Answer:
Acceleration, a= 1.65m/s^2
Acceleration is downward.
Explanation:
y: N- m1gcosalpha=0
x: Ff- FT- m1gsinalpha= m1× alpha
Ff= uN= um1gcosalpha
FT=m2g
Acceleration ,a = g(ucosalpha- (m2/m1)-sin alpha)
a= (m2/m1) + sinalpha= 1.976
Cos alpha= 0.766
U2= 2.8
a= g(2.8×0.766)- 1.976)
a= g× 0.1688
a= 9.8× 0.1688
a=1.65m/s^2
7. Nancy has a mass of 60 kg and sits on the very end of a 3.00 m long plank pivoted in the middle. How much torque must her co-worker provide on the other end of the plank in order to keep Nancy from falling on the ground?
Answer:
Torque = 882Nm
Explanation:
Torque = Mg×distance
But plank's is pivoted ,therefore distance=3/2=1.5m
Mass of Nancy=60jg
Acceleration due to gravity, g=9.8m/s^2
Torque= 60×9.8×1.5
Torque= 882Nm
What is the effect on the force of gravity between two objects if the mass of one object remains unchanged while the distance to the second object and the second object’s mass are both doubled? Choose one:A. It always increases.B. It always decreases.C. It depends on the specific values of the two quantities.D. It depends on the local value of G.E. It cannot be determined.
Answer:
The correct answer to the question is
B. It always decreases
Explanation:
To solve the question, we note that the foce of gravity is given by
[tex]F_G=\frac{Gm_1m_2}{r^2}[/tex] where
G= Gravitational constant
m₁ = mass of first object
m₂ = mass of second object
r = the distance between both objects
If the mass of one object remains unchanged while the distance to the second object and the second object’s mass are both doubled, we have
[tex]F_{G2} =\frac{Gm_1(2m_2)}{(2r)^2}[/tex] = [tex]\frac{2}{4} \frac{Gm_1m_2}{r^2}[/tex]
Therefore the gravitational force is halved. That is it will always decrease
Projectile Motion: A pilot drops a package from a plane flying horizontally at a constant speed. Neglecting air resistance, when the package hits the ground the horizontal location of the plane will
Answer:
Explanation:
The package had the same velocity as the plane when it was dropped. Newton's 1st Law says that "an object in motion tends to stay in motion, at the same velocity, in a straight line unless acted on by an outside force".
There only outside force acting on the package was its weight -- that force is straight down. The horizontal velocity that the plane gave the package continued (as Newton said it would), so as it fell, horizontally it kept pace with the plane.
Suppose our experimenter repeats his experiment on a planet more massive than Earth, where the acceleration due to gravity is g = 30~\rm m/s^2. When he releases the ball from chin height without giving it a push, how will the ball's behavior differ from its behavior on Earth? Ignore friction and air resistance. (Select all that apply.)a.It will smash his face.b.It will stop well short of his face.c.It will take less time to return to the point from which it was released.d.Its mass will be greater.e.It will take more time to return to the point from which it was released
Answer:
C
Explanation:
- Let acceleration due to gravity @ massive planet be a = 30 m/s^2
- Let acceleration due to gravity @ earth be g = 30 m/s^2
Solution:
- The average time taken for the ball to cover a distance h from chin to ground with acceleration a on massive planet is:
t = v / a
t = v / 30
- The average time taken for the ball to cover a distance h from chin to ground with acceleration g on earth is:
t = v / g
t = v / 9.81
- Hence, we can see the average time taken by the ball on massive planet is less than that on earth to reach back to its initial position. Hence, option C
Which of the following physical laws or principles can best be used to analyze the collision between the object and the pendulum bob? Which can best be used to analyze the resulting swing? 1. Newton's first law 2. Newton's second law 3. Newton's third law 4. Conservation of mechanical energy 5. Conservation of momentum
Answer:
4,5
Explanation:
The resulting swing converts potential energy to kinetic energy and kinetic energy to potential energy when the swinging stops. This is line with the law of conservation of mechanical energy which deals with inter conversion of energy forms and energy not being able to get lost.
The conservation of momentum is most suited to the collision. This law states that when a collision occurs the initial momentum before and after the collision is the same(without any external force).
1. The light from polaris travels through space in the form of energy is called
Radiative energy
Explanation:
The light from polaris travels through space in the form of energy is called
Radiative energy.
This energy is transferred by means of electromagnetic radiation like X-rays, gamma rays, light, heat radiation and so on. It can travel through space in the form of radiation. For instance, we get the heat through the sun, that is located far away from the Earth by means of radiation. Through the electromagnetic waves, sun's heat is transmitted and not through any kind of solid medium, but by means of vacuum.
What is the maximum number of f orbitals that are possible?
Explanation:
The number of subshell present are s, p, d, and f
The number of orbitals in each are as follows -
The s subshell - 1 orbital consists of 2 electrons The p subshell - 3 orbitals consists of 6 electrons The d subshell - 5 orbitals consists of 10 electrons The f subshell - 7 orbitals consists of 14 electronsThe number of orbitals can be calculated by the degeneracy, 2 l + 1 , where l denoted is angular momentum quantum number that determines the shape of an orbital. For s, p, d, and f the angular momentum quantum number is 0, 1, 2 3 respectively.
So, maximum number of f orbitals that are possible can be calculated as -
2 × l + 1 = 2 × 3 + 1 = 7
A(n) ____ line is a dedicated telephone line that can be used for data communications to connect two different locations for continuous point-to-point communications.
Answer:
T- carrier
Explanation:
The T-carriers are frequently used for trunking between switching centers in a telephone network. It makes use if the same twisted pair copper wire that analog trunks employs. One pair for transmitting and the other pair for receiving.
A person in the passenger basket of a hot-air balloon throws a ball horizontally outward from the basket with a speed of 10.0 m/s. What initial velocity (magnitude and direction) does the ball have relative to a person standing on the ground if the hot-air balloon is rising at 6.0 m/s relative to the ground during this throw?
Answer:
The ball travels at a speed of 11.662 m/s, making a 30.96° angle from the horizontal ground.
Explanation:
If the ball is thrown horizontally with a speed of 10.0 m/s and the hot air balloon is rising at a speed of 6.0 m/s then we can make the following deductions:
1. The ball is ALSO rising at a speed of 6.0 m/s
2. The vertical speed of the ball is 6.0 m/s
Thus the ball travels with 10 m/s horizontal and 6 m/s vertical speed relative to the ground.
To find the total speed and direction:
Total speed = [tex]\sqrt{(V_X)^2+(V_Y)^2}[/tex]
Total speed = [tex]\sqrt{10^2 + 6^2}[/tex]
Total speed = 11.662 m/s
Angle from the horizontal:
Tan( Angle ) = Perpendicular / Base
Tan (Angle) = Vertical Speed / Horizontal Speed
Tan (Angle) = 6/10
Angle = 30.96°
The initial velocity of the ball thrown horizontally from the basket of a hot-air balloon relative to a person on the ground is 10.0 m/s in the horizontal direction.
Explanation:The initial velocity of the ball relative to a person standing on the ground can be found by adding the velocities of the ball and the hot-air balloon together. Since the ball is being thrown horizontally outward, its initial velocity in the horizontal direction will be 10.0 m/s. The vertical velocity of the balloon is 6.0 m/s, but since the ball is not thrown vertically, this velocity does not affect its horizontal velocity.
Therefore, the initial velocity (magnitude and direction) of the ball relative to a person on the ground will be the same as its initial velocity when thrown from the basket, which is 10.0 m/s horizontally.
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If a car is taveling with a speed 6 and comes to a curve in a flat road with radius ???? 13.5 m, what is the minumum value the coefficient of friction must be so the car doesn’t slide of the road?
Answer:
The minimum friction coefficient required is 0.3
(friction coefficients have no units)
Explanation:
To find a force we need to know something about a mass, and we haven't been told the mass of the car. Let's just call it 'm' and leave it at that for the moment, because it will cancel out in the end.
The centripetal force is given by F = ma = mv2/r
We have values for the velocity and the radius, so:
Fcent=m×6 × 6/13.5 = 2. 667m N
The frictional force must be equal to or greater than this force in order for the car to successfully make it around the curve without sliding out.
The frictional force will be given by:
Ffrict = μFnorm
Where Fnorm is the normal force, equal to mg.
We can equate these two forces, the frictional force and the centripetal force:
Fcent = Ffrict
2.667m=μmg
We can cancel out a factor of m in both sides and rearrange to make μ the subject:
μ = 2.667g
Substituting in the value g=9.8 ms−2,
μ = 2.667/9.8 = 0.27
Approximately = 0.3
Explanation:
Below is an attachment containing the solution.
What is the mass of a bullet moving at 970m/s if the bullet’s KE is 3.9x 10^3J
Answer:
0.08kg
Explanation:
K.E = 1/2 mv^2
v = 970m/s
K.E = 3.9x 10^3J= 3900J
K.E = 1/2 mv^2
3900 = 1/2 m x 970x 970
3900 = 1/2 ×940900m
3900 = 470450m
m = 3900/470450 = 0.00828993516 = 0.008kg
I think the Answer is 0.08kg
Two large, parallel, conducting plates are 12 cm apart and have charges of equal magnitude and opposite sign on their facing surfaces. An electric force of 15 3.9 10 N − ⋅ acts on an electron if it is placed anywhere between the two plates. (a) Find the electric field magnitude at the position of the electron. (b) What is the potential difference between the plates?
Answer:
a) 2.4×10^4N/C
b) 2.9 ×10^3V
Explanation:
Correct ststement: An electric force of 3.9×10^-15N acts on the electron if it is placed anywhere between the two plates.
a) The electric field magnitude is given by E= F/e
Where F = electric force
e= elementary charge carried by a single proton e= 1.6×10^-19C
E= (3.9×10^-15)/(1.6×10^-19)
E= 2.4×10^4NC
b) Ptential difference is given by:
Change in V= E×change in distance
Potential difference= (2.4×10^4)× (0.12)
Potential difgerence= 2.9×10^3V
Two forces act on a 8.50-kg object. One of the forces is 14.0 N. If the object accelerates at 3.50 m/s2 , what is the greatest possible magnitude of the other force
Answer:
The magnitude of the other force is 43.75 N.
Explanation:
Given that,
Mass of the object, m = 8.5 kg
Force 1, [tex]F_1=14\ N[/tex]
Acceleration of the object, [tex]a=3.5\ m/s^2[/tex]
To find,
The greatest possible magnitude of the other force.
Solution,
Let [tex]F_2[/tex] is the magnitude of other force that is acting on the object. For the greatest force, the two forces must be act in opposite direction such that :
[tex]F_2-F_1=ma[/tex]
[tex]F_2=ma+F_1[/tex]
[tex]F_2=14+8.5\times 3.5[/tex]
[tex]F_2=43.75\ N[/tex]
So, the magnitude of the other force is 43.75 N.
The magnetic field about a straight length of current-carrying wire is _________.
Explanation:
The magnetic field about a straight length of current carrying wire is circular in shape. As we know that the electric current passing through the wire is producing magnetic field. One can find out the direction of the magnetic field lines by using right hand rule or a compass. If the conductor is a straight wire then the magnetic field lines will form a concentric circles around the wire. Put you thumb in the direction of the electric current in the wire then the fingers will curl to show the direction of magnetic field which thus form the circular loop.
Answer:
circular in shape.
Explanation:
This magnetic field can be visualized as a pattern of circular field lines surrounding a wire. One way to explore the direction of a magnetic field is with a compass, as shown by a long straight current-carrying wire in.
Because the magnetic field created by the electric current in the wire is changing directions around the wire, it will repel both poles of the magnet by bending away from the wire.
The maximum distance at which a highway sign can be read is determined for a sample of young people and a sample of older people. The mean distance is computed for each age group. What's the research hypothesis about the means of the two groups?
Answer:
The population mean are the same
Explanation:
Answer:
The population means are the same.
Explanation:
The hypotheses for a difference in two population means are similar to those for a difference difference two population proportions.
At null point, Ha=0
Let the mean population of the young one be u1
Let the mean population of the old one be u2.
Then, the difference between their mean population distance is given as
Ha=u2-u1
Since, Ha is null point, Ha=0
0=u2-u1
u2=u1
This shows that the mean population distance of the old is equal to the mean population distance of the young.
Therefore their mean population distance is the same
Since it is null alternative then, the population mean are the same.
We must sample the population using
1. Samples must be random to remove or minimize bias.
2. Sample must be representative of the populations in question.
What is the sum of the kinetic energies of the alpha particle and the new nucleus?
Answer: The total energy created by the Alpha decay.
Explanation: The sum total of the kinetic energy of the alpha particle and the new nucleus is the total energy created by the alpha decay.
Consider the decay of a radioactive nuclide by the spontaneous emission from its nuclei of alpha particles. An alpha particle which is composed of two protons and two neutrons and has a charge of +2. With an appreciable mass and its ejection from the nuclide creates a certain amount of recoil energy in the nucleus. The total energy (Ex) created by alpha decay is therefore the sum of the kinetic energy of the particle, the recoil energy given to the new nucleus, and the total energy of any emitted gamma rays.
The sum of the kinetic energies of an alpha particle and the new nucleus after alpha decay equals the initial energy (Q-value) of the reaction, most of which is carried by the alpha particle due to mass differences.
Explanation:The sum of the kinetic energies of the alpha particle and the new nucleus after an alpha decay can be determined by considering the conservation of energy and momentum. The energy released during the decay, known as the Q-value, is primarily carried away by the alpha particle due to its relatively smaller mass compared to the daughter nucleus.
The energy of the alpha particle can be measured experimentally, which then allows us to determine the energy of the new nucleus. According to conservation of energy, the sum of the kinetic energies of the alpha particle and the new nucleus is equal to the Q-value of the reaction. If the Q-value (Qa) is known to be 4.3 MeV, and assuming the potential energy is zero in the final state, this energy will be distributed between the alpha particle and the new nucleus.
Using the example values provided, if the kinetic energy of the new nucleus (KEnucleus) is calculated to be 23.3 eV, then the remainder of the Q-value minus the kinetic energy of the new nucleus will represent the kinetic energy of the alpha particle. Since the alpha particle carries away most of the kinetic energy, the sum of the kinetic energies will be very close to the initial Q-value.
If a home uses a large supply of solar panels to generate electricity, but has no battery system, surplus electricity that is produced is usually __________.
Answer:
Passed into the power grid for others to use the electricity
Explanation:
If a home uses a large supply of solar panels to generate electricity, but has no battery system, surplus electricity that is produced is usually passed into the power grid for others to use the electricity, generating a income to the homeowner
When a home using solar panels produces surplus electricity and has no battery system, the excess power is typically fed back into the electricity grid. This process, known as net metering, can often result in a credit from the electricity company.
Explanation:If a home uses a large supply of solar panels to generate electricity, but has no battery system, surplus electricity that is produced is usually fed back into the grid. This feed-in process involves the excess electricity being transmitted to the local electricity network where it can be used by other homes or businesses. In many places, electricity companies provide a credit to the solar power producer for this extra electricity, which can lower the overall utility bill.
This concept is known as net metering which allows homeowners to offset the cost of power drawn from the utility grid by pushing their surplus electricity into the grid. However, it's crucial to note that this process might depend on the policies of the local utility or the regional grid operator.
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Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance
Explanation:
As we know that
time = distance/speed
The time used for firs half of the trip was
(1 mi)(12 mi/hour) = 1/12 hours = 5 minutes
The last half of the trip will took 10 minutes, 1/6 hour.
Speed = distance/ time
(1 mil) = (1/6h) = 6 mil/h
so the speed for last half of the trip was = 6mph
the average speed was
(2mil)(1/4 hour) = 8 mil/hour
So the ling's average speed was 8mph.
While traveling to and from a certain destination, you realized increasing your speed by 30 mph saved 3 hours on your return. If the total distance of the roundtrip was 560 miles, find the speed driven while returning.
Answer 62.78mph
Explanation:
Answer:
The returning speed = 70 miles per hour (mph)
Explanation:
9) Cart 1 has a mass of 4 kg and an initial speed of 4 m/s. It eventually elastically collides with cart 2, whose mass is 6 kg, and which moves at an initial speed of 4 m/s toward cart 1. How fast are the carts moving after their collision? [Enter cart 1's final speed in answer box 1 and cart 2's final speed in answer box 2.]
Answer:
Cart 1 = 4 m/s
Cart 2 = 4 m/s
Explanation:
See attachment
A piece of copper wire is formed into a single circular loop of radius 9.1 cm. A magnetic field is oriented parallel to the normal to the loop, and it increases from 0 to 0.90 T in a time of 0.66 s. The wire has a resistance per unit length of 2.9 x 10-2 /m. What is the average electrical energy dissipated in the resistance of the wire
Given Information:
Radius of circular loop = r = 9.1 cm = 0.091 m
Change in time = Δt = 0.66 seconds
Change in magnetic field = ΔB = 0.90 T
Resistance of wire per unit length = R = 2.9x10⁻² Ω/m
Number of turns = N = 1
Required Information:
Electrical energy dissipated = E = ?
Answer:
Electrical energy dissipated = 50.09x10⁻³ Joules
Step-by-step explanation:
We know that energy is given by
E = Pt
Where power is given by
P = ξ²/R
Where ξ is the induced EMF in the wire and is given by
ξ = -NΔΦ/Δt
Where ΔΦ is the change in flux and is given by
ΔΦ = ΔBAcosφ
Where φ is the angle between magnetic field and circular loop
A = πr² and R = 2.9x10⁻²*2πr
Substituting the above relations into the energy equation and simplifying yields,
E = [-Nπr²cosφ(ΔB/Δt)²]*t/R
E = [-1*π(0.091)²*cos(0)(0.90/0.66)²*0.66]/2.9x10⁻²*2π*(0.091)
E = 0.050094 Joules
E = 50.09x10⁻³ Joules
Therefore, the average electrical energy dissipated in the circular loop of the wire is 50.09x10⁻³ Joules.
Imagine that you know the mass of a nearby star and you know that there is a planet orbiting around the star with a mass much smaller than the mass of the star. Explain with a sentence or two how, using the Doppler effect technique, you can measure the semi-major axes of a planet orbiting the star.]
Answer:
By measuring the time taken for the stars line of sight velocity to cycle from peak to Peak, and by calculation using newtons version of Kepler's third law
Explanation:
The motion of orbiting planets using planet-hunting techniques can rely on doppler effect. The light from the stars they orbit, as seen from Earth. As the star moves back and forth, the Doppler shift causes a slight change in its apparent colour which can be detected using spectroscopy. The blue shift and the red shift.
The Doppler technique of blue shift and the red shift can be used to estimate the semi major axis of the planets orbit by
Measuring the time it takes for the stars line of sight velocity to cycle from peak to Peak, and using newtons version of Kepler's third law
A policeman investigating an accident measures the skid marks left by a car on the horizontal road. He determines that the distance was 23.74 n. The coefficient of kinetic friction between the tires and the road is μk = 0.29 How fast was the car going when the driver applied the brakes
Final answer:
To find the initial speed of the car, we use the work-energy principle and the equation μk × g × d = ½ × v². By substituting the given coefficient of kinetic friction (0.29) and skid mark distance (23.74 meters), we calculate the initial speed to be approximately 11.68 m/s.
Explanation:
The question involves calculating the initial speed of a car at the moment the driver applied the brakes, which resulted in skid marks on the road. The length of the skid marks and the coefficient of kinetic friction (μk) between the tires and the road are known.
To calculate the initial speed of the car, we use the work-energy principle, which states that the work done by the friction force is equal to the change in kinetic energy of the car:
Work done by friction = Change in kinetic energy
μk × m × g × d = ½ × m × v²
Since mass (m) cancels out and gravitational acceleration (g) is a constant (9.81 m/s²), we can simplify the equation to:
μk × g × d = ½ × v²
Now we can solve for the initial velocity (v):
v = √(2 × μk × g × d)
Plugging in the given values, μk = 0.29 and d = 23.74 meters, we have:
v = √(2 × 0.29 × 9.81 m/s² × 23.74 m)
v ≈ √(2 × 0.29 × 9.81 × 23.74)
v ≈ √(136.4)
v ≈ 11.68 m/s (approximately)
Thus, the initial speed of the car when the brakes were applied was approximately 11.68 meters per second.
What is the fundamental frequency of a 0.003 kg steel piano wire of length 1.3 m and under a tension of 2030 N? Answer in units of Hz. 005 (part 2 of 2) 10.0 points What is the fundamental frequency of an organ pipe 1.38 m in length, closed at the bottom and open at the top? The speed of sound is 340 m/s. Answer in units of Hz.
The fundamental frequency of a piano wire can be calculated using the formula f = sqrt(T/(4L^2*m)). Plugging in the given values, the fundamental frequency of the piano wire is 116.6 Hz.
The fundamental frequency of a piano wire can be calculated using the formula:
f = √(T/(4L2m))
Where f is the fundamental frequency, T is the tension, L is the length, and m is the mass per unit length.
Plug in the given values:
T = 2030 N
L = 1.3 m
m = 0.003 kg/m
f = √(2030/(4*1.32*0.003))
Solving this equation gives the fundamental frequency f = 116.6 Hz.
given the initial ( 0 , − 2 ) and terminal ( 3, 6 ) points of a vector, how do you write a linear combination of the standard unit vector ˆ i and ˆ j ? socratic.org
Answer:
Explanation:
Given that,
The initial point A=(0,-2)
And the final point B=(3,6)
O is a reference point (0,0)
OA=r1=(0,-2)
OB=r2=(3,6)
Then we want to find their combination vector i.e AB.
AB is given as position vector B - position vector A
So, AB=OB-OA
AB=r2-r1
AB=(3,6)-(0,-2). Note -×-=+
Then, AB=(3-0,6--2)
AB=(3,6+2)
AB=(3,8)
In vector form
AB=3•i +8•j
In doing a load of clothes, a clothes drier uses 18 A of current at 240 V for 41 min. A personal computer, in contrast, uses 2.2 A of current at 120 V. With the energy used by the clothes drier, how long (in hours) could you use this computer to "surf" the Internet
Answer:
The time taken by the personal computer to 'surf' the internet is 11.13 h.
Explanation:
The expression for the energy in terms of current and time is as follows;
E= Vit
Here, V is the potential, i is the current and t is the time.
According to question, in doing a load of clothes, a clothes drier uses 18 A of current at 240 V for 41 min.
Convert time from minute to second.
[tex]t=\frac{41}{60}s[/tex]
Calculate the energy used by the clothes drier.
Put V= 240 V, [tex]t=\frac{41}{60}s[/tex] and i=18 A in the expression for the energy.
[tex]E= (240)(18)\frac{41}{60}[/tex]
E'= 2937.6 W
Therefore, the energy of a clothes drier is E'= 2937.6 W.
It is given in the problem that a personal computer, in contrast, uses 2.2 A of current at 120 V. With the energy used by the clothes drier, this computer is used to surf the internet.
Calculate the time taken by the computer to 'surf' the internet.
E'=V'i't'
Here, V' is the voltage used by the a personal computer, i' is the current and t' is the time taken by the personal computer.
Put E'= 2937.6 W, V= 120 V and i'= 2.2 A.
2937.6 = (120)(2.2)t'
[tex]t'=\frac{2937.6}{264}[/tex]
t'= 11.13 h
Therefore, the time taken by the personal computer to 'surf' the internet is 11.13 h.
If the bonds in the reactants of Figure 7-3 contained 432 kJ of chemical energy and the bonds in the
products contained 478 kJ of chemical energy, what would be the amount of energy change during the
reaction? Would this energy be absorbed or released? Show your work.
Answer:
The energy change would be 46kJThe energy would be absorbedExplanation:
The energy change during a chemical reation, i.e. the reaction energy, is equal to the chemical energy stored in the bonds of the products less the chemical energy stored in the bonds of the reactants.
Hence:
Energy change = 478 kJ - 432kJ = 46kJThe change is positive, this is, the chemical energy of the products is greater than the chemical energy of the reactants.
That corresponds to the second graph, where the level of the energy of the products in the graph is higher than the level of the energy of the reactants. Therefore, the conclusion is that the reaction absorbed energy and it is endothermic.
What is the speed of a beam of electrons when under the simultaneous influence of E = 1.64×104 V/m B = 4.60×10−3 T Both fields are normal to the beam and to each other and produce no deflection of the electrons. When the electric field is removed, what is the radius of the electron orbit? What is the period of the orbit?
Answer: v = 3.57×10^6 m/s; R = 4.42×10^-3m; T = 7.78×10^-9 s
Explanation:
Magnetic force(B) = 4.60×10^-3 T
Electric force(E) = 1.64×10^4 V/m
Both forces having equal magnitude ;
Magnetic force = electric force
qvB = qE
vB = E
v = (1.64×10^4) ÷ (4.60×10^-3)
v = 3.57×10^6 m/s
2.) Assume no electric field
qvB = ma
Where a = v^2 ÷ r
R = radius
a = acceleration
v = velocity
qvB = m(v^2 ÷ R)
R = (m×v) ÷ (|q|×B)
q=1.6×10^-19C
m = 9.11×10^-31kg
R = (9.11×10^-31 * 3.57×10^6) ÷ (1.6×10^-19 * 4.6×10^-3)
R = 32.5227×10^-25 ÷ 7.36×10^-22
R = 4.42×10^-3m
3.) period(T)
T = (2*pi*R) ÷ v
T = (2* 4.42×10^-3 * 3.142) ÷ (3.57×10^6)
T = (27.775×10^-3) ÷(3.57×10^6)
T = 7.78×10^-9 s
Which of the following classes of biomaterials would be most appropriate for use to fabricate an artificial tendon, a tissue that must sustain substantial deformation at low forces and return rapidly to its original dimensions upon release of the stress why?1. metals2. ceramics3. polymers
Final answer:
The most appropriate biomaterials for artificial tendons are polymers, due to their high toughness, elasticity, and ability to mimic natural extracellular matrices.
Explanation:
For fabricating an artificial tendon, which requires the capacity to sustain substantial deformation at low forces and quickly return to its original dimensions after stress release, polymers would be the most appropriate class of biomaterials. Biopolymers like collagen are noted for high toughness and elasticity, vital properties for mimicking the natural structure and function of tendons. Modern bioengineering strategies also involve creating synthetic extracellular matrices (ECM) which utilize peptides and polymer conjugates to mimic natural ECM, providing both structural support and facilitating tissue integration and regeneration.
Metals and ceramics, while being strong and rigid, do not offer the same flexibility and elastomeric properties required by tissues such as tendons that undergo repeated and significant strain. Semi-flexible polymers and polymer gels on the other hand, have been engineered to possess a balance of strength and flexibility, similar to that of natural tendon tissue.
If an object oscillates in simple harmonic motion, with the position described by the equation: x(t) = 42.5*cos(21t) What is the angular frequency of oscillation w ?
Answer:
The angular frequency of oscillation w = 21
Explanation:
To solve the question, we note that x(t) is the point in the motion of the object. Therefore to find the angular frequency of oscillation, we find the relationship between the angular velocity and time
The angular frequency, ω is a scalar quantity used to depict the rate of rotation per unit time
When there is a function in simple harmonic motion (SHM) with the following equation then ω is the angular frequency
x(t) = A·cos (2πft) = A·cos(ωt) which is similar to 42.5*cos(21t)
then 21 = angular frequency