direction action force. Newton's third law of motion addresses these two forces, referred to as action and reaction forces. Newton's third law states that there is an equal and opposite reaction to every action.
Here,
2 ℎ ℎ 11.2 O2=11.2*2=22.4 moles
mols of SO3 produced=13.5*2/2
13.5 mols
mols of O2 consumed=13.5*1/2
=6.75 mols
mols of O2 remaining=11.2-6.75
=4.45 mols of O2
The moles of O2 remaining is 4.45 moles when initially containing 13.5 moles of sulfur dioxide and 11.2 moles of oxygen.
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Complete question:
When initially containing 13.5 moles of sulfur dioxide and 11.2 moles of oxygen, the remaining moles of O2 are 4.45 moles. What is reaction? What amount of oxygen is remaining?
demonstrate a voltage measurement across one of the leds using the digital multimeter (dmm). to make this measurement, turn the dial on the dmm to voltage. place the dmm black test lead on the led cathode terminal and the red lead on the led anode terminal. if this is done correctly, your dmm should display the threshold value of your led.
To measure the voltage across an LED using a digital multimeter (DMM), follow these steps:
1. Turn the dial on the DMM to the voltage measurement setting.
2. Place the DMM black test lead on the LED cathode terminal and the red lead on the LED anode terminal.
3. The DMM should display the threshold voltage of the LED.
It is important to note that the cathode is the negative terminal, and the anode is the positive terminal of the led.
What is electric potential difference?Electric potential energy per unit charge in an electrical circuit is measured by voltage, sometimes referred to as electric potential difference. It is commonly measured in units of volts (V). Voltage is the force that causes electric current to flow in a circuit, and it can be thought of as the "pressure" that pushes the electrons through the circuit.
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An empty Erlenmeyer flask weighs 246.3 g. When filled with water (density = 1.00 g/cm^3), the flask and its contents weigh 495.0 g.(a) What is the flask's volume? (b) How much does the flask weigh when filled with chloroform (d = 1.48 g/cm^3)?
The volume of the Erlenmeyer flask when filled with water is 249 cm^3.
What is volume?Volume is a measure of the amount of three-dimensional space an object occupies. It is measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in many areas of science, including physics, chemistry and geology. It can also be used to describe the capacity of a container, such as a bottle, or the amount of liquid it can hold. Knowing the volume of a substance or object is important in many everyday situations, from measuring food portions to calculating the amount of paint needed to cover a wall.
This is calculated by subtracting the weight of the empty flask (246.3 g) from the weight of the flask filled with water (495.0 g) and then dividing by the density of water (1.00 g/cm^3).
When filled with chloroform, the flask and its contents weigh 581.1 g. To calculate this, we multiply the density of chloroform (1.48 g/cm^3) by the volume of the flask (249 cm^3), which gives us 371.52 g. We then add the weight of the flask (246.3 g) to the weight of the chloroform (371.52 g), which gives us a total of 617.82 g. The weight of the flask when filled with chloroform is 581.1 g.
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A stone is dropped from rest at an initial height h above the surface of the earth. Show that the speed with which it strikes the ground is v= 2gh. Let x(t) be the position of the stone above the ground. The differential equation ____ relates the position of the stone to the acceleration due to gravit
A stone is dropped from rest at an initial height h above the surface of the earth. Show that the speed with which it strikes the ground is v= 2gh.
Let x(t) be the position of the stone above the ground.
The differential equation x'= - g relates the position of the stone to the acceleration due to gravity.
Differential Equation DefinitionA differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable)
dy/dx = f(x)
Here “x” is an independent variable and “y” is a dependent variable
For example, dy/dx = 5x
A differential equation contains derivatives which are either partial derivatives or ordinary derivatives. The derivative represents a rate of change, and the differential equation describes a relationship between the quantity that is continuously varying with respect to the change in another quantity. There are a lot of differential equations formulas to find the solution of the derivatives.
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the shaft is supported by a smooth thrust bearing at b and a journal bearing at c. determine the resultant internal loadings acting on the cross section at e. suppose that p1
Determine the normal force, shear force and moment at a section passing through (a) point C, which is just to right of bearing at A, and (b) point D, which is just to the left of the Force F2.
What is thrust bearing ?
Thrust bearings support the axial thrust of both horizontal and vertical shafts. The functions are to prevent the shaft from drifting in the axial direction and to transfer thrust loads applied on the shaft.A thrust bearing is a bearing which allows parts to rotate with little friction whilst absorbing an axial thrust. The single plate dry clutch, with ball thrust bearing, is assembled with the engine and three-speed gearbox. A thrust bearing must be used to control end thrust.These thrust bearings are located at a specific main bearing location, generally at the center main or rear main, depending on engine design. A thrust bearing is either integrated with a specific main bearing assembly or independent of the main journal bearing.To learn more about shaft refers to:
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which of the labeled parts of the microscope would you adjust to move your specimen left, right, forward, and backward?
The labeled parts of microscope that you would adjust to move the specimen left, right, forward, and backward are called the stage controls.
What is microscope?Microscope is an instrument that is used to observe small objects, even the cells. The lens bends light toward the eye and makes object appear larger than it actually is.
The stage controls consist of two knobs, one for moving the specimen left and right (x-axis), and one for moving specimen forward and backward (y-axis). The knobs are located on the lower part of the microscope's base, near stage where the specimen is placed. These controls allow you to position specimen correctly under the objective lens for observation.
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In the late 1960's and 1970's the Apollo program landed many astronauts on the Moon. On one of
the trips the astronauts left a corner reflector. This is a special mirror which reflects light exactly in
the direction from where it came. This enabled scientists on Earth to determine the distance to the
Moon within a few centimeters. This is one of the most accurate measurements ever made between
the Earth and the Moon.
In one experiment, scientists on earth shone a laser beam onto the corner reflector and measured
how long it took for the beam to return to Earth. The time they measured was 2.63 seconds. How
many kilometers away was the moon at the time of the experiment?
"laser beam" can be handled as "light".
Speed of light in vacuum = 300,000 km/sec
Distance = (speed) x (time)
Distance light traveled = (300,000 km/sec) x (2.63 sec)
Distance the light traveled = 789,000 km
But this is DOUBLE the distance to the moon, because the laser light had to GO and COME BACK in order to be detected back on Earth.
So the distance to the moon was (1/2) of (789,000 km) = 394,500 km
(b) In an experiment to magnetize two substances P and Q using electric current, two curves(graphs) were obtained as shown in figure 1 Magnetisation Magnetising Current I Fig. 1 explain the difference between p and q with reference to domain theory
Single-touch method: The magnetic substance is moved from one end to the other by rubbing a magnet along it.
what are magnetic substance?Double-touch technique: Placed next to one another in the middle of the magnetic substance, the opposite poles of two magnets are stroked along it in the opposite direction.Making temporary magnets by induction is a technique that uses a magnetic field to do so. Once the magnetising force is no longer there, the magnetic qualities vanish.(A permanent magnet is brought close but not in contact with the magnetic substance.) Electromagnets are created utilising electric current and are referred to as such. It is a passing magnet that loses its magnetic properties when the current is cut off. If specific materials, such as steel and particular alloys, are put in a coil and a powerful current is run through it, electromagnets can turn into permanent magnets.To learn more about magnetic refer to:
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Skills, which include balance and reaction time, are the talents or abilities that allow one to perform task.
True
False
True. Skills, which include balance and reaction time, are the talents or abilities that allow one to perform task.
What are skills?
Skills are the ability to perform a task due to training and experience.
The term skill is used to describe specific action or level of performance of an individual.
There are three types of skills and they include;
functional, self-management and special knowledge.Functional skills are abilities or talents that are inherited at birth and developed through experience and learning
Thus, we can conclude that Skills, which include balance and reaction time, are the talents or abilities that allow one to perform task.
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Can anyone please help me answer this question?
A body of mass 5 kg, projected at an angle 60 degrees from the ground at an initial velocity of 25 m/s, acceleration due to gravity is 10 m/s^2. What is the maximum horizontal range covered?
a.) 54.13 m b.) 49 m c.) 49.16 m d.) 60 m. Explain.
Answer:
a) 54.13m
Explanation:
The formula for horizontal range is R = v2 (sin 2θ)/g. Here, v = 25, θ = 60°, g = 10. Hence, on solving we will get range as 54.13 m.
In the video, the loaded car accelerated less than the unloaded car when the same force was applied. This was noticeable because the loaded car
Choose one or more:
A. was traveling faster after a little time had passed.
B. reached the end of the track more slowly.
C. reached the end of the track faster.
D. was traveling less quickly after a little time had passed.
When the same force was supplied to the loaded and unloaded cars, the loaded car accelerated less, which was visible since the laden car arrived at the track's finish more slowly. and after a little while, she started moving less swiftly. so Option B and option Dare correct
The rate at which an object's velocity with respect to time changes is referred to as the mechanics of acceleration. Acceleration is a vector quantity (in that they have magnitude and direction). The direction of an object's acceleration is determined by the direction of the net force acting on it.According to Newton's Second Law, an object's acceleration is determined by a combination of two factors: its mass, which depends on the materials it is made of, and the net balance of all external forces acting on it. The magnitude of an object's acceleration is inversely proportional to the mass of the object.
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A kangaroo can jump over an object 2.50 m high. (a) Calculate its vertical speed when it leaves the ground, in meters per second(b) How long is it in the air?
Since the velocity at the highest location is 0, we are searching for the beginning velocity. The kangaroo will thus be moving vertically at a speed of 7 m/s when it leaves the ground.
The formula v = may be used to determine a kangaroo's vertical speed as it takes off from the ground (2gh). where h is the height of the kangaroo's leap, g is the acceleration caused by gravity (9.8 m/s2), and v is the vertical speed (2.5 m). After entering the numbers, we obtain the following: v = (49) = 7 m/s (2 * 9.8 * 2.5)
Therefore, the kangaroo's vertical speed when it lifts off the ground is 7 metres per second.
The equation t = (2h/g), where t is the duration in the air and h is the height the kangaroo is jumping from, may be used to determine how long it has been in the air (2.5 m). The values are entered, and the result is: t = ((2 * 2.5 / 9.8)) = (0.51) = 0.71 s.
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A long distance runner has an average speed of 3.4 m/s. How far (in m) does the runner travel in 20 min?
Two point charges are arranged as shown In which region could a third charge +1 C be placed s0 that the net electrostatic force on it is Zero? Ionly III only and II only II only
It might be limited to Region I exclusively. The electric field caused by the charge +2C is directed away from the charge, but the one caused by the charge -4C is directed towards it.
What is charge?When put in an electromagnetic field, the physical feature of matter known as electric charge causes that matter to experience a force. A positive or negative electric charge can exist. Like charges repel one another, whereas unlike charges attract one another. A neutral object is one that does not have any net charge. Charge, also known as electric charge, electrical charge, or electrostatic charge, and denoted by the symbol q, is a property of matter that reflects the amount to which it contains more or less electrons than protons.
Here,
It may only be available in Region I. The electric field caused by charge +2C is directed away from the charge, but the one caused by charge -4C is directed towards it.
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a small block of mass m slides on a horizontal frictionlesssurface as it travels around the inside of a hoop of radiusr. the coefficient of friction between the block and the wallis u; therefore, the speed v of the block decreases. in termsof m, r, u, and v, find expressions for each of thefollowing.
The expressions are [tex]F = m g[/tex] , [tex]F = \frac{m v^{2} }{r}[/tex].
The frictional force: This force opposes motion and is created as a result of friction between two surfaces.
[tex]F = m g[/tex]
where m is the object's mass and g is the acceleration brought on by gravity, is a formula for expressing the frictional force.
The centripetal force: To keep an object moving in a circular path, the centripetal force, which is directed toward the centre of the path, must be present.
[tex]F = \frac{m v^{2} }{r}[/tex]
where m is the object's mass, v is its speed, and r is its circular path's radius, is a formula for the centripetal force.
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A pinball bounced around its machine before resting between two bumpers. Before the ball came to rest, its displacement was recorded as a series of vectors. All the angles are measured counterclockwise from the horizontal ‑axis.
⃗ 1:83.0 cm at 90.0∘
⃗ 2:57.0 cm at 159∘
⃗ 3:67.0 cm at 221∘
Find the magnitude and direction of the ball's total displacement.
The magnitude and direction of the ball's total displacement is 119.6 cm and 29.8⁰ respectively.
What is the magnitude of the ball's total displacement?
The magnitude of the ball's total displacement is calculated by applying the following formula.
The sum of the horizontal displacement is calculated as follows;
∑X = 83 cm x cos (90) + 57 cm x cos (159) + 67 cm x cos (221)
∑X = -103.78 cm
The sum of the vertical displacement is calculated as follows;
∑Y = 83 cm x sin (90) + 57 cm x sin (159) + 67 cm x sin (221)
∑Y = 59.47 cm
The magnitude of the displacement is calculated as follows;
d = √ [ ( -103.78 )² + ( 59.47)² ]
d = 119.6 cm
The direction of the displacement is calculated as follows;
θ = arc tan ( 59.47 / 103.78 )
θ = 29.8⁰
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21. A 110-V household circuit that contains an
1800-W microwave, a 1000-W toaster, and an
800-W coffeemaker is connected to a 20-A fuse.
Determine the current. Will the fuse melt if the
microwave and the coffeemaker are both on?
The final current will be 32.7 A and Yes, the fuse will melt if the microwave and the coffeemaker are both on at the same time.
How to determine current and whether or not a fuse has melted?
To determine the current, we can use Ohm's Law, which states that current (I) is equal to power (P) divided by voltage (V).
I = P/V
The total power of the three appliances is 1800 W + 1000 W + 800 W = 3600 W.
Therefore, the current is:
I = 3600 W / 110 V = 32.7 A
The fuse is rated at 20 A, so it will melt if the current exceeds 20 A. Since the current is 32.7 A, the fuse will melt if the microwave and the coffeemaker are both on at the same time.
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determine the average normal stress developed in rod ab if the load has a mass of 56 kg . the diameter of rod ab is 8 mm .
The gratis diagram idea, force equilibrium, arrive at a solution. To find the stress in rod AB, first design a model of the free items but then apply equilibria. Next, calculate the stress using the rod's diameter and force.
Definition of diametera straight line that cuts through the middle of a body or figure. especially: the distance along a line passing thru the center of the circle and having its endpoints on the circumference.
Definitions of diameter and circumferenceA circle's circumference is indeed the width of one full "lap," and its diameter is indeed the length of line segment that divides it in half. Imagine that diameter is an interior measurement, whereas circumference is an outside measurement.
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assume that a person skiing high in the mountains at an altitude of 15,000 ft takes in the same volume of air with each breath as she does while walking at sea level. determine the ratio of the mass of oxygen inhaled for each breath at this high altitude compared to that at sea level.
The ratio of the mass of oxygen inhaled for each breath at high altitude and at sea level is 0.629.
Let the mass of oxygen inhaled at sea level, = m₀
Let the mass of oxygen inhaled at 15000 ft, = m₁₅
The volume of air inhaled is same for both case, = v
Density of the air at mean seal level, ρ₀ = 2.337 × 10⁻³ sl/m³
Density of the air at 15000 ft, ρ₁₅ = 1.469 × 10⁻³ sl/m³
m₀ = ρ₀V, m₁₅ = ρ₁₅V
m₁₅/m₀ = ρ₁₅V/ρ₀V
m₁₅/m₀ = (1.469 × 10⁻³)/(2.337 × 10⁻³)
m₁₅/m₀ = 0.629
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In our warmup today we're looking closer at our aquariums. We need to get them clean so we can start a new aquarium setup , but there's something on the inside of the glass, the outside of the hood, and the outside of the filter.
1. What is that white residue on our aquariums?
2. How does it form?
3. Where does it come from?
4. How do we get rid of it?
The white residue on aquariums could be mineral , such as hard water stains, and it formed as a result of the hard substance remaining after water evaporation. It is from the water, and to remove it, a white vinegar and water mixture should be used.
What is the significance of the aquarium?Its significance includes that an aquarium can be a place for people to learn about aquatic animals, for the conservation of some animals, for entertainment, and also for use in research proposals, etc.
Hence, the white residue on aquariums could be mineral , such as hard water stains, and it formed as a result of the hard substance remaining after water evaporation. It is from the water, and to remove it, a white vinegar and water mixture should be used.
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An object moves from location D to location F on a trajectory (dotted line) in the direction indicated; arrows representing the momentum at locations D, E, and F. ' EP 9 zero magnitude 10 more info needed (a 15pts) Using the numbered direction arrows shown, indicate (by number) which direction arrow best represents the direction of the quantities listed below. If the quantity has zero magnitude or cannot be determined, indicate using the corresponding number listed below. • The position vector at location D • The change in position the displacement) between location D and location F • The change in velocity between location D and location F_ • The change in momentum between location D and location F • The average net force between location D and location F
• The position vector at location D: 1
• The change in position (the displacement) between location D and location F: 3
• The change in velocity between location D and location F: 2
• The change in momentum between location D and location F: 4
• The average net force between location D and location F: EP (zero magnitude)
The position vector at location D is represented by arrow 1, as it indicates the location of the object at that point. The change in position, or displacement, between location D and location F is represented by arrow 3, as it shows the overall change in position of the object from one location to the other. The change in velocity between location D and location F is represented by arrow 2, as it shows the overall change in the object's velocity during that time.
The change in momentum between location D and location F is represented by arrow 4, as it shows the overall change in the object's momentum during that time. The average net force between location D and location F cannot be determined with the information given.
The complete question is given below in the image.
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which of the following helps explain why the buoyant force exerted on an object submerged in a fluid on earth is always directed upward? a. the buoyant force forms a newton's third law pair with the force of gravity on the object
b. the fluid pressure exerts a force that balances the weight of the object, which mean pressure is only exerted upward on the object
c. fluid pressure is exerted on all surfaces of an object and increases with depth. the horizontal forces due to the pressure cancel, but the vertical forces do not d. the surface tension between fluid molecules tends to resist the object moving downward through the surface of the fluid. the resistive force causes a net force upward
The buoyant force forms a newton's third law pair with the force of gravity on the object helps explain why the buoyant force exerted on an object submerged in a fluid on earth is always directed upward.
What is buoyancy, exactly?The term "buoyancy" refers to the upward push a liquid applies to an object submerged in it. An upward force is imposed on an object when you try to submerge it in water, and this force grows as the object is pushed deeper. The tendency of a fluid to exert an upward force on an item that is partially or completely submerged in that fluid is known as buoyancy or a buoyant force. Newton is the SI unit for buoyant force. An object in water experiences an upward force known as buoyancy that is equal to the weight of the water that the object has displaced.
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A constant net force, F net is applied to a cart with mass,m, causing an acceleration,a. If the mass of the cart is doubled, but the net force remains the same, what will the acceleration of the car be?
The acceleration of the car if the mass of the cart is doubled is ½a (option A).
How to calculate acceleration?Acceleration refers to change of velocity with respect to time (can include deceleration or changing direction).
Newton's first law of motion explains the relationship between the mass, force and acceleration of a body using the following expression;
Force = mass × acceleration
Mass and acceleration of a body are indirectly related. This means that if mass increases, acceleration decreases, hence, the acceleration in this question will decrease by half i.e. ½a.
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which substances could be present in earths spectrum, but it is difficult to say that they are definitely present? why?
Traces gases and heavy elements are the examples of the substances that could be in the earths spectrum. They cannot be detected because the technology to do this is not available.
Which substances could be present in earths spectrum?There are several substances that could be present in Earth's spectrum, but it is difficult to say that they are definitely present due to the limitations of current technology and methods for detecting and analyzing these substances. Some examples include:
Trace gases: Gases such as methane, nitrous oxide, and carbon monoxide can be present in small concentrations in the Earth's atmosphere, but it is difficult to detect them with high accuracy due to the limitations of current sensing technology.
Heavy elements: Elements such as gold, platinum, and mercury are present in trace amounts in the Earth's crust, but it is difficult to detect them using current analytical methods.
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two identical springs are attached to two different masses, ma and mb , where ma is greater than mb . the masses lie on a frictionless surface. both springs are compressed the same distance, d , as shown in the figure. which of the following statements descibes the energy required to compress spring a and spring b?
The amount of energy required to compress spring A and spring B would be the same.
What is energy?Energy is the capacity to do work. It is the ability to cause change and is found in many forms, including chemical, electrical, mechanical, nuclear, radiant, and thermal energy. It is often referred to as the "lifeblood" of our modern society, as it is necessary for everything from powering homes and businesses, to providing energy for transportation and communication.
This is because the springs are identical and the amount of compression (d) is the same. The masses of the objects don't affect the energy required to compress the springs since the objects are lying on a frictionless surface and will not resist the springs being compressed.
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A bullet of mass 10 g strikes a ballistic pendulum of mass 2.0 kg. the center of mass of the pendulum rises a vertical distance of 12 cm. assuming that the bullet remains embedded in the pendulum, calculate its initial speed
a. 425 ms
b. 256 ms
c. 321 ms
d. 308 ms
It's initial speed is 308 m/s.
The kinetic energy of the bullet is converted to potential energy for the whole system therefore we have:
[tex]\frac{1}{2}(m_{1} + m_{2} )V^{2} = (m_{1} + m_{2} )gh[/tex]
i.e. [tex]V = \sqrt{2gh}[/tex]
Now by conservation of momentum,
[tex]m_{1} v = (m_{1}+ m_{2} )V[/tex]
[tex]v = (m_{1}+ m_{2} )V / m_{1}[/tex]
[tex]v = (m_{1}+ m_{2} )\sqrt{2gh} / m_{1}[/tex]
Where,
v = initial speed
m1 = mass of pendulum = 2 kg
m2 = mass of bullet = 10 g = 0.01 kg
h = vertical distance = 12 cm = 0.12m
Putting these values in above equation we get : V = 308 m/s
Conservation of momentum is a crucial law of physics. It expresses that the total momentum of a detached or isolated system/framework is conserved. As such, the total momentum of a system of objects stays steady during any interaction, if no external force follows up on the system.To know more about kinetic energy visit:
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A car weighs 15,000 n and its tires are I flared to a pressure of 190 kPa. How large is the area of the cars tires that are in contact with the road
From pressure definition, the area of the car tires that are in contact with the road is 0.079 m
What is Pressure ?Pressure can be defined as the ratio of force to area. It is measured in Pascal.
Given that a car weighs 15,000 N and its tires are I flared to a pressure of 190 kPa. How large is the area of the cars tires that are in contact with the road ?
From the definition of Pressure, P = F/A
Where
P = 190 KPaF = 15,000 NA = ?190000 = 15000/A
A = 15000/190000
A = 0.079 m
A car will have 4 tires. The area of one in contact with the road will be
A = 0.079/4
A = 0.02 m
Therefore, the area of the car tire that is in contact with the road is 0.02 m
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imagine you looked up the accelerations of the following objects: snails, humans, thomson's gazelles, the space shuttle, formula one race cars, and f-16 fighter jets. which of the following statements about the acceleration of a cheetah would you expect to be true?
The acceleration of a cheetah is higher than that of a Thomson's gazelle but lower than that of the space shuttle during takeoff.
What is the most straightforward explanation of acceleration?The amount upon which velocity decreases is known as accelerate. Acceleration typically indicates that the speed is changing, but not necessarily. An item that is moving in a circle while maintaining a constant speed is still accelerating because the direction of its motion is shifting.
What exactly is acceleration?The measurement of a change in an object's velocity is known as acceleration. A car accelerates faster and quicker when the gas pedal is depressed. Acceleration is indicated by this change in velocity.
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Can anyone please help me answer this question?
An object moving in a straight line has a velocity v in m/s that varies with time t in s according to the following function.
v = 8 + 2.5 t2
11. The instantaneous acceleration of the object at t = 2 s is
(A) 2 m/s2 (B) 4 m/s2 (C) 6 m/s2 (D) 8 m/s2 (E) 10 m/s2
12. The displacement of the object between t = 0 and t = 6 s is
(A) 120 m (B) 180 m (C) 228 m (D) 242 m (E) 260 m
Show working
The basketball passed through the hoop even though it barely cleared the hands of the player B who attempted to block it Suppose that s 4.5 ft . Neglect the size of the ball. (Figure 1) Part A Determine the magnitude vA of its initial velocity Express your answer to three significant figures and include the appropriate units Value Units Submit Request Answer ▼ Part B Determine the height h of the ball when it passes over player B Express your answer to three significant figures and include the appropriate units
A) The initial velocity of the ball is 20.14 m/s, B) the height of the ball when it passes over player B is 11.36 ft.
Let the initial velocity of the basketball, = v
Horizontal component, = vcos30 = 0.866 v
Vertical component, = vsin30 = 0.5 v
Horizontal distance travelled by the ball, H = 25 + 4.5 = 29.5 ft
We know vcos30 × t = 29.5
vt = 29.5/0.866 = 34.06 ft
vt = 34.06
Now by the third equation of motion, vertical height(10 - 7 =3 ft) travelled by the vertical component of the ball
(10 - 7) = vsin30 × t - 0.5gt²
3 = 0.5vt - 0.5 × 9.81 × t²
we know vt = 34.06
3 = 0.5 × 34.06 - 4.9t²
t = 1.69 sec
So, v = 34.06/1.69 = 20.14 m/s
Now part B,
Height of the ball above the player B, = h
horizontal range, R = 25 ft
Time taken to reach 25 ft = 25/(20.14 cos30)
= 25/17.44 = 1.43 sec
vertical distance travelled by the ball in 1.43 sec,
d = 20.14×sin30×1.43 - 0.5 × 9.81 × 1.43²
d = 4.37 ft
Total height above the ground, H = 7 + 4.37 = 11.34 ft.
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A toy car of mass 2-kg travels along a horizontal surface with negligible friction at a speed of 1.0 m/s. The car then collides with a vertical wall. The wall applies a force of magnitude 20 N for 0.2 s on the toy car. Which of the following predicts the motion of the toy care immediately after the collision?
A: The speed of the car will increase, and the car will travel in the opposite direction.
B: The speed of the car will decrease, and the car will travel in the opposite direction.
C: The speed of the car will remain the same, and the car will travel in the opposite direction.
D: The car will stop and remain motionless.
The speed of the car will remains the same but the direction will be changed, if the force applied by the wall is 20 N for 0.2 s.
Mass of the toy car, m = 2 kg
Initial velocity of the car, v₁ = 1 m/s
The force applied by the car, F = 20 N
Duration of the applied force, Δt = 0.2 s
So the impulse applied by the wall, = F×Δt = 20 × 0.2 = 4 N-s
We know, impulse = change in momentum
Let the final velocity of the car is v, then
4 = m₁v₁ - m₁v₂
4 = 2 × 1 - 2 × v₂
4 = 2 - 2v₂
v₂ = (4-2)/-2 = -1 m/s
So v₂ = -1 m/s
A negative sign indicates that the direction of the car will be opposite to the initial velocity.
Hence the correct option is C.
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