The period of oscillation of the sphere is 161 seconds.
What is oscillation?
Oscillation is the repetitive movement of a particle or system about a central position or equilibrium point. Oscillations can occur in a variety of forms, such as periodic oscillations (which repeat at regular intervals), damped oscillations (which gradually decrease in amplitude over time), and driven oscillations (which are driven by an external force).
To find the period of oscillation of the sphere, you need to know its angular frequency, which is given by the following formula:
angular frequency = sqrt(k / I)
where k is the angular spring constant (also known as the torsional spring constant), and I is the moment of inertia of the sphere.
The angular spring constant is given by the following formula:
k = torque / angle of twist
Plugging in the values from the problem, you get:
k = 0.20Nm / 0.85rad = 0.235Nm/rad
The moment of inertia of a solid sphere is given by the following formula:
I = (2/5) * mass * radius^2
Plugging in the values from the problem, you get:
I = (2/5) * 95kg * (15cm)^2 = 6750kg*cm^2
Plugging these values into the formula for angular frequency, you get:
angular frequency = sqrt(0.235Nm/rad / 6750kg*cm^2) = 0.0062rad/s
The period of oscillation is the reciprocal of the angular frequency, so you can calculate it using the following formula:
period = 1 / angular frequency
Plugging in the value for angular frequency that you calculated above, you get:
period = 1 / 0.0062rad/s = 161s
Therefore, the period of oscillation is 161 seconds.
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While operating around buildings, the remote PIC should be aware of the creation of wind gusts that
answer choices
— change rapidly in direction and speed causing turbulence.
— enhance stability and imagery.
— increase performance of the aircraft.
The remote PIC should be aware of the wind gust because of a) the rapid change in direction and speed which causes turbulence.
The wind gust is a sudden short-term increase in wind speed. According to US weather observation practice, a gust is reported when the maximum wind speed reaches at least 16 knots and the difference between the maximum wind speed and the light wind speed reaches at least 9 knots. Wind forces can disrupt a building's load path or pierce the building's skin. Doors and windows can burst in really high winds. In other cases, nearby debris can be caught in the wind and flung into the building's envelope.
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16. The diagram shows a design for an electrically operated model railway signed. a) Explain, step by step, how it works. b) Explain how, by adding a scale and a spring, you could use it as an ammeter.
Answer:
Below
Explanation:
When the switch is closed the circuit is complete....the coil in the circuit will act as a solenoid magnet and draw the iron in thus raising the sign.
an ideal vapor-compression refrigeration cycle operates at steady state with refrigerant 134a as the working fluid. saturated vapor enters the compressor at 2 bar, and saturated liquid exits the condenser at 8 bar. the mass flow rate of refrigerant is 7 kg/min. determine
the refrigeration capability, in tons, is 4.905 tons, the coefficient of performance, in kW, is 4.17 KW, and the compressor power, in kW, is 4.1336 KW.
Describe the compressor formula.Electrical Expense = HP *.746 * hours * Kw cost * motor efficiency. As an illustration, consider a 50 HP compressor that consumes $.06 per Kwh of electricity and has a 90% efficiency electric motor. $5,172.26 is the yearly cost for 50 HP multiplied by.746 over 2,080 hours.
Compressor definition and operationIn order to create energy which can be kept in a tank for later use, air compressors work by applying pressure to atmospheric air. Similar to an open balloon, when the compressed air is purposefully released, pressure builds up, transforming the potential energy into productive kinetic energy.
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2a) A 50 kg sled is pulled across a frictionless surface by a rope with a tension of 30 N at an angle of 30 degrees from the horizontal. Determine the normal force on the sled.
(keep in mind that a portion of the force of tension is in the vertical direction... therefore the normal force will not be the full force of gravity).
2b) Determine the sleds acceleration in the horizontal direction.
PLEASE HELP MEEEEE
(a) The normal force on the sled is 490 N.
( b ) The sleds acceleration in the horizontal direction is 0.52 m/s².
What is the normal force on the sled?
The normal force on the sled is the upward force on the sled due to weight of the sled acting downwards.
The normal force on the sled is calculated as follows;
N = mg
where;
m is the mass of the sledg is acceleration due to gravityN = 50 kg x 9.8 m/s²
N = 490 N
The acceleration of the sled is calculated by applying Newton's second law of motion as shown below;
Fx = ma
F cosθ = ma
a = Fcosθ / m
where;
θ is the inclination of the applied forcea = ( 30 N x cos30 ) / ( 50 )
a = 0.52 m/s²
Thus, the acceleration of the sled is a function of net force and mass of the sled.
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What is the range of a projectile?
The range of a projectile is the horizontal distance the projectile travels from the time it is launched to the time it comes back down to the same height at which it is launched.
Answer:
Explanation:
The horizontal displacement of the projectile is called the range of the projectile. The range of the projectile depends on the object's initial velocity.
a spring with a spring constant of 49 n/m has a 7.2 kg mass hanging from the bottom of it how fast is the mass moving when it passes the equilibrium point
Answer:
ω = (K / M)^1/2 fundamental frequency for Simple Harmonic Motion
ω = (49 kg-m / (sec^2 - m) * 7.2 kg)^1/2 = 2.61 /sec
F = -K A Hooke's Law and spring constant
A = 7.2 kg * 9.80 m/s^2 / 49 n/m = 1.44 m amplitude
V = ω A = 2.61 / sec * 1.44 m = 3.6 m/s maximum speed
argue that this value of the field will be the same at all positions of the bar to the right of the midpoint of the rails. at other points along the bar, the field is in the same direction as at the midpoint, but is larger in magnitude. assume the average effective magnetic field along the bar is five times larger than the field at the midpoint.
This argument is valid because the bar is a homogeneous linear conductor, and the magnetic field around it must be constant.
What is magnetic field?A magnetic field is a region of space in which a magnetic force is exerted on any magnet, electric current, or magnetic material. It is created by an electric current, such as the electric current in a wire. It is also created by the motion of electric charges, such as those found in an electromagnet. The strength of the magnetic field increases as the electric current increases. The direction of the magnetic field is determined by the direction of the electric current.
The field at any point along the bar is proportional to the current passing through it, which remains constant for a homogeneous conductor. Therefore, the field at any point along the bar must be the same as at the midpoint, just with a larger magnitude. This implies that the average effective magnetic field along the bar is five times larger than the field at the midpoint.
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9. In the two-factor theory of intelligence, what does the s-factor stand for?
specific ability
spatial ability
special ability
score factor
He explains two components of intelligence: the "g" factor (general ability) and the "s" factor (specific ability). The "g" factor of a person's general mental tasks, while the "s" factor is solely intellectual skills.
What does the S factor of intelligence mean?certain g and s abilities. According to Spearman's two-factor theory, intelligence is divided into two categories: general intelligence ("g") and specific ability ("s"). Spearman proposed that the "s" component was particular to a certain feature of intelligence to account for variations in performance on various tasks.
What does biology's S factor mean?S component Individual factors, or empirically the tiniest subclusters of intercorrelations or common variance, are identified in several intelligence tests (specific). The most recent update was on September 30, 2022. Features of the "S" Factor: It is absorbed and learned from the surroundings. Within a single person, it varies from activity to activity. Each person has a different level of "S" ability.
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Which of the following scenarios involves at least one chemical change happening? (2 points)
Group of answer choices
Before you go swimming, you need to fill up the pool because evaporation has decreased the volume.
During the summer time, you are hired to sand your neighbor's fence and paint it white.
In the fall, one of your chores is to cut up wood and stack it in the basement for your parents.
Your summer job for the year is to pick strawberries. At the end of the day you have to crush the ones turning rotten to make strawberry jam.
The scenario that involves at least one chemical change happening is your summer job for the year is to pick strawberries. At the end of the day, you have to crush the ones turning rotten to make strawberry jam. The correct option is D.
What is a chemical change?When bonds between molecules or atoms are created, disrupted, or both, chemical changes result. This implies that a substance with a particular set of properties—such as melting point, color, flavor, etc.—becomes a substance with a different set of characteristics.
Three essential chemical components are used in the production of jam: Acids, sugar, and pectin.
Therefore, the correct option is D, Your summer job for the year is to pick strawberries. At the end of the day, you have to crush the ones turning rotten to make strawberry jam.
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The figure depicts the motion of a particle moving along an xâaxis with a constant acceleration. The figure's vertical scaling is set by xs =6.0m. What are the magnitude and direction of the particle's acceleration?
The given question is incomplete. Hence, can not be answered. Still, adding some relevant information for your reference.
What is acceleration?
In mechanics, acceleration is the rate of change of an object's velocity with respect to time. Acceleration is a vector quantity (as long as it has magnitude and direction). The direction of an object's acceleration is given by the direction of the net force acting on that object.
For example, if a vehicle starts from rest (zero velocity in the inertial frame) and moves in a straight line while increasing speed, the vehicle accelerates in the direction of travel. When the vehicle turns, it experiences acceleration in a new direction and changes its motion vector. Acceleration in the vehicle's current direction of travel is called linear (or tangential, in the case of circular motion) acceleration, and the passenger perceives that response as pushing back into the seat.
The given question is incomplete. Hence, can not be answered. Still, adding some relevant information for your reference.
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A liquid having a mall depth but a large volume is forced by an applied pressure p
The magnetic domains of an unmagnetised object are found___________A.) Parallel to each otherB.) Perpendicular to each otherC.) Pointing towards southD.) Pointing in different direction
All of the magnetic domains in an unmagnetized item, such as the original piece of metal in our experiment below, point in different directions.
When a metal gets magnetized, as when it is rubbed with a strong magnet, all like magnetic poles line up and point in the same direction. Atoms in ferromagnetic materials form formations known as domains. A domain is an internal region of a material in which groups of magnetic moments spontaneously align in the same direction. When the external field is withdrawn, the domain walls are pinned in their new orientation, and the aligned domains generate a magnetic field. This is what happens when a ferromagnetic material is "magnetized" and transformed into a permanent magnet.
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In an experiment, a student measured the volume of a substance while the mass was changed. The student measured up to five kilograms. The graph of the data is plotted below.
A volume versus mass graph is shown with mass on the vertical axes from 1 to 10 kilograms and volume on the horizontal axis from 1 to 5 milliliters. A line from the origin through all points and beyond.
Which of the following is an error the student made in creating an accurate graph?
The axes and graph are based only on measured values.
The axes are labeled with the incorrect variables.
The plotted points do not show all data collected.
The title has the incorrect order for the variables.
Answer:
let the first point be a second be b third be c fourth be d and last point be e.
The point a and d are incorrect. because tye plotting of the is incorrect
In which of the following situations is the gravitational force the dominant force? Select two answers. A A satellite is in orbit around a planet. B An object is in free fall just after it is released from rest. C An electron and a proton are bound together in an atom. D A proton and a neutron are bound together in an atom's nucleus.
As soon as something is liberated from rest, it enters free fall. AND An orbiting satellite is subject to the gravitational pull of a planet.
What do you mean by gravitational?Rising and falling ocean tides are a result of the moon's gravitational pull. Strong movement or a natural propensity toward something or someone, whether or whether it is related: A lot of research has been done on their gravitational pull toward harmful conduct.
What does the name "gravitational force" mean?Any two mass-bearing objects are drawn together by the gravitational pull. Since the gravitational force never attempts to push masses away, it is said to as attractive since it constantly seeks to draw masses together.
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For the chain: linear density =ρ, length =l. The chain is placed on the smooth plane. As shown in the figure, the drooping length =b, the chain is stationary at this moment (v=0). Then, under the action of the gravity, the chain drop freely. Determine the speed of the chain when the left end of leave the plane.
For the chain: linear density =ρ, length =l. The chain is placed on a smooth plane. The speed of the chain when the left end leaves the plane is the same as its initial speed, which is zero.
What is speed?Generally, To determine the speed of the chain when the left end leaves the plane, we need to consider the forces acting on the chain and use Newton's second law to find the acceleration of the chain.
The forces acting on the chain are the force of gravity and the normal force from the plane. The force of gravity is downward and is equal to the weight of the chain, which is given by the equation:
Fg = mg
where m is the mass of the chain and g is the acceleration due to gravity. The normal force from the plane is upward and is equal to the force of gravity, since the chain is stationary at this moment.
Newton's second law states that the acceleration of an object is equal to the net force acting on it divided by its mass. Therefore, the acceleration of the chain is given by:
a = (Fg - Fn)/m = (mg - mg)/m = 0 m/s^2
Since the acceleration of the chain is zero, the speed of the chain does not change as it drops.
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CQ not found
at a given temperature, the values of rate constants for the forward and reverse reaction are ____ and the ratio of k is equal to the ____ constant for the reaction.
The ratio of k is equal towards the temperature constant for such reaction constants at a certain temperature, and the values of the rate constants for the forward or reverse reactions are concentrations at that temperature.
What are forward and reverse reactions?A forward response is a reversible reaction wherein products are created from reactants so it moves from left to right. A reversible reaction that moves from right to left is referred to as a backward reaction since reactants are created from products.
What do you call a reversible reaction?In some oxidation processes, the reaction's products might combine to form the reactants' original form. Reversible reactions are what they are referred to as. To illustrate them, use the formula: A + B C + D.
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The values of the rate constants for the forward or reverse reactions are concentrations at that temperature, and the ratio of k is equal towards the temperature constant for such reaction constants.
Why is a reaction reversible?
A chemical reaction that is reversible occurs when the reactants generate products, which then combine to return the reactants to their original state.
When the rate of the forward reaction and the rate of the reverse reaction are equal, equilibrium is reached. At equilibrium, the concentrations of all the reactants and products are fixed. The amount of reactant to product in a chemical reaction can be compared to derive the equilibrium constant, which is used to predict chemical behavior. The rate constants are fixed at some temperature.
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The resistors in the circuit below have the following values: R1 = 7.20 Ω, R2 = 7.00 Ω, and R3 = 4.10 Ω. The two batteries each have a voltage of 4.00 V.
The total voltage in the circuit is 8 V. Then, the current passing through the resistor R3 is 1.95 A. The power supply to this resistor by the batteries is 15.6 W.
What is Ohm's' law?According to Ohm's law, the voltage through a closed circuit is the product of the current passing through the circuit and resistance through it.
Hence, V = I R.
Given that the resistance through the resistor R3 = 4.10 Ω
The voltage across each batteries = 4 V
Total voltages = 4 + 4 = 8V
Current = voltage/ resistance
= 8 V/ 4.10 Ω
= 1.95 A.
Power through a circuit is the product of current and voltage through it.
P = I V
Power supplied to R3 = 1.95 A × 8 V = 15.6 W.
Therefore, the power supplied by the batteries to the resistor R3 is 15.6 W.
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How much work is done on a 6.4N box of books that you move horizontally across a 6.1 meter room?
Answer:
39.04 J
Explanation:
Definition of work
[tex]W=fd[/tex]
[tex]W=[/tex] Work
[tex]f=[/tex] force
[tex]d=[/tex] displacement
In this case,
[tex]f=6.4[/tex]
[tex]d=6.1[/tex]
[tex]W=6.4*6.1[/tex]
[tex]W=39.04[/tex]
An ant starts at one edge of a long strip of
paper that is 30.8 cm wide. She travels at
0.6 cm/s at an angle of 40◦ with the long edge.
How long will it take her to get across?
Answer in units of s.
it take the ant 68.9 seconds to get across the other edge of a long strip.
How do we calculate for velocity?If the ant is moving at a constant speed, the velocity vector will have the same magnitude at any point, and can be decomposed in two vectors, along directions perpendicular each other.
So then, if we choose these directions coincident with the long edge of the paper, and the other perpendicular to it, the components of the velocity vector, along these axes, can be calculated as the projections of this vector along these axes.
We only are interested in the component of the velocity across the paper, that can be calculated as follows:
vₓ = v* sin θ, where v is the magnitude of the velocity, and θ the angle that forms v with the long edge.
We know that v= 0.6 cm/s, and θ = 40º, so we can find vₓ as follows:
vₓ = 0.6 cm/s x sin 40 º
Vx = 0.6 cm/s x 0.7451 = 0.447 cm/s
Applying the definition of average velocity, we can solve for t:
time = 30.8 cm/ 0.447
time = 68.9 seconds
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What method do you use to purify water contaminated with salt and microorganisms
The water purification procedure, such as filtration, sedimentation, distillation, etc.
Which method of purification disinfect water from microorganisms?Analysis of the reduction in microbes that is enough to protect against the transmission of pathogens in water is debated below. Chlorination is the most widely used method for disinfecting water supplies in the United States.
The most efficient way to desalinize salt water is by using a method called distillation. This is where you boil the water and then assemble the condensation. The steam will provide fresh salt-less water for you to drink.
So we can conclude that Chlorination is the activity of adding chlorine to drinking water to kill parasites bacteria and viruses.
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An acrobat of mass ma jumps upwards off a trampoline with an initial velocity vg . At a height h0, the acrobat grabs a clown of mass mg . Assume that the time the acrobat takes to grab the clown is negligibly small. a) What is the velocity of the acrobat immediately before grabbing the clown?
b) What is the velocity of the acrobat immediately after grabbing the clown?
c) How high do the acrobat and clown rise? How high would the acrobat go in the limit that the mass of the acrobat is much heavier than the mass of the clown?
d) If the acrobat missed the clown, how high would the acrobat go? How does this compare to your limit in part c)?
The velocity of the acrobat immediately before grabbing the clown is three times as much mass is in the larger portion and than in the smaller piece, m2 due to air resistance .
How would one describe air resistance?Air resistance is the name for the force that air produces. The force acts in the opposite direction when an object is flying through the air. A truck with a flat forward will experience significant air resistance in comparison to a sports car with a streamlined design.
the velocity of the acrobat immediately after grabbing the clown is twice then before grabbing the clown.Why does air resistance exist?Air resistance is a function of the object's speed, area, and shape as it moves through the atmosphere. Altitude, temperature, and humidity all have an impact on air resistance and density.
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200 grams of ice at -10 c is added to 1000 grams of room temperature water to cool it down. which of the following best describes the final composition of the mixture
At 0 °C, combine 200 grams of ice with 1000 grams of liquid. The following relational models overall final composition of a mixture at 6.7 °C:
How are compositional mixes and compounds defined?Atoms from various elements are chemically mixed in a predetermined ratio to form a compound. When there is no biochemical combination or reaction, two or more chemicals are combined to form a mixture. Different elements are found in compounds in fixed ratios organised in predetermined ways by chemical bonds.
Is a mixture's composition subject to change?A mixture is a chemical that has a varied composition, indicating that it is made up of different sorts of molecules or atoms. These might have intermolecular bonds or bonds among molecules, but these are far weaker than the bonds created when elements combine to form compounds.
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an object is thrown into the air and follows the path shown in the diagram above. Neglecting air resistance, which vector best represents the acceleration of the object at point A?
Answer: 3 (c)
Explanation: The only force acting on the object is the force of gravity, mg, which acts straight downward. Even though the object has horizontal velocity, there is no horizontal force after the object is done being thrown.
A certain type of glass is used in making flat-panel computer monitors. For light with a wavelength in air of 656.3 nm, the refractive index of the glass is nA = 1.5160. For light with a wavelength in air of 435.8 nm, nB = 1.5290. Determine the difference, lA - lB, in their wavelengths inside the glass.
The answer is 147.9 nm. Can you please show the work? Thanks
nB = 1.5290 for light having a 435.8 nm air wavelength. The difference, lA - lB, in their wavelengths inside the glass is 221.4nm.
The refractive index of a medium is defined as the speed of light in a vacuum (c) divided by the speed of light in the medium (v). This can be expressed mathematically as:
= n
= c / v
The wavelength of light in a medium is related to its frequency (f) and its speed in the medium (v) according to the following equation:
= lambda
= v / f
where lambda is the wavelength of the light in the medium.
We can use these equations to find the difference in the wavelengths of the two types of light inside the glass. Letting lA and lB represent the wavelengths of the light with wavelengths 656.3 nm and 435.8 nm inside the glass, respectively, we can set up the following equation:
for nA
= nA
= c / v
= c / (f x lA)
for nB
= nB
= c / v
= c / (f x lB)
Dividing the eq. we know:
=> nA / nB = (f x lB) / (f x lA)
= lB / lA
Inserting the known values for nA, nB, and lA, we get:
=> 1.5160 / 1.5290 = lB / 656.3 nm
Solving for lB, we find that lB = 434.9 nm.
The difference in the wavelengths inside the glass is then:
=> lA - lB = 656.3 nm - 434.9 nm
= 221.4 nm
Therefore, the difference in the wavelengths of the two types of light inside the glass is 221.4 nm.
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Write the equation for the velocity component in the x-direction?
Answer:
The equation for the velocity component in the x-direction is : vx(t) = v(0) Cosθ.
Explanation:
here v(0) is the initial velocity
By definition, if one coulomb of charge passes between two electrodes that differ in potential by one volt, one __________ of energy is released. This relationship is correctly expressed as V = ______/______.
one of released energy for each coulomb of charge that travels across electrodes with a one volt potential difference. V joule, J/C is the correct way to describe this relationship.
What do the electrodes in your body do?A tool that transfers electricity from just an instrument to something like a patient for therapy or surgery. Examples include a tiny metal plate or needle. In order to help recorders diagnose certain problems, electrodes can also transport electrical impulses from the heart, brain, muscles, skin, or other physiological regions.
Simply put, what is an electrode?An electrode is a conductor for electricity that establishes electrical contact with nonmetallic components of a circuit, like an electrolyte, a semiconductor, or a vacuum. This may also go by the names anode or cathode if it is a part of an electrochemical cell.
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In this figure, why is the kinetic energy gained by the falling ball equal to the change of potential energy? (Assuming no loss of energy due to friction.)
Kinetic energy gained by the falling ball is equal to the change of potential energy is because mechanical energy remains conserved ,it only converts from one form to another form.
The mechanical energy stays rationed when just inner powers follow up on the body and no outside powers are in real life. It implies that motor and potential might continue to change all through the excursion. Be that as it may, their total is steady at each point.
The forces are moderate, i.e., they don't rely upon the way of the moving article and are just subject to the beginning and last position. For instance, the gravitational power is moderate in nature, though the opposition presented via air is non-moderate in nature as it relies upon the way.
From the diagram,we can see that object has potential energy =mgh because of height h.When it was dropped from height h potential energy starts decreasing and kinetic energy starts increasing because of velocity attained by the body.Since mechanical energy is conserved,therefore kinetic and potential energy is equal.
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A car with mass m is travelling around a flat circular track. the coefficient of static friction between the tires and track is 0.90. which of these changes is the most likely to cause the car to skid off the track? (for each change, assume that all other factors remain constant)
Change in friction force and acceleration is the most likely changes to cause the car to skid off the track when the coefficient of static friction between the tires and track is 0.90.
What is a friction example?Walking - When we walk on the ground or a surface, our feet are kept firmly planted by the frictional force. We frequently slip on icy or slippery surfaces due to there is less friction present.What is friction means in science?Between the two surfaces which are sliding or attempting to slide over one another, there is a force named friction. For instance, friction makes it challenging to push a book down the floor. Friction always moves an object in the direction that is counter to the direction that it is traveling or attempting to move.
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A block with mass M slides down an incline of angle θ at constant velocity v.
Which of the following expressions is equal to the magnitude of frictional force between the block and the incline? (Note: The acceleration of gravity g = 10 m/s2.)
A.M∙g∙sin θ
B.M∙g∙cos θ
C.M∙g / sin θ
D.M∙g / cos θ
Mgsin, As a result, at a state of dynamic equilibrium, the frictional force exerted on a mass sliding down an incline is proportional to the object's weight times the sine of the incline angle.
What are velocity and speed?In contrast to velocity, which describes the speed and direction of such an object's movement, speed is the speed of moves along a path. Alternatively, velocity is a vector while speed is a scalar quantity.
Is speed also known as velocity?A motion or activity has velocity when it moves quickly. Another term for speed is celerity, which is also a synonym. The measurement of an object's rate and direction of positional change is known as its velocity in physics.
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HELPPPPPPPPPPPP PLLSSSSSSS
The Mars rover, Spirit, has a mass of 836 kg.
Calculate its weight on Earth.
Answer:
The weight of an object is a measure of the force of gravity on the object. It is calculated by multiplying the mass of the object by the acceleration due to gravity. On Earth, the acceleration due to gravity is approximately 9.8 meters per second squared (m/s^2).
Therefore, to calculate the weight of the Mars rover Spirit on Earth, we can use the formula:
weight = mass * acceleration due to gravity
In this case, the mass of the Mars rover is 836 kg, and the acceleration due to gravity on Earth is 9.8 m/s^2. Plugging these values into the formula, we get:
weight = 836 kg * 9.8 m/s^2
This simplifies to:
weight = 8194.8 kg*m/s^2
The weight of the Mars rover Spirit on Earth is approximately 8195 kg*m/s^2.