Given,
The radius of the loop of the roller coaster, r=22.8 m
The forces that are acting on the roller coaster when it is at the top of the loop are the centripetal force directed upwards and the weight of the roller coaster including the passengers directed downwards.
For the passengers to stay in the seat, the centripetal force must be, at the least, equal to the weight of the passengers and the rollercoaster.
That is,
\(\frac{Mv^2}{r}=Mg\)Where M is the combined mass of the rollercoaster and the passengers, v is the minimum speed of the roller coaster when it is at the top of the loop, and g is the acceleration due to gravity.
On simplifying the above equation,
\(v=\sqrt[]{gr}\)On substituting the known values,
\(\begin{gathered} v=\sqrt[]{9.8\times22.8} \\ =14.95\text{ m/s} \end{gathered}\)Thus the minimum speed that the roller coaster must have when it is at the top of the loop so that the passengers stay in contact with the seats is 14.95 m/s.
doing the same amount of work in less time requires more power true or false
F = kx
k = ?
Select one:
a. F/x
b .x/F
c. F + x
d. F − x
Answer:
\(F = kx \\ k = \frac{F }{x} \)
so the answer is a
A neutron star has a mass of between 1.4-2.8 solar masses compressed to the size of:
A. Earth
B. The state of Oregon
C. North America
D. An average city
The correct answer is D. An average city
Explanation:
A neutron star differs from others due to its massive density, this means a lot of matter is compressed in a small area. Indeed, neutron stars have a mass of around 1.4 to 2.8 times the mass of the sun. But these are considerably small as they only measure around 20 kilometers, which is the size of an average city. Additionally, neutron stars are this dense because they are the result of a regular star exploding, which leads to a super-dense core, or neutron star. In this context, the mass of a neutron star is compressed to the size of an average city.
What is the period of a wave with a frequency of 0.75 Hz?
Answer:
Period = 1.33 seconds
Explanation:
Period = 1/0.75
Violet light of 425 nm is reflected from a thin film of air between two glass plates. The thickness of the film is 1.70 x 10^-6 m.
(a) How much farther does the light reflected from the bottom surface of the film travel than that reflected from the top surface?
(b) How many wavelengths of light does this present?
a) The path length difference between the light reflected from the bottom and top surfaces of the film is 3.4 x 10⁻⁶ m
b) It is equivalent to 8 wavelengths of violet light with a wavelength of 425 nm.
a) When light reflects off a thin film of air between two glass plates, interference between the reflected waves can result in constructive or destructive interference, depending on the thickness of the film and the wavelength of the light. This can lead to a range of optical phenomena, including coloration, reflection, and transmission.
In this scenario, violet light of 425 nm is reflected from a thin film of air with a thickness of 1.70 x 10⁻⁶ m. To find the difference in path length between the light reflected from the bottom surface of the film and the light reflected from the top surface, we can use the formula:
path length difference = 2 x thickness of the film
= 2 x 1.70 x 10⁻⁶ m
= 3.4 x 10⁻⁶ m
b) To find the number of wavelengths of light this presents, we can divide the path length difference by the wavelength of the light:
number of wavelengths = path length difference / wavelength
= (3.4 x 10⁻⁶ m) / (425 x 10⁻⁹ m)
= 8 wavelengths
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What type of tv uses a VfL for backlighting
A VfL (Vertical Field LED) backlighting system is commonly used in LCD (Liquid Crystal Display) televisions.
LCD TVs rely on a backlight to illuminate the liquid crystal layer, which controls the passage of light to create the visual image. The VfL technology is a specific type of LED backlighting arrangement used in certain LCD TV models. In a VfL backlighting system, the LEDs (Light-Emitting Diodes) are positioned vertically along the edges of the LCD panel.
The light emitted by these LEDs is directed across the panel using light guides or optical films, illuminating the liquid crystal layer uniformly. One advantage of VfL backlighting is its ability to provide consistent illumination across the LCD panel, reducing any potential inconsistencies in brightness or color uniformity. The vertical orientation of the LEDs allows for more precise control over light distribution, improving overall image quality.
Additionally, VfL backlighting offers potential advantages in terms of power efficiency. By selectively dimming or turning off specific zones of LEDs, local dimming techniques can be employed to enhance contrast and black levels, resulting in improved picture quality while conserving energy. It's important to note that VfL backlighting is just one of several backlighting technologies available for LCD TVs.
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A current of 4.00 mA flows through a copper wire. The wire has an initial diameter of 4.00 mm which gradually tapers to a diameter of 1.00 mm. The wire length is
2.00 m and copper has a number density of 8.50 × 1028 m–3.
Find the change in mean drift velocity for electrons as they pass from one end of the wire to the other and therefore calculate the average acceleration of the electrons.
The change in mean drift velocity for electrons as they pass from one end of the wire to the other is 3.506 x 10⁻⁷ m/s and average acceleration of the electrons is 4.38 x 10⁻¹⁵ m/s².
The given parameters;
Current flowing in the wire, I = 4.00 mAInitial diameter of the wire, d₁ = 4 mm = 0.004 mFinal diameter of the wire, d₂ = 1 mm = 0.001 mLength of wire, L = 2.00 mDensity of electron in the copper, n = 8.5 x 10²⁸ /m³The initial area of the copper wire;
\(A_1 = \frac{\pi d^2}{4} = \frac{\pi \times (0.004)^2}{4} =1.257\times 10^{-5} \ m^2\)
The final area of the copper wire;
\(A_2 = \frac{\pi d^2}{4} = \frac{\pi (0.001)^2}{4} = 7.86\times 10^{-7} \ m^2\)
The initial drift velocity of the electrons is calculated as;
\(v_d_1 = \frac{I}{nqA_1} \\\\v_d_1 = \frac{4\times 10^{-3} }{8.5\times 10^{28} \times 1.6\times 10^{-19} \times 1.257\times 10^{-5}} \\\\v_d_1 = 2.34 \times 10^{-8} \ m/s\)
The final drift velocity of the electrons is calculated as;
\(v_d_2 = \frac{I}{nqA_2} \\\\v_d_2 = \frac{4\times 10^{-3} }{8.5\times 10^{28} \times 1.6\times 10^{-19} \times 7.86\times 10^{-7}} \\\\v_d_2 = 3.74\times 10^{-7} \ m/s\)
The change in the mean drift velocity is calculated as;
\(\Delta v = v_d_2 -v_d_1\\\\\Delta v = 3.74\times 10^{-7} \ m/s \ -\ 2.34 \times 10^{-8} \ m/s = 3.506\times 10^{-7} \ m/s\)
The time of motion of electrons for the initial wire diameter is calculated as;
\(t_1 = \frac{L}{v_d_1} \\\\t_1 = \frac{2}{2.34\times 10^{-8}} \\\\t_1 = 8.547\times 10^{7} \ s\)
The time of motion of electrons for the final wire diameter is calculated as;
\(t_2 = \frac{L}{v_d_1} \\\\t_2= \frac{2}{3.74 \times 10^{-7}} \\\\t_2 = 5.348 \times 10^{6} \ s\)
The average acceleration of the electrons is calculated as;
\(a = \frac{\Delta v}{\Delta t} \\\\a = \frac{3.506 \times 10^{-7} }{(8.547\times 10^7)- (5.348\times 10^6)} \\\\a = 4.38\times 10^{-15} \ m/s^2\)
Thus, the change in mean drift velocity for electrons as they pass from one end of the wire to the other is 3.506 x 10⁻⁷ m/s and average acceleration of the electrons is 4.38 x 10⁻¹⁵ m/s².
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Answer:
The change in mean drift velocity for electrons as they pass from one end of the wire to the other is 3.506 x 10⁻⁷ m/s and average acceleration of the electrons is 4.38 x 10⁻¹⁵ m/s².
The given parameters;
Current flowing in the wire, I = 4.00 mA
Initial diameter of the wire, d₁ = 4 mm = 0.004 m
Final diameter of the wire, d₂ = 1 mm = 0.001 m
Length of wire, L = 2.00 m
Density of electron in the copper, n = 8.5 x 10²⁸ /m³
The initial area of the copper wire;
The final area of the copper wire;
The initial drift velocity of the electrons is calculated as;
The final drift velocity of the electrons is calculated as;
The change in the mean drift velocity is calculated as;
The time of motion of electrons for the initial wire diameter is calculated as;
The time of motion of electrons for the final wire diameter is calculated as;
The average acceleration of the electrons is calculated as;
Thus, the change in mean drift velocity for electrons as they pass from one end of the wire to the other is 3.506 x 10⁻⁷ m/s and average acceleration of the electrons is 4.38 x 10⁻¹⁵ m/s².
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Explanation:
1. Which distance is the greatest?
O 7000 meters
O 99.99 meters
O 4.5 x 10³ meters
O 9.0 x 10² meters
Answer:
7000 meters
Explanation:
obviously 99.99 is less than 7000
10 cubed is 10 × 10 × 10, 1000, × 4.5 is 4500, which is less than 7000
10 squared is 100, which × 9 is only 900, which is also less than 7000
have a good day
Which correctly describes a different evolutionary stage of a star like the sun?
A) it’s forms from a cold, dusty molecular cloud
B) During a yellow giant stage, it burns carbon in its core and helium in the shell surrounding the core.
C) After leaving the main sequence, its core is stable due to electron degeneracy
D) It becomes a white dwarf after exploding as a supernova
E)During a red giant stage, its core contracts and cools
Answer:
Explanation:
The correct option that describes a different evolutionary stage of a star like the sun is:
D) It becomes a white dwarf after exploding as a supernova
This is because a star like the sun does not have enough mass to undergo a supernova explosion. After it has exhausted all the fuel in its core, it will evolve into a red giant and then a planetary nebula, leaving behind a small, hot, dense remnant known as a white dwarf. Supernovae occur in much more massive stars that have cores that can collapse to form a neutron star or black hole.
A 1.55 kg frictionless block is attached to an ideal spring with force constant 340 N/m . Initially the spring is neither stretched nor compressed, but the block is moving in the negative direction at 14.0 m/s.
A.) Find the amplitude of the motion.
B.) Find the maximum acceleration of the block.
C.) Find the maximum force the spring exerts on the block.
Answer:
Explanation:
Let amplitude be A . At displacement A , velocity will be zero , so
1/2 k A² = 1/2 m v²
340 A² = 1.55 x 14²
A = .9452 m
= 94.52 cm
B ) angular frequency of oscillation ω = √ ( k / m )
= √ ( 340 / 1.55 )
ω = 14.81 radian /s
maximum acceleration = ω²A
= 14.81² x 0.9452
= 207.32 m/s²
C) Maximum force = mass x maximum acceleration
= 1.55 x 207.32
= 321.36 N .
1. A 15.0 kΩ resistor is hooked up to a 45.0 V battery in a circuit with a switch.
(a) Draw a circuit diagram for the circuit described. Label all parts and values.
(b) What is the current flowing through the resistor?
(c) What is the power dissipated by the resistor?
(a) The circuit diagram is in the image attached.
(b) The current flowing through the resistor is 0.003 A.
(c) The power dissipated by the resistor is 0.135 W.
What is current flowing through the resistor?(b) The current flowing through the resistor is calculated by applying Ohm's law as follows;
V = IR
I = V/R
where;
V is the voltageR is resistanceI = 45 V / 15,000Ω
I = 0.003 A
(c) The power dissipated by the resistor is calculated as follows;
P = IV
where;
I is the current V is the voltageP = 0.003 x 45 V
P = 0.135 W
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b. How tar from the li u
b. Obtain the value of g from the motion of the moon assuming that its period
of rotation round the earth is 27 days 8 hours and the radius of its orbit is
60.1 times the radius of the earth.
0.
7.2 m. Compute
Answer:
Approximately \(9.79\; \rm m \cdot s^{-2}\) at the surface of the earth, given that the radius of the earth is known to be approximately \(6.371\times 10^{6}\; \rm m\). Assumptions: the earth is a sphere, the orbit of the moon is circular, and that the gravitational pull of the earth is the only force on the moon.
Explanation:
Convert the orbital period of the moon around the earth to seconds:
\(\begin{aligned}t &= (27\; \text{day} \times 24\; \text{hours} \cdot \text{day}^{-1} + 8\; \text{hour})\times 3600\; \rm \text{s}\cdot \text{hour}^{-1}\\ &= 2361600\; \text{s} \end{aligned}\).
Calculate the angular velocity of the moon around the earth using the formula\(\displaystyle \text{angular velocity} = \frac{2\pi}{\text{orbital period}}\):
\(\begin{aligned}\omega = \frac{2\pi }{t} = \frac{2\pi}{2361600\; \rm s} \approx 2.66056\times 10^{-6}\; \rm s^{-1}\end{aligned}\).
Let \(m(\text{moon})\) denote the mass of the moon. Let \(g\) denote the gravitational field strength at the surface of the earth (not at the position of the moon.) Let \(r\) denote the radius of the earth.
The orbital radius of the moon would thus be \(60.1\, r\). Note that in the gravitational field due to a single spherical mass, the field strength is inversely proportional to the square of distance from the center of that mass.
The surface of the earth is at a distance of \(r\) away from the center of the earth. The distance between the moon and the center of the earth would then be \(60.1\) times that number (that is: \(60.1\, r\).)The gravitational field at the surface of the earth is \(g\). Therefore, at the position of the moon (\(60.1\) times further away from the center of the earth compared to the earth surface,) the gravitational field strength would be:
\(\displaystyle \left( \frac{r^2}{(60.1\, r)^2} \right)\, g = \frac{g}{60.1^2}\),
Hence, the gravitational pull of the earth on the moon would be \(\displaystyle \frac{m(\text{moon})\, g}{60.1^2}\).
Assume that the gravitational pull of the earth is the only force on the moon. That gravitational pull would then be the equal (in size) to the net force on the moon. That is:
\(\displaystyle \text{Net force on the moon} = \frac{m(\text{moon})\, g}{60.1^2}\).
On the other hand, the rotation (assumed to be perfectly circular) of the moon would give the net force on the moon in terms of:
the mass of the moon, the angular speed of the rotation, andthe radius of the orbit.\(\displaystyle \text{Net force on the moon} = m(\text{moon})\, \omega^2\, (60.1\, r)\).
Combine the two expressions for the net force on the moon to obtain an equation for \(g\):
\(\displaystyle \frac{m(\text{moon})\, g}{60.1^2} = m(\text{moon})\, \omega^2\, (60.1\, r)\).
Simplify and solve for \(g\):
\(\displaystyle g = 60.1^3 \, \omega^2\, r\).
The angular velocity of this rotation, \(\omega\), has already been found to be approximately \(2.66056\times 10^{-6}\; \rm s^{-1}\). Look up the radius of the earth: \(r = 6.371\times 10^{6}\; \rm m\). Evaluate this expression for \(g\):
\(\begin{aligned}g &= 60.1^3 \, \omega^2\, r \\ &\approx 60.1^3 \times \left( 2.66056\times 10^{-6}\; \rm s^{-1}\right) \times 6.371\times 10^{6}\;\rm m \\ &\approx 9.79\; \rm m \cdot s^{-1}\end{aligned}\).
Using a conventional two-slit apparatus with light of wavelength 605 nm, 34 bright fringes per centimeter are observed on a screen 3.1 m away. What is the slit separation
Answer:
d = 6.38 x 10⁻³ m = 6.38 mm
Explanation:
Since, the no. of bright fringes is 34 in a centimeter, therefore, the fringe spacing must be equal to:
Fringe Spacing = Δx = 1 cm/34
Δx = 0.0294 cm = 2.94 x 10⁻⁴ m
But, the formula for fringe spacing in a double slit experiment is:
Δx = λL/d
where,
λ = wavelength of light = 605 nm = 6.05 x 10⁻⁷ m
L = Distance between screen and slits = 3.1 m
d = slit separation = ?
Therefore,
2.94 x 10⁻⁴ m = (6.05 x 10⁻⁷ m)(3.1 m)/d
d = (18.755 x 10⁻⁷ m²)/(2.94 x 10⁻⁴ m)
d = 6.38 x 10⁻³ m = 6.38 mm
Based on the diagram, which statement explains how energy is conserved
during this chemical reaction?
A
Reaction progress
Potential energy
of a system
B
OA. The potential energy lost by the reaction system (B) is gained by
the surroundings.
B. The potential energy lost by the reaction system (C) is also lost by
the surroundings.
← PREVIOUS
OC. The potential energy changes indicated by C and B involve energy
lost by the surroundings.
The potential energy changes indicated by C and B involve energy lost by the surroundings. Therefore, option B is correct.
Potential energy is the energy possessed by an object due to its position or condition. It is often associated with the potential for the object to do work or undergo a change. The concept of potential energy arises from the interactions between objects or within a system.
Potential energy is converted into other forms of energy, such as kinetic energy (energy of motion) when the object or system undergoes a change or is acted upon by external forces.
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Your question is incomplete, most probably the correct answer is this:
Based on the diagram, which statement explains how energy is conserved during this chemical reaction? (A) is also gained by the surroundings. B. The potential energy changes indicated by C and B involve energy lost by the surroundings. C. The potential energy lost by the reaction system (C) is also lost by the surroundings. D. The potential energy lost by the reaction system (B) is gained by the surrounding
calculate the difference between
the points B (-2, 3) and C (-5,8)
Explanation:
the answer to this question would be mj.us 1 and minus 3
How much heat is contained in 100 kg of water at 60.0 °C?
Answer:
so how much heat is there at 0 C? That's zero. But for every degree above that you have 4.184 J. You take it from there. Remember q = mc*delta T.
In which of the following situations would it NOT be wise to estimate?
a.
the number of miles per gallon an automobile can provide
b.
the time it would take to walk to the grocery store from home
c.
the amount of food to prepare for twelve people
d.
the amount of medicine to give a patient
A car has a velocity of 21.3 m/s. It then accelerates at a uniform rate of 3.6 m/s per second for the next 5.0 seconds. What distance does the car cover during this time? Round to 4 decimal places if necessary
Explanation
U uniformly accelerated motion is the one in which the acceleration of the particle throughout the motion is uniform,the formula to find the distance is as follows:
\(\begin{gathered} x=v_ot+\frac{1}{2}at^2 \\ where \\ v_o\text{ is the initial velocity} \\ t\text{ is the time} \\ a\text{ is the acceleration} \end{gathered}\)so
Step 1
a)let
\(\begin{gathered} v_o=21.3\text{ }\frac{m}{s} \\ a=3.6\frac{m}{s^2} \\ t=5\text{ s} \end{gathered}\)b) now,replace in the formula and calculate
\(\begin{gathered} x=v_{o}t+\frac{1}{2}at^{2} \\ x=21.3\frac{m}{s}*5s+\frac{1}{2}3.6\frac{m}{s^2}*(5\text{ s\rparen}^2 \\ x=106.5\text{ m}+45\text{ m} \\ x=151.5\text{ m} \end{gathered}\)therefore, the answer is 151.5 meters
I hope this helps you
I need ideas of what kind of simple motor i can build and how i can build it. The simple motor MUST spin without using your own force. What materials would i use and how would i create it. what would i create
Answer:
i don't know but my father i think he can't answer this
the radiation that is least damaging to humans is
The radiation that is least damaging to humans is non-ionizing radiation.
What is non ionizing radiationNon-ionizing radiation refers to the type of radiation that does not have enough energy to remove tightly bound electrons from atoms or molecules, thus not causing significant damage to biological tissues.
Examples of non ionizing radiation include radio waves, microwaves, visible light and low energy ultraviolet (UV) radiation. while excessive exposure to any form of radiation can have adverse effects, non-ionizing radiation is generally considered to be less harmful compared to ionizing radiation, which includes X-rays and gamma rays.
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A force of 345 N is applied to a 70 kg scooter. What will the scooter's
acceleration be?
Explanation:
here, force applied (N) = 345 N
or, mass of scooter (m) = 70 kg
now, acceleration (a) = ?
we know, force = mass × acceleration
or, 345 = 70 × acceleration
or, acceleration = 345/70
therefore, acceleration = 4.9 m/s2 (meter/second square)
5. Elements combine to form
O compounds
O molecules
atoms
mixtures the gen
Elements combine to form compounds. The correct answer is A.
Elements combine with each other in chemical reactions to form compounds. A compound is a substance composed of two or more different elements chemically combined in a fixed ratio by mass. For example, water is a compound composed of hydrogen and oxygen in a fixed ratio of 2:1 by mass.
B. Molecules are formed when two or more atoms combine chemically, but these atoms can be of the same element or different elements. For example, oxygen gas (O2) is a molecule composed of two oxygen atoms.
C. Atoms are the smallest unit of matter that retains the properties of an element. Atoms do not combine to form other atoms or compounds.
D. Mixtures are composed of two or more substances physically mixed together, but the substances retain their individual properties and can be separated by physical means. Mixtures are not formed by the chemical combination of elements. Examples of mixtures include air and saltwater.
Therefore, The correct answer is option A.
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In a pipe of 90mm diameter, water is flowing with a mean velocity of 2m/s at a gauge pressure of 350KN/M². Determine the total head, if the pipe is 8m above the datum.
The total head of the pipe is 430,400 Pa.
What is the total head of the pipe?
The total head of the pipe is the total pressure of the pipe and it is calculated as follows;
Pt = Pi + ¹/₂ρv² + ρgh
where;
Pi is the gauge pressure ρ is density of waterv is the speed of the waterh is the height of the water above the groundPt = ( 350,000) + ¹/₂(1000)(2)² + (1000 x 9.8 x 8)
Pt = 430,400 Pa
Thus, the total head or total pressure of the pipe depends on the density of water, speed of water and height above datum.
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what are the five uses of bad conductors in our homes
Explanation:
I have only 4 of them ,hope they help
Which of the statements about the effect of solutes on solutions is true
Select one:
O a. Solutes raise the boiling point of a solvent.
O b. Water with a solute dissolved in it will freeze at 0°C.
O c. Solutes raise the freezing point of a solvent
d. Antifreeze boils at a lower temperature than pure water.
Answer:
Solutes raise the boiling point of a solvent.
Explanation:
When the solutes is non volatile and dissolved in a solvent, it lowers the vapour pressure of the solvent hence elevating the boiling point of the solvent.
A sound wave is traveling with a frequency of 880Hz. It has a wavelength of 0.75. What is the speed of the sound wave
The speed of the sound wave is 660 meters per second.
To calculate the speed of the sound wave, we need to use the formula:
Speed = Frequency x Wavelength
Here, the frequency of the sound wave is given as 880Hz, and the wavelength is given as 0.75. To get the answer, we just need to plug these values into the formula and solve for the speed:
Speed = 880 x 0.75
Speed = 660 meters per second
It's important to note that the speed of sound depends on the medium through which it is traveling. In air, the speed of sound is approximately 343 meters per second at standard temperature and pressure. However, this value can change depending on factors such as temperature, humidity, and altitude.
Understanding the speed of sound is important in various fields, such as music, engineering, and physics. For example, in music, the speed of sound determines the pitch of a note, while in engineering, it can be used to design and optimize acoustic systems. In physics, it's used to study the properties of waves and to explain phenomena such as Doppler effect and sonic booms.
Therefore, the speed of the sound wave is 660 meters per second.
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Which statement best describes the liquid state of matter?
ОА.
It has definite shape but indefinite volume.
OB.
It has definite shape and definite volume.
Ос.
It has indefinite shape and indefinite volume.
OD.
It has indefinite shape but definite volume.
Answer:
OB.It has definite shape and definite volume
A spring scale hung from the ceiling stretches by 5.9 cm
when a 1.6 kg
mass is hung from it. The 1.6 kg
mass is removed and replaced with a 2.1 kg
mass.
Part A
What is the stretch of the spring?
Express your answer with the appropriate units.
The stretch of the spring is proportional to the weight of the mass hung from it. Since the spring stretches by 5.9 cm when a 1.6 kg mass is hung from it, we can use this information to find the stretch when a 2.1 kg mass is hung from it.
The stretch of the spring is given by:
stretch = (mass x gravity x length) / (spring constant)
where mass is the mass hung from the spring, gravity is the acceleration due to gravity (9.81 m/s^2), length is the stretch of the spring, and the spring constant is a measure of the stiffness of the spring (measured in N/m).
We can rearrange this equation to solve for the stretch of the spring:
stretch = (mass x gravity x length) / (spring constant)
length = (spring constant x stretch) / (mass x gravity)
Substituting the given values, we get:
length = (spring constant x 0.059 m) / (1.6 kg x 9.81 m/s^2)
Simplifying, we get:
length = 0.236 m
Therefore, the stretch of the spring when a 2.1 kg mass is hung from it is 0.236 m.
You are a passenger in a truck that gets stuck in mud. You and the driver use a tree branch as a lever to lift up the truck. You apply an effort force of 600 N to the branch. The back of the truck weighs 2400 N. What is the mechanical advantage of the branch-lever?
The truck's cargo weighs 2400 N. The department has a mechanical advantage of 4.
What do mechanical talents entail?Combining hard and soft abilities in areas like arithmetic, computing, design, and interaction make up the talents required for mechanical engineering. Because they operate in a variety of fields, such as the manufacturing, science, and automotive manufacturing, engineers in the mechanical technology profession have one of the broadest scopes.
What three categories of mechanical are there?Longitudinal, transversal, as well as pressure waves are the three different forms of physical phenomena. They differ based on how the medium's atomic constituents behave when the stage's energy goes through. Wind farms that are powered by steam, water, winds, gas, or hydrocarbons are a few examples of this. Other sources of energy are frequently produced through machinery.
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assume that the initial speed is 25 m/s and the angle of projection is 53 degree above the hroizontal. the cannon ball leaves the uzzel of the cannon at a highet of 200 m.( the cannon is at the edge of the cliff) A: find the horizontal distance the cannon travles. B: when does the cannon ball reach the ground? C: find the maximum highet the cannon ball reaches.
Answer:
A. xmax = 131.49 m
B. t = 8.74 s
C. ymax = 220.33 m
Explanation:
A. In order to find the horizontal distance which cannon travels you first calculate the flight time. The flight time can be calculated by using the following formula:
\(y=y_o+v_osin\theta-\frac{1}{2}gt^2\) (1)
yo: height from the projectile is fired = 200m
vo: initial velocity of the projectile = 25m/s
g: gravitational acceleration = 9.8 m/s^2
θ: angle between the direction of the initial motion of the ball and the horizontal = 53°
t: time
You need the value of t when the projectile hits the ground. Then, in th equation (1) you make y = 0m.
When you replace the values of all parameters in the equation (1), you obtain the following quadratic formula:
\(0=200+(25)sin53\°t-\frac{1}{2}(9.8)t^2\\\\0=200+19.96t-4.9t^2\) (2)
You use the quadratic formula to obtain the value of t:
\(t_{1,2}=\frac{-19.96\pm\sqrt{(19.96)^2-4(-4.9)(200)}}{2(-4.9)}\\\\t_{1,2}=\frac{-19.96\pm65.71}{-9.8}\\\\t_1=8.74s\\\\t_2=-4.66s\)
You use the positive value because it has physical meaning.
Now, you can calculate the horizontal range of the projectile by using the following formula:
\(x_{max}=v_ocos\theta t\)
\(x_{max}=(25m/s)(cos53\°)(8.74s)=131.49m\)
The cannon ball travels a horizontal distance of 131.49 m
B. The cannon ball reaches the canon for t = 8.74s
C. The maximum height is obtained by using the following formula:
\(y_{max}=y_o+\frac{v_o^2sin^2\theta}{2g}\) (3)
By replacing in the equation (3) the values of all parameters you obtain:
\(y_{max}=200m+\frac{(25m/s)^2(sin53\°)^2}{2(9.8m/s^2)}\\\\y_{mac}=200m+20.33m=220.33m\)
The maximum height reached by the cannon ball is 220.33m