The wavelength of visible light range of 400 to 750mm .what is the corresponding range of photon energies for visible light
Answer:
The range of the photon energies is between:
2.652 x 10⁻²⁵ J to 4.973 x 10⁻²⁵ J
Explanation:
The energy of a photon is calculated using the following equation;
E = hf
where;
h is Planck's constant = 6.63 x 10⁻³⁴ Js
f is frequency of the photon
[tex]E = h \frac{c}{\lambda} \\\\where;\\\\\lambda \ is \ the \ wavelength\\\\c \ is \ the \ speed \ of \ light \ = 3\times 10^8 \ m/s\\\\When \ \lambda = 400 \ mm = 400 \ \times 10^{-3} \ m\\\\E = \frac{(6.63 \times 10^{-34})(3\times 10^8)}{400 \times 10^{-3}} \\\\E = 4.973 \times 10^{-25} \ J[/tex]
[tex]When \ \lambda = 750 \ mm = 750 \ \times 10^{-3} \ m\\\\E = \frac{(6.63 \times 10^{-34})(3\times 10^8)}{750 \times 10^{-3}} \\\\E = 2.652 \times 10^{-25} \ J[/tex]
The range of the photon energies is between:
2.652 x 10⁻²⁵ J to 4.973 x 10⁻²⁵ J
A peach pie in a 9.00 in diameter plate is placed upon a rotating tray. Then, the tray is rotated such that the rim of the pie plate moves through a distance of 208 in. Express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.
Answer:
a) [tex]X_1=7.36rev[/tex]
b) [tex]X_2=46.22radians[/tex]
c) [tex]X_3=2649.6^o[/tex]
Explanation:
From the question we are told that:
Diameter [tex]d=9.00[/tex]
Distance [tex]x=208[/tex]
Generally the equation for circumference of a circle is mathematically given by
[tex]C=2 \pi r\\\\C=2*\pi*4.5[/tex]
[tex]C=28.3[/tex]
Therefore
Angular distance that the pie plate has moved through in revolutions is
[tex]X_1=\frac{x}{C}[/tex]
[tex]X_1=\frac{208}{28.3}[/tex]
[tex]X_1=7.36rev[/tex]
Generally Angular distance that the pie plate has moved through in radians is
[tex]X_2= 7.36rev* 2 \pi[/tex]
[tex]X_2=46.22radians[/tex]
Generally Angular distance that the pie plate has moved through in degrees is
[tex]X_3=7.36rev* 360[/tex]
[tex]X_3=2649.6^o[/tex]
Choose the CORRECT statements. A standing wave is resulted from the superposition of
two waves in such a way both waves:
I. have the same direction.
II. are opposite in direction.
III. have the same frequency.
IV. have different frequency.
V. have the same amplitude.
VI. have different amplitude
A. I, III and V
B. II. IV and VI
C. I, IV and V
D. II, III and V
E I and III
F. Ill and V
Answer:
The answer is D
Assuming the earth is a uniform sphere of mass M and radius R, show that the acceleration of fall at the earth's surface is given by g = Gm/R2 . What is the acceleration of a satellite moving in a circular orbit round the earth of radius 2R
Explanation:
The weight of an object on the surface of the earth is equal to the gravitational force exerted by the earth on the object.
[tex]W=F_G[/tex]
[tex]mg = G \dfrac{mM}{R^2}[/tex]
which gives us an expression for the acceleration due to gravity g as
[tex]g = G\dfrac{M}{R^2}[/tex]
At a height h = R, the radius of a satellite's orbit is 2R. Then the acceleration due to gravity [tex]g_h[/tex] at this height is
[tex]mg_h = G \dfrac{mM}{(2R)^2}= G \dfrac{mM}{4R^2}[/tex]
Simplifying this, we get
[tex]g_h= G \dfrac{M}{4R^2} = \dfrac{1}{4} \left(G \dfrac{M}{R^2} \right) = \dfrac{1}{4}g[/tex]
state what is meant by graviration potential at a point in an orbit 6.5×10^7
Explanation:
The gravitational potential at a point in a gravitational field is the work done per unit mass that would have to be done by some externally applied force to bring a massive object to that point from some defined position of zero potential,
Match each term to the best description
a. Coefficient of friction
b. Friction
c. Kinetic friction
d. Normal
e. Static friction
1. A force that acts parallel to the surface.
2. A force that acts perpendicular to the surface.
3. A force that increases as applied force increases up to some maximum value
4. Magnitude depends on the interacting materials
5. A force that is constant regardless of the applied force
Answer:
Coefficient of friction = Magnitude depends on the interacting materials
Friction = A force that acts parallel to the surface.
kinetic friction = A force that is constant regardless of the applied force
Normal = A force that acts perpendicular to the surface
Static friction = A force that increases as applied force increases up to some maximum value
Explanation:
Let's define all the forces, and then let's solve the problem.
Normal force:
When an object rests on some place (like a book on the table) the force that causes the book to not fall through the table is called the normal force, which is usually equal to the weight of the object and acts perpendicular to the surface where the object is resting.
Friction force.
When an object moves (or tries to move) parallel to a surface, such that the object is in contact with that surface, there appears a force that opposes to the movement (the force is parallel to the surface, and in the opposite direction to the movement).
And this force can be written as:
F = -N*μ
Where μ is the coefficient of friction and N is the normal force.
If the object is not moving yet (but there is applied a force that would move the object) the coefficient is called the coefficient of static friction which increases in a given range, until it can't keep increasing and the object starts to move, while if the object is moving, the coefficient is called the coefficient of kinetic friction and it is constant, where usually the first one is larger than the second, and these coefficients depend on both materials, the surface one and the object one.
Then we have two friction forces, one called the kinetic friction and the other called the static friction.
Then:
Coefficient of friction = Magnitude depends on the interacting materials
Friction = A force that acts parallel to the surface.
kinetic friction = A force that is constant regardless of the applied force
Normal = A force that acts perpendicular to the surface
Static friction = A force that increases as applied force increases up to some maximum value
The length of a cylindrical axon is 8 cm and its radius of 8μm,and the thickness of the membrane is 0.01μm,dielectric constant ( ε=24.78x10-12 F/m),the capacitance of nerve cell is
Answer:
9.965 nF
Explanation:
The capacitance of the axon C = εA/d where ε = dielectric constant = 24.78 × 10⁻¹² F/m, A = surface area of axon = 2πrL where r = radius of axon = 8 μm = 8 × 10⁻⁶ m and L = length of axon = 8 cm = 8 × 10⁻² m and d = thickness of membrane = 0.01 μm = 0.01 × 10⁻⁶ m
So, C = εA/d
C = ε2πrL/d
Substituting the of the values variables into the equation, we have
C = ε2πrL/d
C = 24.78 × 10⁻¹² F/m × 2π × 8 × 10⁻⁶ m × 8 × 10⁻² m/0.01 × 10⁻⁶ m
C = 9964.63 × 10⁻²⁰ Fm/0.01 × 10⁻⁶ m
C = 996463 × 10⁻¹⁴ F
C = 9.96463 × 10⁻⁹ F
C = 9.96463 nF
C ≅ 9.965 nF
Describe an experiment to find the density of copper turning using a density bottle and kerosene
The density is the ratio of mass to volume of a substance.
What is the density bottle?The density bottle is used to obtain the density of substance by measuring the volume of the fluid displaced.
If the mass of copper turnings are previously weighed and known, the volume of the fluid displaced in the density bottle is the volume of the copper turning.
Hence;
Density = mass/ volume
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An object is 70 micrometer long and 47.66 micrometer wide. How long and wide is the object in km
Answer:
The length of the object in kilometer (km) is 70 x 10⁻⁹ km
The width of the object in kilometers (km) is 47.66 x 10⁻⁹ km
Explanation:
Given;
length of the object = 70 micrometer = 70 μm
the width of the object = 47.66 micrometer = 47.66 μm
The length of the object in meter:
70 micrometer = 70 μm = 70 x 10⁻⁶ m
The length of the object in kilometer (km):
70 x 10⁻⁶ m = 70 x 10⁻⁹ km
The width of the object in meters:
47.66 micrometer = 47.66 μm = 47.66 x 10⁻⁶ m
The width of the object in kilometers (km):
47.66 x 10⁻⁶ m = 47.66 x 10⁻⁹ km
ADvantage of friction
Answer:
1. Friction enables us to walk freely.
2. It helps to support ladder against wall.
3. It becomes possible to transfer one form of energy to another.
4. Objects can be piled up without slipping.
How is wind generated?
O A. Air molecules move from areas of low pressure to areas of high
pressure.
O B. Air molecules move more slowly where the temperature is higher
and the pressure is lower.
C. Air molecules move more quickly where the temperature is lower
and the pressure is higher.
D. Air molecules move from areas of high pressure to areas of low
pressure.
Answer:
Explanation:
Wind is caused by the uneven heating of the atmosphere by the sun, variations in the earth's surface, and rotation of the earth. ... Wind turbines convert the energy in wind to electricity by rotating propeller-like blades around a rotor. The rotor turns the drive shaft, which turns an electric generator
While a mason was working concrete into formwork, the formwork collapses. Who is BEST suites to rectify this problem? Mason Carpenter Project Manager O Construction Technician A device made in a workplace had defects. To address this issue the workshop manager should communicate directly with the workshop
Answer:
1. Carpenter
2. True
Explanation:
While a mason was working concrete into the formwork, the formwork collapses. The best person to rectify this problem is CARPENTER.
This is because it is the job of the Carpenter to design and build formwork, most especially wooden formwork. Formwork is like casing built to receive concrete and reinforcement during construction. Hence, when formwork collapses either due to stress, tension, or improper construction, it is the job of Carpenter to reconstruct the formwork or rectify the problem.
It is TRUE that when a device made in a workplace had defects. To address this issue the workshop manager should communicate directly with the workshop. However, this communication will be an instruction on what to do next, and it usually directs those responsible to take action where necessary. For example, a workshop manager communicates to a carpenter about the need to rectify a chair or table that has a defect.
A block is projected with speed v across a horizontal surface and slides to a stop due to friction. The same block is then projected with the same speed v up an incline where is slides to a stop due to friction. In which case did the total mechanical energy of the block decrease the least
Answer: C. The case on the inclined surface had the least decrease intotal mechanical energy.
Explanation:
First and foremost, it should be noted that the mechanical energy is the addition of the potential and the kinetic energy.
From the information given, it should be known that when the block is projected with the same speed v up an incline where is slides to a stop due to friction, the box will lose its kinetic energy but there'll be na increase in the potential energy as a result of the veritcal height. This then brings about an increase in the mechanical energy.
Therefore, the total mechanical energy of the block will decrease the least when the case on the inclined surface had the least decrease intotal mechanical energy.
The process of finding the age of fossil is called which answer carbondating,urinumdating ,both of them,none
Answer:
the process of finding the age of fossils is called carbon dating because they use samples of carbon and compare it's characteristics to the samples of carbon from each set time
Honeybees acquire a charge while flying due to friction with the air. A 100 mg bee with a charge of 33 pC experiences an electric force in the earth's electric field, which is typically 100 N/C, directed downward.
1. What is the ratio of the electric force on the bee to the bee's weight?
2. What electric field strength would allow the bee to hang suspended in the air?
3. What electric field direction would allow the bee to hang suspended in the air?
Answer:
A) 3.367 × 10^(-6)
B) 2.97 × 10^(7) N/C
C) Upwards
Explanation:
We are given;
Mass of bee; m = 100 mg = 100 × 10^(-6) kg
Charge on bee;q=33 pC = 33 × 10^(-12)C
Electric field strength; E = 100 N/C
A) Formula for weight of bee; W = mg = 100 × 10^(-6) × 9.8 = 9.8 × 10^(-4) N
Electric force on Bee; F = qE = 33 × 10^(-12) × 100 = 33 × 10^(-10) N
ratio of the electric force on the bee to the bee's weight; F/W = (33 × 10^(-10))/(9.8 × 10^(-4)) = 3.367 × 10^(-6)
B) For the bee to be suspended in the air, it means the weight of the bee must be equal to the electric force. Thus;
mg = qE
100 × 10^(-6) × 9.8 = 33 × 10^(-12) × E
E = (100 × 10^(-6) × 9.8)/(33 × 10^(-12))
E = 2.97 × 10^(7) N/C
C) From Newton's law, sum of forces = 0.
Thus;
F_n + F + W = 0
Where F is the normal force.
Thus;
F_n = -(F + W)
F_n = - ((33 × 10^(-10)) + (9.8 × 10^(-4)))
F_n = -9.8 × 10^(-4) N
Thus, applied electric field is;
E_a = F_n/q = (-9.8 × 10^(-4))/(33 × 10^(-12)) = -2.97 × 10^(7) N/C
This is negative and so it means the direction will be opposite the Earth's electric filed which is upwards.
Certain rifles can fire a bullet with a speed of 950 m/s just as it leaves the muzzle (this speed is called the muzzle velocity). The muzzle is 75.0 cm long and the bullet is accelerated uniformly from rest within it. What is the acceleration (in {g}'s) of the bullet in the muzzle? If, when this rifle is fired vertically, the bullet reaches a maximum height {H}, what would be the maximum height (in terms of H) for a new rifle that produced half the muzzle velocity of this one?
Answer:
a) By [tex]v^2 = u^2 + 2as[/tex] => a= 70291.70.
(b)By [tex]v = u + at[/tex] => t= 1.58 ms.
(c)By [tex]v^2 = u^2 - 2gh[/tex] => H = 46045.92 m.
Explanation:
a) By [tex]v^2 = u^2 + 2as[/tex]
[tex](950)^2 = 0 + 2 \times a \times 0.75\\a = 601666.67 m/s^2\\a/g = 688858.70/9.8 = 70291.70[/tex]
(b)By [tex]v = u + at[/tex]
[tex]950 = 0 + 601666.67 \times t\\t = 1.58 x 10^-3 sec = 1.58 ms[/tex]
(c)By [tex]v^2 = u^2 - 2gh[/tex]
[tex]0 = (950)^2 - 2 \times9.8 \times H\\H = 46045.92 m[/tex]
Question 18/55 (2 p.)
A vibrating object produces ripples on the surface of a liquid. The object completes 20 vibrations
every second. The spacing of the ripples, from one crest to the next, is 3.0 cm.
What is the speed of the ripples?
D
C 60 cm/s
120 cm/s
A 0.15cm/s
B 6.7 cm/s
Answer:
the correct answer is C v = 60 cm / s
Explanation:
The speed of a wave is related to the frequency and the wavelength
v = λ f
They indicate that the object performs 20 oscillations every second, this is the frequency
f = 20 Hz
the wavelength is the distance until the wave repeats, the distance between two consecutive peaks corresponds to the wavelength
λ = 3 cm = 0.03 m
let's calculate
v = 20 0.03
v = 0.6 m / s
v = 60 cm / s
the correct answer is C
Describes the relationship between the free energy change, the reaction quotient, and the equilibrium constant.
Explanation:
Reaction quotient is defined as the ratio of the concentration of the products and reactants of a reaction at any point of time with respect to some unit. It is represented by the symbol Q.
The ratio of the concentration of products and reactants of a reaction in equilibrium with respect to some unit is said to be equilibrium constant expression. It is represented by the symbol K.
The relationship between Gibbs free energy change and reaction quotient of the reaction is:
[tex]\Delta G=\Delta G^o+RT ln Q[/tex] ......(1)
where,
[tex]\Delta G[/tex] = Gibbs free energy change
[tex]\Delta G^o[/tex] = Standard Gibbs free energy change
R = Gas constant
T = Temperature
At equilibrium, the free energy change of the reaction becomes 0 and standard Gibbs free energy change can be related to the equilibrium constant by the equation:
[tex]\Delta G^o=-RT ln Q[/tex] ...(2)
To understand the nature of electric current and the conditions under which it exists.Electric current is defined as the motion of electric charge through a conductor. Conductors are materials that contain movable charged particles. In metals, the most commonly used conductors, such charged particles are electrons. The more electrons that pass through a cross section of a conductor per second, the greater the current. The conventional definition of current isI=Qtotal/Δtwhere I is the current in a conductor and Qtotalis the total charge passing through a cross section of the conductor during the time interval Δt.The motion of free electrons in metals not subjected to an electric field is random: Even though the electrons move fairly rapidly, the net result of such motion is that Qtotal=0 (i.e., equal numbers of electrons pass through the cross section in opposite directions). However, when an electric field is imposed, the electrons continue in their random motion, but in addition, they tend to move in the direction of the force applied by the electric field.In summary, the two conditions for electric current in a material are the presence of movable charged particles in the material and the presence of an electric field.Quantitatively, the motion of electrons under the influence of an electric field is described by the drift speed, which tends to be much smaller than the speed of the random motion of the electrons. The number of electrons passing through a cross section of a conductor depends on the drift speed (which, in turn, is determined by both the microscopic structure of the material and the electric field) and the cross-sectional area of the conductor.In this problem, you will be offered several conceptual questions that will help you gain an understanding of electric current in metals.You are presented with several long cylinders made of different materials. Which of them are likely to be good conductors of electric current?
Answer:
The metallic conductors
Explanation:
The metallic conductors has more free electrons that are movable, thus they conduct electricity better.
If the distance between a neutral atom and a point charge is increased by a factor of six, by what factor does the force on the atom by the point charge change
Answer:
A neutral atom has no net charge and should not be affected by a point charge, and the distance of separation is not a factor.
The force will remain the same and is equal to zero.
We have a point charge and a neutral atom.
We have to investigate if the distance between a neutral atom and a point charge is increased by a factor of six, by what factor does the force on the atom by the point charge change.
State Coulomb's Law of Electrostatic force.The Coulomb's law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. Mathematically -
[tex]$F=\frac{q _{1}\cdot q _{2}}{4\cdot \pi \cdot \varepsilon \cdot \varepsilon _{0}\cdot r^{2}}[/tex]
According to question, we have -
A point charge and a neutral atom.
If initially the distance between the point charge and neutral atom is r meters, then -
q(1) = Q (say)
q(2) = 0 ( Neutral atom has zero charge)
Using Coulomb's law -
[tex]$F=\frac{Q\times 0}{4\cdot \pi \cdot \varepsilon \cdot \varepsilon _{0}\cdot r^{2}}[/tex]
F = 0 Newtons.
Now, if you will increase the distance by the factor of six, still the force will remain zero as there is only one point charge and other is neutral atom. There is no electrostatic force between a charged and uncharged particle.
Hence, the force will remain the same and is equal to zero.
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a system absorb 500 J of heat and the same time 400J of work is done one the system find change in internal enery ?
Answer:
+ 900 J
Explanation:
Since the total energy change ΔE = internal energy change ΔU since there is no change in kinetic and potential energy,
ΔE = ΔU
ΔE = Q - W where Q = heat absorbed by system and W = work done by system
Now since the system absorbs 500 J of heat, Q = + 500 J and work of 400 J is done on the system, W = -400 J
So, the values of the variables into the equation, we have
ΔE = Q - W
ΔE = + 500 J - (-400 J)
ΔE = + 500 J + 400 J
ΔE = + 900 J
So, the internal energy change, ΔE = + 900 J
PAY ATTENTION MY QUESTION ASK FOR RADIATION!!!
You sit with friends around a campfire, roasting marshmallows. Which
transfer of thermal energy involved in this system is an example of radiation
Answer:
The answer is c
Thermal energy moves within the air from the flames to the marshmallow.
Explanation:
Hope it helps
You sit with friends around a campfire, roasting marshmallows. then the transfer of thermal energy involved in this system is an example of radiation Thermal energy moves within the air from the flames to the marshmallow. Hence option C is correct.
What is thermal Energy ?In physics and engineering, the phrase "thermal energy" is thrown around in a lot of different situations. It can relate to a variety of distinct physical notions. Included in this are the internal energy, or enthalpy, of a body of matter and radiation; heat, which is a form of energy transfer (as is thermodynamic work); and the characteristic energy of a degree of freedom in a system described in terms of its microscopic particulate constituents (where T denotes temperature and k denotes the Boltzmann constant.
Hence option C is correct.
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A person is driving a car down a straight road. The instantaneous acceleration is constant and in the direction of the car's motion. 1) The speed of the car is increasing. decreasing. constant. increasing but will eventually decrease. decreasing but will eventually increase.
Answer:Increasing
Explanation:
Given
Car is driven on the straight road with instantaneous acceleration in the direction of car's motion.
If instanateneous acceleration is constant then speed of car is increasing at a constant pace. As there are no turns on the road, therefore speed of car is increasing.
The speed of the car is "decreasing". A further description is provided in the below paragraph.
It's because the individual would be in a straightforward fashion. This same acceleration inclination comes contrary to the movement of the automobile. It indicates that it exerts pressure against the movement of the automobile. So, when it moves forward, the speed of the automobile decreases.
Thus the above answer is correct.
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Rahul sits in a chair reading a book. Which force is equal to the force Rahul exerts on Earth?
Answer:
Rahul's weight
Explanation:
In fact, the force Rahul exerts on Earth corresponds to the force of gravity. But Rahul's weight is, in fact, the force of gravity exerted by the Earth on Rahul, and these two forces correspond to the action-reaction pair of Newton's third law, which states that the two forces are equal.
Using formulas, Rahul's weight is equal to
W=mg
where m is Rahul mass and g is the gravitational acceleration (g=9.81 m/s^2).
PLEASE HELP!! Newton's second law of motion states that force equals mass times acceleration.
How would this law apply to a runner in a track and field event?
The runner needs to take a few steps to slow down after crossing the finish line.
To win the race, the runner must slow down on the turns and speed up on the straight sections.
The shoes of the runner help increase his mass so he can run faster.
Newton's second law of motion does not apply to track and field.
A student wishes to construct a mass-spring system that will oscillate with the same frequency as a swinging pendulum with a period of 3.45 S. The student has a spring with a spring constant of 72.0 N/m. What mass should the student use to construct the mass-spring system?
Answer:
21.73 kg
Explanation:
Applying,
T = 2π√(m/k)............... Equation 1
Where T = period, m = mass on the spring, k = spring constant, π = pie.
make m the subject of the equation
m = T²k/4π²................. Equation 2
From the question,
Given: T = 3.45 s, k = 72.0 N/m, π = 3.14
Substitute these values into equation 2
m = (3.45²×72)/(4×3.14²)
m = 21.73 kg.
Hence the mass should be 21.73 kg
Guys please help me
Answer:
1)[tex]t=2.26\: s[/tex]
2)[tex]S=33.9\: m[/tex]
3)[tex]v=26.77\: m/s[/tex]
4)[tex]\alpha=55.92[/tex]
Explanation:
1)
We can use the following equation:
[tex]y_{f}=y_{0}+v_{iy}t-0.5*g*t^{2}[/tex]
Here, the initial velocity in the y-direction is zero, the final y position is zero and the initial y position is 25 m.
[tex]0=25-0.5*9.81*t^{2}[/tex]
[tex]t=2.26\: s[/tex]
2)
The equation of the motion in the x-direction is:
[tex]v_{ix}=\frac{S}{t}[/tex]
[tex]15=\frac{S}{2.26}[/tex]
[tex]S=33.9\: m[/tex]
3)
The velocity in the y-direction of the stone will be:
[tex]v_{fy}=v_{iy}-gt[/tex]
[tex]v_{fy}=0-(9.81*2.26)[/tex]
[tex]v_{fy}=-22.17\: m/s[/tex]
Now, the velocity in the x-direction is 15 m/s then the velocity will be:
[tex]v=\sqrt{v_{x}^{2}+v_{fy}^{2}}=\sqrt{15^{2}+(-22.17)^{2}}[/tex]
[tex]v=26.77\: m/s[/tex]
4)
The angle of this velocity is:
[tex]tan(\alpha)=\frac{22.17}{15}[/tex]
[tex]\alpha=tan^{-1}(\frac{22.17}{15})[/tex]
[tex]\alpha=55.92[/tex]
Then α=55.92° negative from the x-direction.
I hope it helps you!
a motor car reaches a velocity of 15m/s in 6s from rest on a perfect test track . what is the average acceleration
Answer:
[tex]{ \tt{initial \: velocity, \: u = 0}} \: (at \: rest) \\ { \tt{final \: velocity, \: v = 15 { {ms}^{ - 1} }}} \\ { \tt{time, \: t = 6s}} \\ { \bf{from \: first \: newtons \: equation \: of \: motion : }} \\ { \bf{v = u + at}} \\ { \tt{15 = 0 + (a \times 6)}} \\ { \tt{6a = 15}} \\ { \tt{acceleration, \: a = 2.5 \: {ms}^{ - 2} }}[/tex]
Calculate the forces that the supports \rm A and \rm B exert on the diving board shown in when a 58-\rm kg person stands at its tip.
A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: μkmgcosθ=mgsinθ−ma, where g=9.80meter/second2, a=3.60meter/second2, θ=27.0∘, and m is not given. Which of the following represents a simplified expression for μk?A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: , where , , , and is not given. Which of the following represents a simplified expression for ?tanθ− agTo avoid making mistakes, the expression should not be simplified until the numerical values are substituted.gsinθ−agcosθThe single equation has two unknowns and cannot be solved with the information given.
Solution :
Given expression :
[tex]$\mu_k$[/tex]mgcosθ = mgsinθ − ma
Here, g = 9.8 [tex]m/s^2[/tex] , a = 3.60 [tex]m/s^2[/tex] , θ = 27°
Therefore,
[tex]$\mu_k mg \cos \theta = mg \sin \theta - ma$[/tex]
[tex]$\mu_k mg \cos \theta = m(g \sin \theta - a)$[/tex]
[tex]$\mu_k g \cos \theta = (g \sin \theta - a)$[/tex]
[tex]$\mu_k =\frac{(g \sin \theta-a)}{g \cos \theta}$[/tex]
Mow calculating the coefficient of kinetic friction as follows :
[tex]$\mu_k=\frac{g \sin \theta-a}{g \cos \theta}$[/tex]
[tex]$\mu_k=\frac{9.8 \times \sin 27^\circ-3.60}{9.8 \times \cos 27^\circ}$[/tex]
[tex]$\mu_k=0.097$[/tex]
