(a) By using the law of conservation of energy, the distance moved by the solid disk along the ramp is 0.96 m.
(b) The answer does not depend on the mass and radius of the disc as these values are canceled when the law of conservation of energy is applied.
What is the law of conservation of energy?
The law of conservation of energy states that the total energy of an isolated system is conserved.
The total initial energy Ei of the disc rolling down an inclined plane is given by the formula,
Ei=1/2*mv^2 + 1/2*Iω^2
where m is the mass of the disc, v is the velocity of the disc, I is the moment of inertia and ω is the angular velocity of the disc.
For a solid disc, I=1/2mr^2, and since it is rolling without slipping, the rolling velocity of the disc will be equal to its translational velocity, that is,
v=ωr or ω=v/r
So using ω=v/r and I=1/2mr^2, it can be written,
Ei=1/2*m(v)^2 + 1/2*(1/2mr^2)(v/r)^2
Ei=1/2*m(v)^2*(1+1/2*)
Ei=3/4*mv^2
If the height covered by the disc is h before stopping, then its final total energy Ef will be equal to the potential energy, that is,
Ef=m*g*h
From the law of conservation of energy, it can be written,
Ei=Ef
3/4*mv^2=m*g*h
h=3v^2/(4g)
The length of the ramp is then given by the formula,
l=hcosecθ
where θ is the inclination angle. So
l= 3v^2/(4g)*cosecθ
Here g=9.8 m/s^2, v=2.5 m/s and θ=30.0 degree. Using these values,
l= 3*(2.5 )^2/(4*9.8)*cosec( 30)
l= 0.96 m
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What is the mass moment of inertia of a 20kg sphere with a radius of 0.2m about a point on the sphere's perimeter
Answer:
I = M R^2 is the moment of inertia about a point that is a distance R from the center of mass (uniform distributed mass).
The moment of inertia about the center of a sphere is 2 / 5 M R^2.
By the parallel axis theorem the moment of inertia about a point on the rim of the sphere is I = 2/5 M R^2 + M R^2 = 7/5 M R^2
I = 7/5 * 20 kg * .2^2 m = 1.12 kg m^2
What do you mean by focus in science
An 8000-N car is moving at 12 m/s along a horizontal road. The driver applies the breaks and the car skids to a stop. How much kinetic energy is lost? Group of answer choices 4.8*104 J 4.8*106 J 5.8*105 J 5.9*104 J 1.2*105 J
58775.51 J kinetic energy is lost,
Energy lost = 0.5*mv²
= 0.5*8000/9.8 * 12*12
= 58775.51 J
To calculate the energy loss of a moving object, subtract the initial kinetic energy from the final kinetic energy, where the initial and final kinetic energies are calculated using the formula 1/2*M*V^2.
When energy is transformed from one form to another or moved from one area to any other, or from one device to another there's energy loss. This means whilst energy is converted to a different form, some of the entering energy is become an especially disordered form of energy, like heat.
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Use the concepts on which maxwell’s equations are based to explain why a compass needle is deflected when the compass is brought near a wire that is carrying an electric current.
A conductor that is conducting current generates a magnetic field everywhere around it. This magnetic field exerts force on the compass's magnetic needle, causing the needle to deviate.
Definition of Maxwell's rule
A current-conducting conductor creates a magnetic field everywhere around it. The magnetic needle of the compass experiences force from this magnetic field, which causes the needle to veer.
Equation for deflection
We have so far established that the total flux of electric field out of a closed surface is just the total enclosed charge multiplied by 1/ε0, ∫→E⋅d→A=q/ε0. This is Maxwell's first equation. It represents completely covering the surface with a large number of tiny patches having areas d→A.
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Which of the following is true about a theory?
A. It is almost always controversial among scientists.
B. It is the first step toward scientific knowledge
OC. It will be modified or replaced.
D. It is a guess about how something in nature happens.
Answer:
D. It is a guess about how something in nature happens.
Explanation:
Nature is not controlled by anyone else, so people have to guess in order to know if something happend in nature.
The period of a pendulum depends on _____. Select all that apply. The period of a pendulum depends on _____. Select all that apply. its mass the string length the amplitude of the motion gravity the value of the pendulum constant
Answer:
Period is proportional to (L / g)^1/2
Only the length of the string and the force of gravity will affect the motion of a simple pendulum.
The time period of a pendulum depends on the length of pendulum, acceleration due to gravity and to some extends its amplitude also.
What is simple pendulum?A simple pendulum is a suspended body with one of its end fixed on a support and it is free to swing back and forth. The equation for the time period of simple pendulum is written as:
[tex]\rm T = 2\pi \sqrt{ \frac{l}{g} }[/tex]
Hence, the factors which affects the time period of pendulum are length and acceleration due to gravity g. This time period of the pendulum is the time taken to cover one complete oscillation.
Up to some extend the amplitude of the swing may affect the time period. However, mass has no effect on the period of a simple pendulum.
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The info below shows three kettles with their powers and the time they take to boil 500cm3 of water. If electricity costs 9p per unit, how much does it cost to boil 500cm3 of water using the 3kW kettle?
Kettle 1= 3mins =3kW
Kettle 2= 3.5mins= 2.2kW
Kettle 3=4.5mins=1.4kW
The cost of boiling 500 cm³ of water using the 3 KW Kettle is 1.35p
What is power?This is defined as the rate in which energy is consumed. Electrical power is expressed mathematically as:
Power (P) = Energy (E) / time (t)
P = E / t
How to determine the energyPower (P) = 3 KWTime (t) = 3 mins = 3 / 60 = 0.05 hEnergy (E) =?E = Pt
E = 3 × 0.05
E = 0.15 KWh
How to determine the costEnergy (E) = 0.15 KWhCost per unit = 9pCost =?Cost = Energy × cost per unit
Cost = 0.15 × 9
Cost = 1.35p
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If a mineral contains only atoms of oxygen and a metal, it is most likely
O an oxide.
O a sulfate.
a phosphate.
a silicate.
A sphere of radius 6cm is moulded into a thin cylindrical wire of length 32cm. Calculate the radius of the
wire in SI Units
Answer:
4/3 pi R^3 = pi r^2 L equating volume of sphere and wire
r = (4 R^3 / 3 * L)^1/2 solving for radius of wire
r = (4 * 6^3 / 3 * 32)^1/2
r = 9^1/2 cm = 3 cm = .03 meters
A car travels around a curve. What can you say about the centripetal force if the velocity is tripled?
Group of answer choices
A) Nothing - there is no information on the mass of the car.
B) Nothing - there is no information on the radius of the curve.
C) The centripetal force will increase by a factor of nine
D) The centripetal force will increase by a factor of three.
Answer:
F = M a = M v^2 / R
If v is increased by three the force will be increased by nine,
C) is correct
Suppose you are an engineer building a road across a mountain. From a prudential point of view, it would be easier and cheaper to build it through a family’s farm. This option would require compelling the family to move, which would be an extreme hardship for them. From a moral point of view, the family should be allowed to stay on their farm. Which view should take precedence?
Compensation may be provided, and a temporary residence provided, to the family so that they may make necessary adjustments to their living arrangements and other work-related matters. Even if it's not the nicest way to go about things, it's the most effective.
What is compensation due to damages?
Generally, Money given to a successful plaintiff in civil litigation is known as "compensatory damages." Damage awards are handed out by the civil justice system.
In conclusion, Engineers have a responsibility to find optimal solutions that satisfy the demands of the public in a manner that is both practical and beneficial to the progress of the country as a whole. In this case, forcing the farm family to relocate would be very difficult and upsetting for them, but it would be quite useful for the community as a whole if a road were to be constructed.
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Acceleration of a particle moving along x axis is given
by a = x. At x = 0, v = 2 m/s. Find velocity as a
function of x.
(a) √√√x+2
(c) √√x +4
(b) √x² +2
2
(d) √x² +4
B. The velocity of the particle with respect to the acceleration is √x + 4.
What is velocity?
Velocity is the rate of change of displacement with time.
The velocity of the particle with respect to the acceleration of the particle is calculated as follows;
vf = v₀ + at
where;
vf is the final velocityv₀ is the initial velocitya is acceleration, assuming a = √x + 2t is timevf(x) = 2 + (√x + 2)
vf(x) = √x + 2 + 2
vf(x) = √x + 4
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You can, in an emergency, start a manual transmission car by putting it in neutral, letting the car roll down a hill to pick up speed, then putting it in gear and quickly letting out the clutch. If the car needs to be moving at 3.5 m/s for this to work, how high a hill do you need
Answer: 0.625 m
Explanation:
Given:
Final velocity of the car = 3.5 m/s
While the car rolls down the hill, there is a conversion of potential energy (PE) to kinetic energy (KE). Therefore, applying the conversion of energy as,
[tex]$$Total energy at height $(\mathrm{h})=$ Total energy at bottom$$\begin{aligned}&K E+P E=K E^{\prime}+P E^{\prime} \\&0+m g h=\frac{1}{2} m v^{2}+O \\&m g h=\frac{1}{2} m v^{2}\end{aligned}$$[/tex]
Here, m denotes the mass of the car, g is the gravitational acceleration, having a value of 9.8 m/s^2. And h is the height of the hill.
Solving for h,
[tex]\begin{aligned}&g h=\frac{l}{2} v^{2} \\&h=\frac{1}{2} \times \frac{v^{2}}{g} \\&h=\frac{1}{2} \times \frac{3.5^{2}}{9.8} \\&h=0.625 \mathrm{~m}\end{aligned}[/tex]
Therefore, the required height of hill is 0.625 m
A 0.500 kg bullet is fired from a gun at 25.0 m/s, how much kinetic energy does it have?
Considering the definition of kinetic energy, the bullet has a kinetic energy of 156.25 J.
Kinetic energyKinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.
Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and in a rest position, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its rest state by applying a force to it.
The kinetic energy is represented by the following expression:
Ec= ½ mv²
Where:
Ec is the kinetic energy, which is measured in Joules (J).m is the mass measured in kilograms (kg).v is the speed measured in meters over seconds (m/s).Kinetic energy of a bulletIn this case, you know:
m= 0.500 kgv= 25 m/sReplacing in the definition of kinetic energy:
Ec= ½ ×0.500 kg× (25 m/s)²
Solving:
Ec= 156.25 J
Finally, the bullet has a kinetic energy of 156.25 J.
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Two charged particles are a distance of 1.72 m from each other. One of the particles has a charge of 8.08 nC, and the other has a charge of 4.02 nC. (a) What is the magnitude (in N) of the electric force that one particle exerts on the other
The magnitude (in N) of the electric force that one particle exerts on the other is A. F=107.6nN.
F=[(9×10^9) ×(7.10×10^-9) ×(4.42×10^-9)] /(1.62^2)
F=(282.4×10^-9)/2.6244
F=107.6×10^-9N
F=107.6nN
Experiments with electric charges have shown that two charged objects exert electrical forces on each other. The magnitude of the force is linearly proportional to the net charge of each object and inversely proportional to the square of the distance between the objects.
Coulomb's law for calculating electrostatic forces. This force arises from the interaction between two charged objects (or point charges), the magnitude of which is calculated by F = kQ1Q2r2 F = k Q 1 Q 2 r2.
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In the experiment you used objects with masses that were not necessarily known. Assume that it is determined that the mass of an object that produces a deformation of size 3, is 120 grams. What is the mass of an object that would produce 1 unit of deformation
Answer:
40 gm
Explanation:
size one is 1/3 of size 3
so the mass is also 1/3
1/3 * 120 gm = 40 gm
A dentist using a dental drill brings it from rest to maximum operating speed of 387,000 rpm in 2.4 s. Assume that the drill accelerates at a constant rate during this time. (a) What is the angular acceleration of the drill in rev/s2
The angular acceleration of the drill is 2687.5 rev/s2
Given that operating speed of drill machine is 387000 rpm and the time given is 2.4s
We need to find the angular acceleration of the drill
Angular Acceleration is defined as the time rate of change of angular velocity.
The angular acceleration is also known as rotational acceleration.
It is a quantitative expression of the change in angular velocity per unit time.
The formula of angular acceleration is α =Δω/Δt
To find angular acceleration
α =Δω/Δt
Where Δω is the change in angular velocity
Δt is the change in time
Substituting the value We get ,
[tex]= \frac{387*10^3*1/60}{2.4}[/tex]
Therefore ,
α = 2687.5 rev/s2
Hence the angular acceleration is 2687.5 rev/s2
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special metal hangers or stirrips called joist hangers are used when joist must be _____ the bottom of the grider or beam
Answer:
Special metal hangers or stirrups called joist hangers are used when joist must be flush with the bottom of the girder or beam.
Explanation:
A joist hanger also known as a beam hanger is a mechanical device which is used to fasten joists and rafters.The rafters are the carried members to beams and headers are the carrying members.Thus, special metal hangers or stirrups called joist hangers are used when joist must be flush with the bottom of the girder or beam.
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Which two theories disagree when it comes to describing the singularity thought to be at the center of a black hole
when it comes to describing the singularity thought to be at the center of a black hole Quantum physics and Einsteinʹ s general theory of relativity theories disagree.
What is the singularity of a black hole?
It is the center of the black hole, a place of infinite density where the known laws of physics cannot describe the conditions.It is place from which the escape velocity exceeds the speed of light.According to Einsteinʹ s general theory of relativity:
Theory of relativity holds that what we perceive as the force of gravity arises from the curvature of space and time. The scientist proposed that objects such as the sun and the Earth change this geometryfrom this we can say that,
It doesn't agree the concept of describing the singularity thought to be at the center of a black hole
Hence,
when it comes to describing the singularity thought to be at the center of a black hole Quantum physics and Einsteinʹ s general theory of relativity theories disagree.
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When you "Rate," or analyze, the consequences of your decisions, HELP can assist you with which of the following?
When you "Rate," or analyze, the consequences of your decisions, HELP can assist an individual with: B. evaluating the consequences of his or her decisions.
What is the decision-making process?The decision-making process refers to a cognitive process that involves obtaining information, analyzing them, and then evaluating alternatives, so as to enable the proper selection of an optimum solution (choice) to a particular problem.
Based on personal health skills, we can infer and logically deduce that HELP can assist an individual with evaluating the consequences of his or her decisions when he or she "Rate," or analyze, the consequences of your decisions.
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Complete Question:
When you "Rate," or analyze, the consequences of your decisions, HELP can assist you with which of the following?
A. identifying what is most important.
B. evaluating the consequences of decisions.
C. determining what decision needs to be made.
D. narrowing the possibilities and acting on the best one.
A piano of mass 852 kg is lifted to a height of 3.5 m. How much gravitational potential energy is added to the piano? Acceleration due to gravity is g = 9.8
m/g2
Answer:
Gravitational Potential Energy = Mass*Gravity*Height.
GPE = 852 * 9.8 * 3.2
GPE = 26718.72 Newtons.
An observer views a spectrum and notes two characteristics of the spectrum:
1) most of the colors of a continuous spectrum are present,
2) at certain wavelengths, light is missing such that several dark lines are seen in the spectrum.
Describe the objects that are causing this spectrum to be seen. Be sure to state the relative temperatures of the objects that are involved in creating this spectrum.
The spectrum seen is the absorption spectrum. The wavelengths corresponding to those of the material through which light is being passed are absorbed, which leads to the occurrence of several dark lines in the spectrum.
White light when the incident with the object caused it to absorb the wavelengths corresponding to its excitation energy. These are characteristics of a particular atom/molecule.
Hence using this those can be identified. The absorption of the external energy leads the atoms to go to an excited state, hence the temperature increases.
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Bring a negatively-charged strip near the neutral electroscope but do not touch the knob. What happens
Positive charges are gathered on the neutral electroscope near the negatively charged strip.
To find the answer , we need to know about the induction of charge.
What's the induction of charge?When an electrically charged object is kept close to an neutral conductor, induced charage is produced in the conductor. This method is induction of charge.The induced charges have opposite sign to that of the charged object. Why are the charges induced in the neutral conductor?A charged particle attracts another oppositely charged particle. Similarly the charged object attracts the opposite charges present in that neutral conductor. So the oppositely charged particles present in the conductor are gathered at the side of the charged object and produce induced charges.Thus, we can conclude that the positive charges are gathered on the neutral electroscope near the negatively charged strip.
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a child is stationary on a swing. The child is given a push by a parent and the child starts swinging
Answer:
you havent given the full question
but im guessing momentum
momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity or the impetus gained by a moving object.
Explanation:
as the child is pushed, it gathers momentum as its weight allows it be pushed forward, and the velocity is the speed driven by the amount of force the parent pushes on the child whilst they are swinging. The momentum is the result of this action
the equation that links these factors together are
p = mv
p = momentum
m = mass
v = velocity
hope i got it right ._.
Two thin wires rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and –q. The potential difference between the centres of the two rings is
Answer:
Q/4πε0 [1/R - 1/√R2+d2]
Explanation:
Q/4πε0 [1/R - 1/√R2+d2] is the answer
explanation is attached.
toppr
false In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of .........RPM for shifting is recommended for gas engines
In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of 2500 RPM for shifting is recommended for gas engines.
A car's fuel efficiency is determined by how well it converts the energy in its fuel into kinetic energy for movement.
Most of the time, it's advisable to maintain a speed below 2500 rpm for economic reasons.
Range of 2000-2500 rpm is the best for shifting as
1) It is the most favorable range for the engine due to economic reasons.
2) It saves fuel.
3) It also keeps the engine heavy.
After this range, the economy usually declines.
Even though moving gears doesn't significantly affect engine life due to technological developments, but shifting for gas engines is recommended at 2000-2500 rpm.
Hence, 2500 rpm is the maximum engine speed recommended for gas engines for shifting.
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The speed of ultrasound in human body is 1540 m/s. A procedure is performed with a frequency of 2.57 MHz is used. To monitor the heart rate of a fetus, the maximum frequency shift is 100 Hz. The maximum speed of a vibrating heart is _____ cm/s.
2.49 cm/s is the maximum speed of vibrating heart.
Given,
Frequency of ultrasonic wave = 2.57 MHz = 2.57 ×[tex]10^{6}[/tex] Hz
Speed of ultrasound = 1540m/s
The maximum frequency shift = 100 Hz
Maximum speed of heart = ?
By using Doppler equation
[tex]f1 = f0(\frac{c + v}{c} )[/tex] …..(1)
[tex]f2 = f1 (\frac{c}{c - v} )[/tex] ….. (2)
From equation (1) & (2)
[tex]f2= f0(\frac{c+v}{c-v} )[/tex]
[tex]f2 = 2.57[/tex] ×[tex]10^{6} + 100 = 2570100[/tex] Hz
[tex]f0 = 2570000[/tex] Hz
c = 1540 m/s
So,
[tex]2570100 = 2570000(\frac{1540 + v}{1540 - v} )[/tex]
1.00003(1540-v) = 1540+v
1540.05 - 1.00003v = 1540 +v
2.00003v = 0.05
v= 0.0249 m/s
v= 2.49 ×[tex]10^{-2}[/tex] m/s
v= 2.49 cm/s
So, the maximum speed of vibrating heart is 2.49 cm/s
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calculate the volume of an object of mass 500g whose density is 70kgm-3
Answer:
Amount Unit
132.48935 kilogram
132489.35 gram
132489350 milligram
0.13248935 ton
292.08925642428 pound (lb)
662446.75 carrat
2044623.1271428 grain
7.9786897063466E+28 atomic mass unit
A car engine changes chemical energy into what types of energy? A. Mechanical and thermal B. Thermal and light C. Mechanical and nuclear D. Electromagnetic and mechanical A car engine changes chemical energy into what types of energy ? A. Mechanical and thermal B. Thermal and light C. Mechanical and nuclear D. Electromagnetic and mechanical
Howdy,
B. Thermal and light.
LSST stands for Long Space Standard Telescope.
True
Or False