The displacement is zero because the mass's starting and final positions are identical (it returns to its initial position).
What is amplitude example?It alludes to the greatest departure from equilibrium that such an object in harmonic oscillator can exhibit. As an illustration, consider how a pendulum moves through its market equilibrium (straight down) and then moves outward to its maximum distance.
Do you mean height by amplitude?The vertical separation of both the wave from average is measured by amplitude. The wave axis, which is typically thought of as zero, is the average size of the wave across one cycle. Positive and negative numbers are assigned to heights between and above the average, accordingly.
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sound is emitted by 20 w speaker (which propagates in all directions). what is the intensity in decibels at 10 m? 100m?
The intensity of sound in decibels at 10 m is 17.6 dB.
The intensity of sound in decibels at 100 m is 14.08 dB.
The formula to calculate intensity when power is given is I = P/A
where, I is the intensity
P is the power
A is the area
Given, P = 20 W
A₁ = 4πr² = 4π* 10² = 1256.64 m²
A₂ = 4πr² = 4π* 100² =125663.71 m²
I₁ = P / A₁ = 20/1256.64 = 0.0159 W/m²
I₂ = P / A₂ = 20/125663.71 = 0.000159 W/m²
The expression between intensity of sound and decibel level is
dB = 10* log (I/ 1.0* 10⁻¹² W/m²) --------(1)
Substituting the values of I₁ and I₂ in (1),
dB₁ = 10* log (1.5* 10⁻²/ 1.0* 10⁻¹²) = 10* log(1.5* 10¹⁰) = 10* [ log 1.5 + 10] = 10*(0.176* 10) = 17.6 dB
dB₂ = 10* log (1.5* 10⁻⁴/ 1.0* 10⁻¹²) = 10* log(1.5* 10⁸) = 10* [ log 1.5 + 8 ] = 10*(0.176* 8) = 14.08 dB
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What is the magnitude of the net force on the first wire in (figure 1)? express your answer in newtons
0.00025 N is the magnitude of the net force on the first wire in (figure 1).
What is net force?The total of all forces exerted on an item is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the phrase "net force" is employed.
From the diagram, first wire has an attracting force from third wire at 0.04 m distance and a repelling force from second wire at 0.02 m distance.
Expression of the force is -
F = [µ ×π×(I)² × L] / (2πd)
When d = 0.02 m,
or, F = [4 ×π× 10⁻⁷(10)² × 0.50] / (2π × 0.02)
or, F = 0.0005 N
And when d = 0.04 m,
or, F = [4 ×π× 10⁻⁷(10)² × 0.50] / (2π × 0.04)
or, F = 0.00025 N
So, the net force on first wire = 0.005 - 0.00025
= 0.00025 N repelling or upward.
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The complete question is as follows:
What is the magnitude of the net force on the first wire in (Figure 1)?
Express your answer in newtons.
find the weight of a car on a 12 degree slope if the force required to push the car up the hill is 650 lbs g
The weight of the car on the 12 degree slope is 546.72 lbs. This weight is important to know for various reasons, such as calculating the amount of force and energy required to move the car up the hill.
The weight of a car on a 12 degree slope can be calculated using the formula:
Weight = Force * sin(Slope Angle)
Therefore, the weight of the car on the 12 degree slope can be calculated as follows:
Weight = 650 lbs * sin(12°)
Weight = 546.72 lbs
The weight of a car on a 12 degree slope is important to know for various reasons. For example, if the car is being driven up the slope, it is important to know the weight of the vehicle to ensure that it will be able to make it up the hill. Additionally, knowing the weight of the car on the slope can help engineers and designers to calculate the amount of force and energy required to move the car up the hill.
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2. what property of tissue does a proton density image show? what tr and te times do we need to achieve proton density imaging?
In a proton density image the tissue magnetization, RF signal intensity, and image brightness are.
Proton Mail is the world's largest cozy e-mail provider. It gives end-to-cease encryption and plenty of different splendid safety capabilities to maintain your communications non-public. Even the company hosting your emails has no manner of reading them, so you can rest confident that they cannot be studied via third events either.
It has a completely, very wealthy internal shape. you could have heard that protons are made up of 3 smaller basic particles known as quarks, two united states, and one down quark to be particular, but it is only the top of the particle iceberg, as proton researcher Paul Reimer explains.
One or extra protons are present in the nucleus of every atom. They provide the attractive electrostatic crucial force which binds the atomic electrons. The quantity of protons in the nucleus is the defining belongings of an element and is referred to as the atomic quantity.
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A block is released from rest on an inclined
plane and moves 3.4 m during the next 5.5 s.
The acceleration of gravity is 9.8 m/s^2
What is the frictional force acting on the
13 kg mass?
Answer in units of N.
The frictional force acting on the 13 kg mass is 40.65 N.
What is the acceleration of the block?
The acceleration of the block is calculated by applying the following kinematic equation as shown below.
s = ut + ¹/₂at²
where;
u is the initial velocity of the block = 0t is the time of motion of the blocka is the acceleration of the blocks is the distance travelled by the blocks = 0 + ¹/₂at²
¹/₂at² = s
at² = 2s
a = 2s / t²
a = (2 x 3.4) / (5.5²)
a = 0.225 m/s²
The frictional force acting on the 13 kg mass is calculated as follows;
W sinθ - F = ma
where;
W is the weight of the blockθ is the angle of inclination of the blockF is the frictional forcem is the mass of the blocka is the acceleration of the block(13 x 9.8 x sin20) - F = 13 x 0.225
43.57 - F = 2.925
F = 43.57 - 2.925
F = 40.65 N
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A simple harmonic wave of wavelength 18.7 cm and amplitude 2.34 cm is propagating in the negative x-direction at 38.0 cm/s.
Part A. Find its angular frequency.
Part B. Find its wave number.
Part C. Write a mathematical expression describing the displacement y of this wave (in centimeters) as a function of position x and time t measured in cantimeters and seconds, respectively. Assume the maximum displacement occurs at x = 0 when t = 0 .
a) Angular frequency is 12.75 rad/s b) The wave number is 33.59m c)
y ( x ,t) = 2.34 x sin(33.59 x - 12.75t)
Given,
wavelength = λ = 18.7 cm
= 0.187 m
amplitude , A = 2.34 cm
v = 0.38 m/s
A) angular frequency = ?
f = v/λ
f = 0.38/1.87 = 2.03
angular frequency ,
ω = 2π f
ω = 2π x 2.03
ω = 12.75 rad/s
B) the wave number,
K = 2π/λ = 33.59m
c) as the wave is propagating in -x direction, the sign is positive between x and t
y ( x ,t) = A sin(k x - ω t)
y ( x ,t) = 2.34 x sin(33.59 x - 12.75t)
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6. An ice skater is spinning at 60 RPM when she pulls in her arms and undergoes an angular acceleration of 10 rad/s"" for 0. 6 seconds. What was her final RPM and how many rotations did she spin during this time?
The final RPM of ice skater is 116.38.
RPM's meaning?RPM's meaning? per revolution
RPM, which stands for revolutions per minute, is a measure of how quickly a machine is operating at any one time. RPM is a measure used in automobiles to indicate how often the crankshaft completes one full rotation each minute as well as how frequently each piston rises and falls in its cylinder.
Briefing:
ω₀ = 6.2π rad/s
α= 10π rad/s
t = 4.2 s
Find: ω
ω = αt + ω₀
ω = 10 (0.6 s) + 6.2π rad/s
ω = 116.38RPM
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thermal expansion, pressure release, and mineral, frost, and root wedging all are weathering processes.
Mechanical weathering mechanisms include pressure release, thermal expansion, frost and root wedging. Weathering that occurs mechanically is sometimes called physical weathering.
This is typically referred to as thermal expansion. The fractional change in volume or length per unit change in temperature can be referred to as thermal expansion. Typically, the linear expansion coefficient is used when dealing with a solid expansion. The force perpendicular to an object's surface that is delivered per unit area over that force is known as pressure (symbol: p or P). The gauge pressure, also known as gauge pressure, is the pressure in relation to the surrounding air pressure. To express pressure, a variety of units are employed.
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The complete question is -
Thermal expansion, pressure release, and mineral, frost, and root wedging all are ________ weathering processes.
what is the resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts?
The resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts = 2 Ω
Electrical resistanceElectrical resistance is the force that opposes the flow of current, it's a component that can reduce the speed and quantity of the flow of electrons in an electric circuit.
The formula for electrical resistance can be seen to have several components, namely R is the resistance (Ω), V is the voltage (V), and I is the current strength (A).
The equation:
R = V/I
We have,
Current strength = 120 A
The potential difference between its ends = 240 V
So, the resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts:
R = 240 V / 120 A
= 2 Ω
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if the demand function for money is m/p = 0.5y – 100r, then the slope of the lm curve is:
As a result, the slope of the LM curve is 0.005.
The ratio of the income sensitivity of real money demand over the interest sensitivity of real money demand determines the slope of the LM curve, which is represented by the coefficient of Y, k over h. With regard to monetary policy, this ratio is crucial.
The money supply function has an impact on the LM curve as well. The supply of money may become more susceptible to interest rates in the current environment of high levels and volatility of interest rates.
The general LM equation is written in terms of Y and r,
Where Money supply = Money demand,
0.5Y – 100r = (M/P) where (M/P) is a constant
100r = 0.5Y - (M/P)
r = 0.005Y - 0.01(M/P)
dr/dY = 0.005 is the slope of the LM function.
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a block of mass 0.482 kg is hung from a vertical spring and allowed to reach equilibrium at rest. as a result, the spring is stretched by 0.630 m. find the spring constant.
The spring constant of the spring is 7.497 N/m.
The given parameters;
mass of the block, m = 0.482 kg
extension of the spring, x = 0.630 m
additional extension, = 0.338 m
The spring constant of the spring is calculated as follow
F = mg
Kx = mg
K = mg/x
K = 0.482 × 9.8 / 0.630 = 7.497N/m
F = -kx.
The spring constant, or k, is the proportional constant. It is a gauge of the spring's rigidity. A spring exerts a force F = -kx in the direction of its equilibrium position when it is stretched or compressed to a length that deviates by an amount x from its equilibrium length. The spring constant is calculated by dividing the force required to extend or compress a spring by the length it goes up or down. It is used to assess the stability or instability of a spring, The spring's stiffness is quantified by the spring constant, or k. For various springs and materials, it differs. The stiffer the spring is and the harder it is to stretch, the greater the spring constant.
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does initial velocity equal final velocity when doing a one dimenstion free fall problem if you throw a ball up
If we assume at time instance t= 0, then the same thing happens. initial velocity is equal to final velocity
During a free fall, only the gravitational force acts on a body. The initial velocity of the body is zero during free fall.
Vertical motion is symmetrical - the distance and time are the same in the rise as in the fall; the final velocity will have the same magnitude as the initial velocity but in the opposite direction. Horizontal components will never be effected by gravity; it is constant velocity motion
The average velocity is the ratio of the total distance traveled to the total time taken. This can happen in two cases, first if the initial velocity and the final velocity are equal to the average velocity and there is no change in the velocity for the entire trip
Velocity is the measure of the amount of distance an object covers in a given amount of time. Here's a word equation that expresses the relationship between distance, velocity and time: Velocity equals distance travelled divided by the time it takes to get there.
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what is the difference between fresnel and fraunhofer diffraction? are they different physical processes? explain.
The Fraunhofer process is typically simpler to study even though they are physically the same processes and have distinct features. Fresnel diffraction, players who are near to one another, and non-parallel light rays
Participants in the Fraunhofer diffraction are far apart, and the light beams are parallel.
When plane waves are incident on a diffracting object and the diffraction pattern is observed far enough away from the object (a distance satisfying Fraunhofer condition) (in the far-field region), as well as when it is observed at the focal plane of an imaging lens, the Fraunhofer diffraction equation is used to model the diffraction of waves in optics. The Fresnel diffraction equation, on the other hand, predicts the diffraction pattern that is produced close to the diffracting object (in the near field area).
Although Joseph von Fraunhofer was not directly engaged in the formulation of the theory, the equation bears his name.
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two initially uncharged metal spheres are mounted on insulating stand and placed in contact with each other, as shown. a student brings a positively charged insulating rod near sphere 1, sphere 2 is then removed, and finally the rod is moved away. what is the net charge on sphere 1?
They represent a simple explanation of our basic charge interactions, best recognized by the jingle "opposites attract, likes repel."
B and C are also untrue for the same reason; they contradict the fundamental statement of charge interactions. E and H are correct. To become charged, an object must either gain or lose electrons. Losing electrons causes more positive charge than negative charge, resulting in a positively charged item. Gaining electrons causes more negative charge than positive charge, resulting in a negatively charged item. Protons are securely linked in atom nuclei and can never be added or withdrawn by regular electrostatic means. The same argument leads to the rejection of options F and G as possible true.
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Fig. 23-11 how the variation of the electric potential V (meaured in Volt) a a function of the radial direction r (meaured in meter). For which range of r i the magnitude of the electric field the larget?
As you walk away from the charge, the potential becomes less negative and actually grows, coming closer and closer to zero.
If you are infinitely far away from the charge, the potential for both positive and negative charges is zero. The electric potential (also known as the electric field potential, potential drop, or electrostatic potential) is defined as the amount of work energy required to transport a unit of electric charge in an electric field from a reference point to a specified place. The Volt difference dropped across a fixed resistance of one ohm with a current of one ampere running through it is the unit of potential difference formed between two locations.
dV
V=5x \s2 \s −10x−9
dx dV \s \s
=10x−10
so, E=−(10x−10)
The value of E=(1010)
=0V/m for
x=1m
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17. two identical waves undergo pure constructive interference. is the resultant intensity twice that of the individual waves? explain your answer.
According to the question, two identical waves undergo pure constructive interference, resultant intensity is quadruple individual wave intensity.
What is sound wave interference?When two or even more sound waves are present at once from distinct sources, they interact with one another to create a new wave. The combination of all previous waves results in the new wave. Interference is the term for wave interaction.
What is a good illustration of interference?The reflecting light from an oil coating floating on water is one of the best illustrations of interference. Another illustration is the thin coating of a soap bubble (shown in Figure 1), which, when illuminated by either natural or synthetic light sources, reflects a variety of lovely colors.
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a 25-kg crate is pushed across a frictionless horizontal floor with a force of 20 n, directed 20o below the horizontal. the acceleration of the crate is:
1.75 m/s2 is the crate's acceleration.
mass=25kg, f=20n.
In terms of physics, what is frictionless?A surface is said to be frictionless if it has a force acting on any thing that is practically zero or insignificant, meaning that there is no resistance between the surface and the material, allowing the object to slide and move freely without any friction.
Can one walk on a frictionless surface?Every every activity that requires the interaction of two surfaces and motion involves friction, with the exception of space walks, which you may conduct without any resistance. Because there won't be any contact force to propel the individual forward, one cannot walk in the absence of friction.
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if the amplitude increases to 0.20 mm , by what factor does the bug's maximum kinetic energy change?
The bug's maximal kinetic energy changes as 16 times of Kinetic energy before amplitude increases when the amplitude approaches 0.20 mm.
The amplitude of a wave is its largest displacement. The wave's greatest velocity is now expressed as its amplitude, which is: v =Aw= K/M.
Now, the square of the wave is directly proportional to the kinetic energy of a system. As a result, the wave's maximum kinetic energy is given by KE = k/2A^2, which means that
KE1/KE2 = A1^2/A2^2 where KE1 is the kinetic energy prior to the amplitude (A1) increasing and KE2 is the kinetic energy following the amplitude increasing (A2)
Due to that,
The bug's entire vertical journey was S = 0.10m
The wave's amplitude is equal to half of the whole distance from the top to the bottom, hence its value is (A) = S/2 = 0.1/2 = 0.05m.
Now that the wave's amplitude has increased to 0.20 m, KEA = KE1/KE2 = A1^2/A2^2
KE1/KE2 = (0.05)^2/(0.20)^2, which equals 0.0025/0.04 = 0.0625.
KE2 then equals 16KE1
Therefore, the largest change in kinetic energy is (KE2) = 16KE1.
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Find complete question: A bug on the surface of a pond is observed to move up and down a total vertical distance of 0.10 m, lowest to the highest point, as a wave passes. What is the amplitude of the wave? If the amplitude increases to 0.20 m, by what factor does the bug's maximum kinetic energy change?
when a nucleus of 235u undergoes fission, it breaks into two smaller, more tightly bound fragments. t or f
The fragments reaction is 7.59 MeV/nucleon and 8.39 MeV/nucleon
What is nucleus ?
Neutrons and protons, which have opposite electric charges, make up atomic nuclei. The strongest basic force now understood, known as the strong force, is what holds these things together. A normal atom's nucleus generally holds more than 99.9% of the atom's mass yet takes up considerably less than.01 percent of its volume.
What is fission ?
When a neutron collides with a bigger atom, it excites it and causes it to split into two smaller atoms, which are known as fission products. This process is known as fission. A chain reaction might start as a result of additional neutrons that are also emitted. Huge amounts of energy are produced during the splitting of each atom.
1) m_proton + m_netron + m_electron - m_U
= 92*1.007276466812 + 92*5.4857990943e-4 + 143*1.008664916 - (235.0439299)
= 1.9151 u
= 931.494061 * 1.9151 MeV
= 1784 MeV
= 1784/235 = 7.59 MeV/nucleon
2) m_proton + m_netron + m_electron - m_Cs
= 55*1.007276466812 + 55*5.4857990943e-4 + 82*1.008664916 - (136.9070895)
= 1.2338 u
= 931.494061 * 1.2338 MeV
= 1149 MeV
= 1145/137 = 8.39 MeV/nucleon
Therefore, the fragments reaction is 7.59 MeV/nucleon and 8.39 MeV/nucleon.
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a pair of french bikers rode from paris to qatar for the world cup. a total of 7,000 kilometers in __ months.
From Paris to Qatar for the world cup, two French riders traveled by bicycle. In three months, 7,000 kilometers overall.
The Fédération Internationale de Football Association (FIFA), the world's governing organization of association football, and its senior men's national teams compete in the FIFA World Cup, commonly referred to as the World Cup. With the exception of 1942 and 1946, when it was postponed due to World War II, the tournament has been conducted every four years since its inception in 1930. The current winners are France, who captured their second championship during the 2018 competition in Russia.
The structure uses a qualification round to choose the teams that advance to the tournament phase, which occurs over the previous three years. 32 teams fight for the title at sites in the host country or nations during the tournament round.
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a graphical presentation that uses vertical bars to display the magnitude of quantitative data is known as a
A graphical presentation that uses vertical bars to display the magnitude of quantitative data is known as a Column chart.
What is a Column chart?Column charts make use of vertical bars to compare several objects or categories. On one axis are the comparison categories, while on the other are the data values. They are helpful in illuminating the conditions at a specific time. Anything that can be counted, such the volume of items sold or website hits, can be represented in a column chart.
Using column charts, you may show how various numbers differ from one another. When there are significant differences in the data values, column charts—which are used to compare changes between groups over time—are easiest to understand.
If there are several categories to compare, a line graph could be easier to comprehend.
Column charts can be created using standard, stacked, or percentage forms. It is simpler to compare and identify trends in the data because the same data is presented in each format in a different way. The steps for creating conventional, stacked, and percentages charts are the same regardless of the outcome.
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The planet mercury orbit around the sun is an ellipse eccentricity 0.206 length of major axis us 1.16×10 the power of 8 km. the sun at one focus
1,What is the maximum distance from mercury to the sun
2,what is the minimum distance b/n them
The maximum distance from mercury to the sun is 0.58 * 10⁸ km.
The minimum distance b/n them is 0.46 * 10⁸ km.
What is the distance about?The shape of an elliptical orbit can be described by its eccentricity, which is a measure of how "flattened" the ellipse is. An eccentricity of 0 indicates a circular orbit, while an eccentricity of 1 indicates a parabolic orbit.
In the case of Mercury's orbit, the eccentricity is given as 0.206, which means that the orbit is slightly flattened, but still close to circular. The length of the major axis of the ellipse is given as 1.16 * 10⁸ km.
To find the maximum distance from Mercury to the sun (also known as the aphelion), we need to find the distance from the center of the ellipse to the farthest point on the ellipse (which is at the top of the major axis). This distance is equal to half of the length of the major axis. Thus, the maximum distance from Mercury to the sun is:
1.16 * 10⁸ km / 2 =0.58 * 10⁸ km
To find the minimum distance between Mercury and the sun (also known as the perihelion), we need to find the distance from the center of the ellipse to the closest point on the ellipse (which is at the bottom of the major axis). This distance is equal to half of the length of the major axis times the square root of 1 - (eccentricity)². Thus, the minimum distance between Mercury and the sun is:
[tex](1.16 x 10^8 km / 2) * \sqrt{(1 - (0.206)^2) } = 0.46 * 10^8 km[/tex]
Therefore, Note that the sun is located at one of the foci of the elliptical orbit, rather than at the center. However, since the eccentricity of Mercury's orbit is relatively small (0.206), the distance from the center of the ellipse to either focus is very close to the distance from the center to the top or bottom of the major axis, and the difference can be ignored for most purposes.
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What are three thing you reearched about how earthquake tart and how they travel
Whenever the ground is hit with enough force to crack or break, an earthquake results. Tectonic plate boundaries are linked to the majority of earthquakes.
What is earthquake explain?An earthquake is a quick movement of geological materials beneath the earth's surface that causes the ground to shake violently or weakly. The tectonic plate boundary is where the earthquakes start.
What is earthquake and its effects?The earthquake is the sudden energy released from the earth's crust that causes the earth's surface to shake. Seismic waves, also called S waves, are consequently produced. The type and severity of an earthquake are based on the local seismic activity.
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a generator supplies 100 v to a transformer's primary coil, which has 50 turns. if the secondary coil has 500 turns, what is the secondary voltage?
According to the question if the secondary coil of transformer has 500 turns, the secondary voltage is 1000 V.
What are transformers and what varieties exist?Transformers for power, transformers for distribution, and transformers for isolation, in that sequence. We have Dual Winding Transformer and Autotransformers based on windings. We offer Core Type Transformers, Shell Type Transformers, and Berry Type Transformers based on core designs.
Briefing:For an ideal transformer
Vs/Vp=Ns/Np
Given that primary voltage V =100 V
Number of turns in primary N = 50 turns
Number of turns in srcondary Ns = 500 turns
Therefore
Vs/100=500/50
Hence voltage across secondary Vs = 1000 V
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you replace a 100-watt light bulb with a 25-watt compact fluorescent bulb. over a 10,000 hr life, how much energy, in kilowatt-hours, do you save? if electricity costs $0.15 per kilowatt-hour how much money do you save?
If you replace a 100-watt light bulb with a 25-watt compact fluorescent bulb, over a 10,000 hr life, you will save electricity bill of $112,5
A fluorescent bulb is more energy efficient than an incandescent bulb. It produces the same amount of light with less electricity.
The energy used by the bulbs is often expressed in Kwh or kilowatt-hour.
The formula is:
Kilowatt-hours = power (in kilowatt) x time usage (in hours)
In the given problem:
Time usage = 10,000 hours
Light bulb:
Power = 100 watt = 0.1 kw
kwh = 0.1 x 10,000 = 1,000 kwh
electricity bill = 1000 kwh x $0.15/kwh = $150
fluorescent bulb
Power = 25 watt = 0.025 kw
kwh = 0.025 x 10,000 = 250 kwh
electricity bill = 250 kwh x $0.15/kwh = $37,5
Money save = $150 - $37,5 = $112,5
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what is the expected mass of a potassium-39 nucleus, based on the total mass of its protons and neutrons?
The total mass of the protons and neutrons in a potassium-39 nucleus is 6.5307 x 10^-26 kilograms.
The mass of a potassium-39 nucleus can be calculated based on the total mass of its protons and neutrons. Potassium-39 is a stable isotope of potassium with 19 protons and 20 neutrons in its nucleus. The mass of a proton is approximately 1.6726 x 10^-27 kilograms, and the mass of a neutron is approximately 1.6749 x 10^-27 kilograms.
Therefore, the total mass of the protons in a potassium-39 nucleus is 19 x 1.6726 x 10^-27 = 3.18094 x 10^-26 kilograms. The total mass of the neutrons in a potassium-39 nucleus is 20 x 1.6749 x 10^-27 = 3.3498 x 10^-26 kilograms.
The total mass of the protons and neutrons in a potassium-39 nucleus is therefore 3.18094 x 10^-26 + 3.3498 x 10^-26 = 6.5307 x 10^-26 kilograms. This is the expected mass of a potassium-39 nucleus, based on the total mass of its protons and neutrons.
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Dad pulls his daughter Sarah (Sarah and sled combined mass 60 kg) on a sled, pulling on a rope with a force of 300 N at an angle of 30° above the horizontal. If we neglect friction force: What is the normal force acting on the sled/Sarah system?
Answer: Fn = 450 N
Explanation:
Part of the tension acts in the upward y-direction, reducing the normal force.
ΣFy = Fn + Ftsin(30)-Fg
0 = Fn + (300 N)sin(30) - (60 kg)(10 m/s^2)
0 = Fn + 150 N - 600 N
0 = Fn - 450 N
Fn = 450 N
where is the center of gravity of the man doing the classic yoga poses shown in (figure 1)?
The center of gravity of the man doing the classic yoga poses will be as shown in first figure.
The Center of Gravity is the theoretical point in the body where the body's total weight is expected to exert force. It is important to know the center of gravity because it predicts the behavior of a body's movement when obeying gravity. It is also used in the construction of static structures such as buildings and bridges.
In a modern gravitational field, the center of gravity is identical to the center of mass. However, the two concepts do not always coincide. For the moon, the center of mass is very close to its geometric center. However, its center of gravity is slightly lower than Earth's due to the strong gravitational force of the nearby moon.
In a symmetrically shaped object made of homogenous materials, the center of gravity will match the body's geometric location. However, an asymmetrical object consisting of many components with different dimensions will have its center of gravity at some distance from its geometric center. In the hollow body or irregularly shaped body, the center of gravity in a point outside the body material.
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a boy rides his bicycle which has wheels of radius 27.0 cm. if the boy accelerates from rest to a speed of 11.2 m/s in 24.0 s, what is the angular acceleration (in rad/s2) of the tires? (enter the magnitude.)
The angular acceleration is 0.01533rad/s.
We are given that,
Radius = r = 27.0cm
Speed = v = 11.2 m/s
Time = t = 24.0 s
Therefore , We shall first find the linear acceleration before calculating the angular acceleration from one of the linear motion kinematics equations and the initial velocity u will be 0.
v = u + at
a = v/t
a = (11.2m/s)/(27.0×10⁻²m)
a = 0.414 ×10⁻²m/s²
Now , calculating the angular acceleration,
a = α × r
α = a/r
α = (0.414 ×10⁻²m/s²)/(27.0×10⁻²m)
α = 0.01533rad/s
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A 150-kg object takes 1.5 minutes to travel a 2,500-meter straight path. It begins the trip traveling 120 meters per second and decelerates to a velocity of 20 meters per second.
What was its acceleration?
Responses
(A) −1.11 m/s2
(B) −0.3 m/s2
(C) +1.11 m/s2
(D) +80 m/s2
Answer: So the answer is (A) -1.11 m/s^2.
Explanation: To solve this problem, we need to use the formula for average acceleration, which is given by:
a = (vf - vi) / t
Where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.
Plugging in the values given in the problem, we get:
a = (20 m/s - 120 m/s) / (1.5 minutes * 60 seconds/minute) = -100 m/s / 90 seconds = -1.11 m/s^2
So the answer is (A) -1.11 m/s^2.