Answer:
198 ms-1
Explanation:
According to the Heisenberg uncertainty principle; it is not possible to simultaneously measure the momentum and position of a particle with precision.
The uncertainty associated with each measurement is given by;
∆x∆p≥h/4π
Where;
∆x = uncertainty in the measurement of position
∆p = uncertainty in the measurement of momentum
h= Plank's constant
But ∆p= mΔv
And;
m= 1.770×10^-27 kg
∆x = 0.15 nm
Making ∆v the subject of the formula;
∆v≥h/m∆x4π
∆v≥ 6.6 ×10^-34/1.770×10^-27 × 1.5×10^-10 ×4×3.142
∆v≥198 ms-1
What is the de Broglie wavelength of an object with a mass of 2.50 kg moving at a speed of 2.70 m/s? (Useful constant: h = 6.63×10-34 Js.)
Answer:
9.82 × [tex]10^{-35}[/tex] Hz
Explanation:
De Broglie equation is used to determine the wavelength of a particle (e.g electron) in motion. It is given as:
λ = [tex]\frac{h}{mv}[/tex]
where: λ is the required wavelength of the moving electron, h is the Planck's constant, m is the mass of the particle, v is its speed.
Given that: h = 6.63 ×[tex]10^{-34}[/tex] Js, m = 2.50 kg, v = 2.70 m/s, the wavelength, λ, can be determined as follows;
λ = [tex]\frac{h}{mv}[/tex]
= [tex]\frac{6.63*10^{-34} }{2.5*2.7}[/tex]
= [tex]\frac{6.63 * 10^{-34} }{6.75}[/tex]
= 9.8222 × [tex]10^{-35}[/tex]
The wavelength of the object is 9.82 × [tex]10^{-35}[/tex] Hz.
Niobium metal becomes a superconductor when cooled below 9 K. Its superconductivity is destroyed when the surface magnetic field exceeds 0.100 T. In the absence of any external magnetic field, determine the maximum current a 5.68-mm-diameter niobium wire can carry and remain superconducting.
Answer:
The current is [tex]I = 1420 \ A[/tex]
Explanation:
From the question we are told that
The diameter of the wire is [tex]d = 5.68 \ mm = 0.00568 \ m[/tex]
The magnetic field is [tex]B = 0.100 \ T[/tex]
Generally the radius of the wire is mathematically evaluated as
[tex]r = \frac{d}{2}[/tex]
substituting values
[tex]r = \frac{ 0.00568}{2}[/tex]
[tex]r = 0.00284 \ m[/tex]
Generally the magnetic field is mathematically represented as
[tex]B = \frac{\mu_o * I}{ 2 \pi r }[/tex]
=> [tex]I =\frac{ B * 2 \pi r }{\mu_o}[/tex]
Here [tex]\mu_o[/tex] is the permeability of free space with value [tex]\mu_o = 4 \pi *10^{-7} N/A^2[/tex]
substituting values
=> [tex]I =\frac{ 0.100 * 2 * 3.142 * 0.00284 }{ 4 \pi * 10^{-7}}[/tex]
=> [tex]I = 1420 \ A[/tex]
In a physics lab, light with a wavelength of 490 nm travels in air from a laser to a photocell in a time of 17.5 ns . When a slab of glass with a thickness of 0.800 m is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light a time of 21.5 ns to travel from the laser to the photocell.What is the wavelength of the light in the glass? Use 3.00×108 m/s for the speed of light in a vacuum. Express your answer using two significant figures.
Answer:
196 nm
Explanation:
Given that
Value of wavelength, = 490 nm
Time spent in air, t(a) = 17.5 ns
Thickness of glass, th = 0.8 m
Time spent in glass, t(g) = 21.5 ns
Speed of light in a vacuum, c = 3*10^8 m/s
To start with, we find the difference between the two time spent
Time spent on glass - Time spent in air
21.5 - 17.5 = 4 ns
0.8/(c/n) - 0.8/c = 4 ns
Note, light travels with c/n speed in media that has index of refraction
(n - 1) * 0.8/c = 4 ns
n - 1 = (4 ns * c) / 0.8
n - 1 = (4*10^-9 * 3*10^8) / 0.8
n - 1 = 1.2/0.8
n - 1 = 1.5
n = 1.5 + 1
n = 2.5
As a result, the wavelength of light in a medium with index of refraction would then be
490 / 2.5 = 196 nm
Therefore, our answer is 196 nm
A loop of wire is at the edge of a region of space containing a uniform magnetic field B. The plane of the loop is perpendicular to the magnetic field. Now the loop is pulled out of this region in such a way that the area A of the coil inside the magnetic field region is decreasing at the constant rate c. That is, dA/dt=−c, with c>0.Required:a. The induced emf in the loop is measuredto be V. What is the magnitude B of the magnetic field that the loop was in?b. For the case of a square loop of sidelength L being pulled out of the magneticfield with constant speed v, What is the rate of change of area c= -dA/dt
Answer:
The question is not clear enough. So i have attached a copy of the correct question.
A) B = V/c
B) c = Lv
Explanation:
A) we know that formula for magnetic flux is;
Φ = BA
Where B is magnetic field and A is area
Now,
Let's differentiate with B being a constant;
dΦ/dt = B•dA/dt
From faradays law, the EMF induced is given as;
E = -dΦ/dt
However, we want to express it in terms of V and E.M.F is also known as potential difference or Voltage.
Thus, V = -dΦ/dt
Thus, we can now say that;
-V = B•dA/dt
Now from the question, we are told that dA/dt = - c
Thus;
-V = B•-c
So, V = Bc
Thus, B = V/c
B) according to Faraday's Law or Lorentz Force Law, an electromotive force, emf, will be induced between the two ends of the sidelength:
Thus;
E =LvB or can be written as; V = LvB
Where;
V is EMF
L is length of bar
v is velocity
From the first solution, we saw that;
V = Bc
Thus, equating both of the equations, we have;
Bc = LvB
B will cancel out to give;
c = Lv
Explanation:
Somebody please help it’s urgent!!!!
In the tug of war game, none of the teams won. What can you conclude about the forces of the two teams ? Write all the evidence to support your answer.
Answer:
Explanation:
We can conclude that the forces of the two teams are equal and opposite and hence they cancel each other. Therefore none of the teams won as the rope did not move.
hope this helps
plz mark as brainliest!!!!!!!
How much time will elapse if a radioisotope with a half-life of 88 seconds decays to one-sixteenth of its original mass?
Answer:
352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.
Explanation:
The decay of radioisotopes are represented by the following ordinary differential equation:
[tex]\frac{dm}{dt} = -\frac{t}{\tau}[/tex]
Where:
[tex]t[/tex] - Time, measured in seconds.
[tex]\tau[/tex] - Time constant, measured in seconds.
[tex]m[/tex] - Mass of the radioisotope, measured in grams.
The solution of this expression is:
[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
Where [tex]m_{o}[/tex] is the initial mass of the radioisotope, measured in kilograms.
The ratio of current mass to initial mass is:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
The time constant is now calculated in terms of half-life:
[tex]\tau = \frac{t_{1/2}}{\ln2}[/tex]
Where [tex]t_{1/2}[/tex] is the half-life of the radioisotope, measured in seconds.
Given that [tex]t_{1/2} = 88\,s[/tex], the time constant of the radioisotope is:
[tex]\tau = \frac{88\,s}{\ln 2}[/tex]
[tex]\tau \approx 126.957\,s[/tex]
Now, if [tex]\frac{m(t)}{m_{o}(t)} = \frac{1}{16}[/tex] and [tex]\tau \approx 126.957\,s[/tex], the time is:
[tex]t = -\tau \cdot \ln\frac{m(t)}{m_{o}}[/tex]
[tex]t = -(126.957\,s)\cdot \ln \frac{1}{16}[/tex]
[tex]t \approx 352\,s[/tex]
352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.
A collector that has better efficiency in cold weather is the:
flat-plate collector due to reduced heat loss
evacuated tube collector due to its larger size
flat-plate collector due to the dark-colored coating
O evacuated tube collector due to reduced heat loss
Question 23 (1 point) Saved
One of the following is not found in Thermosyphon systems
o
Answer:
D. evacuated tube collector due to reduced heat loss
Explanation:
Evacuated tube collectors has vacuum which reduces the loss of heat and increase the efficiency of the collector. It has a major application in solar collector, and converts solar energy to heat energy. It can also be used for heating of a definite volume of water majorly for domestic purpose.
During cold weather, the conservation and efficient use of heat is required. Therefore, evacuated tube collector is preferred so as to reduce heat loss and ensure the maximum use of heat energy.
A woman was told in 2020 that she had exactly 15 years to live. If she travels away from the Earth at 0.8 c and then returns at the same speed, the last New Year's Day the doctors expect her to celebrate is:
Answer:
2035
Explanation:
The doctor does not travel with the woman, and therefore, he won't experience any relativistic effect on his time. The doctor will judge time by the time here on earth. Technically, the last new year's day the doctor, who is here on earth, would expect the woman to celebrate will be in 2020 + 15 years = 2035
When the adjustable mirror on the Michelson interferometer is moved 20 wavelengths, how many fringe pattern shifts would be counted
Answer:
The number of fringe pattern shift is m = 40
Explanation:
From the question we are told that
The Michelson interferometer is moved 20 wavelengths i.e [tex]20 \lambda[/tex]
Generally the distance which the Michelson interferometer is moved is mathematically represented as
[tex]d = \frac{m * \lambda}{2}[/tex]
Here [tex]m[/tex] is the number of fringe pattern shift
So
[tex]20 \lambda = \frac{m * \lambda}{2}[/tex]
[tex]40 \lambda = m * \lambda[/tex]
m = 40
A velocity selector can be used to measure the speed of a charged particle. A beam of particles is directed along the axis of the instrument. A parallel plate capacitor sets up an electric field E which is oriented perpendicular to a uniform magnetic field B. If the plates are separated by 3 mm and the value of the magnetic field is 0.3 T, what voltage between the plates will allow particles of speed 5 x 105 m/s to pass straight through without deflection? A. 70 V B. 140 V C. 450 V D. 1,400 V E. 2,800 V
Answer:
C. 450v
Explanation:
Using
Voltage= B*distance of separation*velocity
3mm x 0.3T x 5E5m/s
= 450v
Astronomers think planets formed from interstellar dust and gases that clumped together in a process called? A. stellar evolution B. nebular aggregation C. planetary accretion D. nuclear fusion
Answer:
C. planetary accretion
Explanation:
Astronomers think planets formed from interstellar dust gases that clumped together in a process called planetary accretion.
Answer:
[tex]\boxed{\sf C. \ planetary \ accretion }[/tex]
Explanation:
Astronomers think planets formed from interstellar dust and gases that clumped together in a process called planetary accretion.
Planetary accretion is a process in which huge masses of solid rock or metal clump together to produce planets.
A cook preparing a meal for a group of people is an example of
O kinetic energy because he has the ability to make a meal
O potential energy because he has the ability to make a meal
O kinetic energy because he is making the meal
o potential energy because he is making the meal
A stone is dropped from the upper observation deck of a tower, 50 m above the ground. (Assume g = 9.8 m/s2.) (a) Find the distance (in meters) of the stone above ground level at time t. h(t) = (b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.) s (c) With what velocity does it strike the ground? (Round your answer to one decimal place.) m/s (d) If the stone is thrown downward with a speed of 9 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)
Answer:
A. Using displacement =Ut + 1/2gt²
=> 0 + 1/2 (-9.8)t²
= -4.9t²
So
h(t) = 50+ displacement
= 50 - 4.9t²
B. To reach the ground
h(t) = 0
So
50-4.9t²= 0
t = √ (50/4.9)
= 3.2s
C. Using
V = u+ gt
U= 0
V= - 9.8(3.2)
= 31.4m/s
D. If u = -9m/s
Then s = ut + 1/2gt²
5t- 1/2gt²
But distance from the ground is
=.> 50-5t- 4.8t²= 0
So t solving the quadratic equation
t= 3.58s
(a) The distance of the stone above the ground level at time t is [tex]h(t) = 50 - 4.9t^2[/tex]
(b) The time taken for the stone to strike the ground is 3.19 s.
(c) The velocity of the stone when it strikes the ground is 31.4 m/s.
(d) The time taken for the stone to reach the ground when thrown at the given speed is 2.41 s.
The given parameters;
height above the ground, h₀ = 50 mThe distance of the stone above the ground level at time t is calculated as;
[tex]h(t) = h_0 - ut - \frac{1}{2} gt^2\\\\h(t) = 50 - 0 -0.5\times 9.8t^2\\\\h(t) = 50 - 4.9t^2[/tex]
The time taken for the stone to strike the ground is calculated as;
[tex]t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2\times 50}{9.8} } \\\\t = 3.19 \ s[/tex]
The velocity of the stone when it strikes the ground is calculated as;
[tex]v =u + gt\\\\v = 0 + 3.2 \times 9.8\\\\v = 31.4 \ m/s[/tex]
The time taken for the stone to reach the ground when thrown at speed of 9 m/s is calculated as;
[tex]50 = 9t + \frac{1}{2} (9.8)t^2\\\\50 = 9t + 4.9t^2\\\\4.9t^2 + 9t - 50 = 0\\\\a = 4.9 \, \ b = 9, \ \ c = -50\\\\solve \ the \ quadratic \ equation\ using \ formula \ method\\\\t = \frac{-b \ \ + /- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\t = \frac{-9 \ \ + /- \ \ \sqrt{(9)^2 - 4(4.9 \times -50)} }{2(4.9)} \\\\t = 2.41 \ s \ \ or \ \ - 4.24 \ s[/tex]
Thus, the time taken for the stone to reach the ground when thrown at the given speed is 2.41 s.
Learn more here:https://brainly.com/question/9527588
What is the separation in meters between two slits for which 594 nm orange light has its first maximum at an angle of 32.8°?
Answer:
1.1micro meter
Explanation:
Given that
Constructive interference is
ma = alpha x sin theta
Alpha = 1 x 594 x10^ -9/ sin 32.8°
= 1.1 x 10^ -6m
Explanation:
Are Quantum Physics, Quantum mechanics,Quantum Engagement same?
or, Do they branch of each others
Answer:
The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics lacking in classical mechanics. ... In the case of entangled particles, such a measurement will affect the entangled system as a wholeExplanation:
Answer:
quantum entanglement is thought to be one of the trickiest concepts in science, but the core issues are simple. And once understood, entanglement opens up a richer understanding of concepts such as the “many worlds” of quantum theory.
Explanation:
Light of wavelength 550 nm is incident on a slit having a width of 0.200 mm. The viewing screen is 1.90 m from the slit. Find the width of the central bright fringe
Answer:
The width of Center bright fringe is 10.2mm
Explanation:
Given that if
Y/ L << 1 then
Sin theta will be approx Y/L
So sin theta approx Y/L = lamda/a
Y= a x lambda/a
By substituting
1.9x 10^ -3m x 550*10^-9/ 0.2 x 10^-3m
= 5.2mm
But
Change in y = 2y = 10.4mm
A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation. With what period does it now oscillate?
Answer:
The new time period is [tex]T_2 = 3.8 \ s[/tex]
Explanation:
From the question we are told that
The period of oscillation is [tex]T = 5 \ s[/tex]
The new length is [tex]l_2 = 0.76 \ m[/tex]
Let assume the original length was [tex]l_1 = 1 m[/tex]
Generally the time period is mathematically represented as
[tex]T = 2 \pi \sqrt{ \frac{ I }{ mgh } }[/tex]
Now I is the moment of inertia of the stick which is mathematically represented as
[tex]I = \frac{m * l^2 }{12 }[/tex]
So
[tex]T = 2 \pi \sqrt{ \frac{ m * l^2 }{12 * mgh } }[/tex]
Looking at the above equation we see that
[tex]T \ \ \ \alpha \ \ \ l[/tex]
=> [tex]\frac{ T_2 }{T_1} = \frac{l_2}{l_1}[/tex]
=> [tex]\frac{ T_2}{5} = \frac{0.76}{1}[/tex]
=> [tex]T_2 = 3.8 \ s[/tex]
A mass M is attached to an ideal massless spring. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is doubled
Answer:
The period of the motion will still be equal to T.
Explanation:
for a system with mass = M
attached to a massless spring.
If the system is set in motion with an amplitude (distance from equilibrium position) A
and has period T
The equation for the period T is given as
[tex]T = 2\pi \sqrt{\frac{M}{k} }[/tex]
where k is the spring constant
If the amplitude is doubled, the distance from equilibrium position to the displacement is doubled.
Increasing the amplitude also increases the restoring force. An increase in the restoring force means the mass is now accelerated to cover more distance in the same period, so the restoring force cancels the effect of the increase in amplitude. Hence, increasing the amplitude has no effect on the period of the mass and spring system.
A hot cup of coffee is placed on a table. Which will happen because of conduction? Answer options with 4 options A. The temperature of the coffee will decrease while the temperature of the table decreases. B. The temperature of the coffee will increase while the temperature of the table increases. C. The temperature of the coffee will decrease while the temperature of the table increases. D. The temperature of the coffee will increase while the temperature of the table decreases.
Answer:
C.Explanation:
C. The temperature of the coffee will decrease while the temperature of the table increases.
Tech A says parallel circuits are like links in a chain. Tech B says total current in a parallel circuit equals the sum of the current flowing in each branch of the circuit. Who is correct?
Answer: Only Tech B is correct.
Explanation:
First, tech A is wrong.
The circuits that can be compared with links in a chain are the series circuit, and it can be related to the links in a chain because if one of the elements breaks, the current can not flow furthermore (because the elements in the circuit are connected in series) while in a parallel circuit if one of the branches breaks, the current still can flow by other branches.
Also in a parallel circuit, the sum of the currents of each path is equal to the current that comes from the source, so Tech B is correct, the total current is equal to the sum of the currents flowing in each branch of the circuit.
Calcular la resistencia de una varilla de grafito de 170 cm de longitud y 60 mm2. Resistividad grafito 3,5 10-5 Ωm
Answer:
R = 0.992 Ω
Explanation:
En esta pregunta, dada la información que contiene, debemos calcular la resistencia de la varilla de grafito.
Matemáticamente,
Resistencia = (resistividad * longitud) / Área De la pregunta;
Resistividad = 3,5 * 10 ^ -5 Ωm
longitud = 170 cm = 1,7 m
Área = 60 mm ^ 2 = 60/1000000 = 6 * 10 ^ -5 m ^ 2
Conectando estos valores a la ecuación anterior, tenemos;
Resistencia = (3.5 * 10 ^ -5 * 1.7) / (6 * 10 ^ -5) =
(3.5 * 1.7) / 6 = 0.992 Ω
As a skydiver falls, his potential energy ___ and his kinetic energy __
increases,increases
increases,decreases
decreases,increases
decreases, decreases
Answer:
Hey there!
PE=mgh, so as height decreases, so does the potential energy.
KE=mv^2, so as velocity increases, kinetic energy increases.
Thus, the correct answer would be Decreases, Increases.
Let me know if this helps :)
A student holds a bike wheel and starts it spinning with an initial angular speed of 7.0 rotations per second. The wheel is subject to some friction, so it gradually slows down.
In the 10.0 s period following the inital spin, the bike wheel undergoes 60.0 complete rotations. Assuming the frictional torque remains constant, how much more time Δ????s will it take the bike wheel to come to a complete stop?
The bike wheel has a mass of 0.625 kg0.625 kg and a radius of 0.315 m0.315 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque ????fτf that was acting on the spinning wheel.
Answer:
a) Δt = 24.96 s , b) τ = 0.078 N m
Explanation:
This is a rotational kinematics exercise
θ = w₀ t - ½ α t²
Let's reduce the magnitudes the SI system
θ = 60 rev (2π rad / 1 rev) = 376.99 rad
w₀ = 7.0 rot / s (2π rad / 1 rpt) = 43.98 rad / s
α = (w₀ t - θ) 2 / t²
let's calculate the annular acceleration
α = (43.98 10 - 376.99) 2/10²
α = 1,258 rad / s²
Let's find the time it takes to reach zero angular velocity (w = 0)
w = w₀ - alf t
t = (w₀ - 0) / α
t = 43.98 / 1.258
t = 34.96 s
this is the total time, the time remaining is
Δt = t-10
Δt = 24.96 s
To find the braking torque, we use Newton's law for angular motion
τ = I α
the moment of inertia of a circular ring is
I = M r²
we substitute
τ = M r² α
we calculate
τ = 0.625 0.315² 1.258
τ = 0.078 N m
The total time taken by the wheel to come to rest is 25.18 s and the magnitude of the frictional torque is 25.18 N-m.
Given data:
The initial angular speed of wheel is, [tex]\omega = 7.0 \;\rm rps[/tex] (rps means rotation per second).
The time interval is, t' = 10.0 s.
The number of rotations made by wheel is, n = 60.0.
The mass of bike wheel is, m = 0.625 kg.
The radius of wheel is, r = 0.315 m.
The problem is based on rotational kinematics. So, apply the second rotational equation of motion as,
[tex]\theta = \omega t-\dfrac{1}{2} \alpha t'^{2}[/tex]
Here, [tex]\theta[/tex] is the angular displacement, and its value is,
[tex]\theta =2\pi \times 60\\\\\theta = 376.99 \;\rm rad[/tex]
And, angular speed is,
[tex]\omega = 2\pi n\\\omega = 2\pi \times 7\\\omega = 43.98 \;\rm rad/s[/tex]
Solving as,
[tex]376.99 = 43.98 \times 10-\dfrac{1}{2} \alpha \times 10^{2}\\\\\alpha = 1.25 \;\rm rad/s^{2}[/tex]
Apply the first rotational equation of motion to obtain the value of time to reach zero final velocity.
[tex]\omega' = \omega - \alpha t\\\\0 = 43.98 - 1.25 \times t\\\\t = 35.18 \;\rm s[/tex]
Then total time is,
T = t - t'
T = 35.18 - 10
T = 25.18 s
Now, use the standard formula to obtain the value of braking torque as,
[tex]T = m r^{2} \alpha\\\\T = 0.625 \times (0.315)^{2} \times 1.25\\\\T = 0.0775 \;\rm Nm[/tex]
Thus, we can conclude that the total time taken by the wheel to come to rest is 25.18 s and the magnitude of the frictional torque is 25.18 N-m.
Learn more about the rotational motion here:
https://brainly.com/question/1388042
A wire carries current in the plane of this paper toward the top of the page. The wire experiences a ma netic force toward the right edge of the page. The direction of the magnetic field causing this force is:
A. in the plane of the page and toward the left edge
B. in the plane of the page and toward the bottom edge
C. upward out of the page
D. downward into the page
Answer:
D) True. In this case the thumb goes up the page, the fingers are extended out of the page and the palm points to the left
Explanation:
The magnetic force on a conductor is given by
F = i L x B
bold letters indicate vectors. We can write this expression in the form of magnitudes
F = i L B sin θ
The direction of the force can be found by the rule of the right hand, the thumb points in the direction of the current, the fingers extended in the direction of the magnetic field and the palm gives the direction of the force
Let's apply this expression to the case presented.
A) False. In this case the force is out of the page and is in contradiction with the real force
B) False. In this case the force is zero since the displacement of the current and the field would be parallel
C) False. In this case the force is to the left
D) True. In this case the thumb goes up the page, the fingers are extended out of the page and the palm points to the left
The A block, with negligible dimensions and weight P, is supported by the coordinate point (1.1/2) of the parabolic fixed grounded surface, from equation y = x^2/2 If the block is about to slide, what is the coefficient of friction between it and the surface; determine the force F tangent to the surface, which must be applied to the block to start the upward movement.
Answer:
μ = 1
F = P√2
Explanation:
The parabola equation is: y = ½ x².
The slope of the tangent is dy/dx = x.
The angle between the tangent and the x-axis is θ = tan⁻¹(x).
At x = 1, θ = 45°.
Draw a free body diagram of the block. There are three forces:
Weight force P pulling down,
Normal force N pushing perpendicular to the surface,
and friction force Nμ pushing up tangential to the surface.
Sum of forces in the perpendicular direction:
∑F = ma
N − P cos 45° = 0
N = P cos 45°
Sum of forces in the tangential direction:
∑F = ma
Nμ − P sin 45° = 0
Nμ = P sin 45°
μ = P sin 45° / N
μ = tan 45°
μ = 1
Draw a new free body diagram. This time, friction force points down tangential to the surface, and applied force F pushes up tangential to the surface.
Sum of forces in the tangential direction:
∑F = ma
F − Nμ − P sin 45° = 0
F = Nμ + P sin 45°
F = (P cos 45°) μ + P sin 45°
F = P√2
A weightlifter works out at the gym each day. Part of her routine is to lie on her back and lift a 43 kg barbell straight up from chest height to full arm extension, a distance of 0.53 m .
Part A: How much work does the weightlifter do to lift the barbell one time?
Part B: If the weightlifter does 23 repetitions a day, what total energy does she expend on lifting, assuming a typical efficiency for energy use by the body?
Part C: How many 500 Calorie donuts can she eat a day to supply that energy?
Answer:
A) Workdone = 223.57 N-m
B) 22357 J of energy
C) Number of donuts = 10.7 donuts
Explanation:
A) The work done is calculated from the formula;. Work done = Force × Distance
We are given;
Mass; m = 43 kg
Distance = 0.53 m
Force(weight) = mg = 43 × 9.81
Thus;
Work done = 43 × 9.81 × 0.53
Workdone = 223.57 N-m
B) We are told she does 23 repetitions a day.
Thus, we assume 23% efficiency.
So, Work = Energy
Thus;
At 100% efficiency;
Energy = (223.57/100%) × 23 repetitions = 5142.11 J
Now, since she is only 23% efficient, she will expend; 5142.11/0.23 J = 22357 J of energy to do 5390 J of work.
C) from conversions; 4.18 J = 1 calorie
Thus;
22357 J ÷ 4.18 J/cal = 5348.565 calories
We how many 500 calorie donuts she can eat in a day to supply that energy.
Thus;
Number of donuts = 5348.565 cal ÷ 500 cal /donut
Number of donuts = 10.7 donuts
A locomotive is pulling three train cars along a level track with a force of 100,000N. The car next to the locomotive has a mass of 80,000kg, next one, 50,000kg, and the last one, 70,000 kg. you can neglect the friction on the cars being pulled.
A) what if the magnitude of the force between that the 80,000-kg car exerts on the 50,000-kg car?
B) what is the magnitude of the force that the 50,000-kg car exerts on the 70,000-kg car?
Answer:
a) 60000 N
b) 35000 N
Explanation:
Force from locomotive = 100000 N
mass of first car = 80000 kg
mass of second car = 50000 kg
mass of third car = 70000 kg
friction is neglected in this system
Total mass of the cars = 80000 + 50000 + 70000 = 200000 kg
All the car in the system will accelerate at the same rate since they are pulled by the same force
We know that force F = ma
where
a is the acceleration of the cars
m is the total mass in the system
from this we can say that
a = F/m
a = 100000/200000 = 0.5 m/s^2
a) The total mass involved in this case = mass of the last two cars after the 80000 kg car = 50000 + 70000 = 120000 kg
therefore force exerted F = ma
F = 0.5 x 120000 = 60000 N
b) The total mass in this case = mass of the third car only = 70000 kg
F = ma
F = 70000 x 0.5 = 35000 N
On a separate sheet of paper, tell why scientists in different countries can easily compare the amount of matter in similar objects in their countries
Answer: no u
Explanation: no u
Find the focal length of contact lenses that would allow a nearsighted person with a 130 cmcm far point to focus on the stars at night.
Answer:
130cmExplanation:
The lens equation is expressed as;
1/f = 1/u+1/v where;
f is the focal length of the lens
u is the object distance
v is the image distance
Since the near sighted person wants focus the starts at nigt, the stars at night are the images located that infinity. Hence the image distance v = ∞.
The object distance u = 130cm
Substituting the given parameters in the formula to get the focal length f
[tex]\frac{1}{f} = \frac{1}{\infty} + \frac{1}{130} \\\\As \ x \ tends \ to \ \infty, \, \frac{a}{x} \ tends \ to \ 0 \ where\ 'a' \ is \ a\ constant \\\\} \\\\[/tex]
[tex]\frac{1}{f} = 0+ \frac{1}{130}\\\\[/tex]
[tex]\frac{1}{f} =\frac{1}{130}\\cross\ multiply\\\\f = 130*1\\\\f = 130cm[/tex]
Hence the focal length of contact lenses that would allow a nearsighted person with a 130 cm far point to focus on the stars at night is 130cm
Select the situation for which the torque is the smallest.
a. A 200 kg piece of silver is placed at the end of a 2.5 m tree branch.
b. A 20 kg piece of marble is placed at the end of a 25 m construction crane arm.
c. A 8 kg quartz rock is placed at the end of a 62.5 m thin titanium rod.
d. The torque is the same for two cases.
e. The torque is the same for all cases.
Answer:
e. The torque is the same for all cases.
Explanation:
The formula for torque is:
τ = Fr
where,
τ = Torque
F = Force = Weight (in this case) = mg
r = perpendicular distance between force an axis of rotation
Therefore,
τ = mgr
a)
Here,
m = 200 kg
r = 2.5 m
Therefore,
τ = (200 kg)(9.8 m/s²)(2.5 m)
τ = 4900 N.m
b)
Here,
m = 20 kg
r = 25 m
Therefore,
τ = (20 kg)(9.8 m/s²)(25 m)
τ = 4900 N.m
c)
Here,
m = 8 kg
r = 62.5 m
Therefore,
τ = (8 kg)(9.8 m/s²)(62.5 m)
τ = 4900 N.m
Hence, the correct answer will be:
e. The torque is the same for all cases.
