"Acceleration" means the rate at which velocity is changing.
If velocity is constant, then it isn't changing.
If velocity isn't changing, then acceleration is zero.
A) A spaceship passes you at a speed of 0.800c. You measure its length to be 31.2 m .How long would it be when at rest?
B) You travel to a star 145 light-years from Earth at a speed of 2.90
Answer:
a
[tex]l_o =52 \ m[/tex]
b
[tex]l = 37.13 \ LY[/tex]
Explanation:
From the question we are told that
The speed of the spaceship is [tex]v = 0.800c[/tex]
Here c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
The length is [tex]l = 31.2 \ m[/tex]
The distance of the star for earth is [tex]d = 145 \ light \ years[/tex]
The speed is [tex]v_s = 2.90 *10^{8}[/tex]
Generally the from the length contraction equation we have that
[tex]l = l_o \sqrt{1 -[\frac{v}{c } ]}[/tex]
Now the when at rest the length is [tex]l_o[/tex]
So
[tex]l_o =\frac{l}{\sqrt{ 1 - \frac{v^2}{c^2 } } }[/tex]
[tex]l_o =\frac{ 31.2 }{ \sqrt{1 - \frac{(0.800c ) ^2}{c^2} } }[/tex]
[tex]l_o=52 \ m[/tex]
Considering b
Applying above equation
[tex]l =l_o \sqrt{1 - [\frac{v}{c } ]}[/tex]
Here [tex]l_o =145 \ LY(light \ years )[/tex]
So
[tex]l=145 * \sqrt{1 - \frac{v_s^2}{c^2 } }[/tex]
[tex]l =145 * \sqrt{ 1 - \frac{2.9 *10^{8}}{3.0*10^{8}} }[/tex]
[tex]l = 37.13 \ LY[/tex]
a car accelerates from 10 m/s to 30 m/s as the traffic break up on the highway. the acceleration occurs over 3.5 seconds of time. determine the acceleration of the car.
Answer:
[tex] \boxed{\sf Acceleration \ (a) = 5.7 \ m/s^2} [/tex]
Given:
Initial velocity (u) = 10 m/s
Final velocity (v) = 30 m/s
Time taken (t) = 3.5 seconds
To Find:
Acceleration (a) of the car
Explanation:
From equation of motion:
[tex] \boxed{ \bold{ v = u + at}}[/tex]
Substituting value of v, u & t in the equation:
[tex] \sf \implies 30 = 10 + a(3.5) \\ \\ \sf \implies 30 - 10 = 3.5a \\ \\ \sf \implies 20 = 3.5a \\ \\ \sf \implies 3.5a = 20 \\ \\ \sf \implies a = \frac{20}{3.5} \\ \\ \sf \implies a = 5.7 \: m/s^2[/tex]
[tex] \therefore[/tex]
Acceleration (a) of the car = 5.7 m/s²
A weight of 35.0 N is suspended from a spring that has a force constant of 220 N/m. The system is undamped and is subjected to a harmonic driving force of frequency 10.5 Hz, resulting in a forced-motion amplitude of 3.00 cm. Determine the maximum value of the driving force.
Answer:
The force is [tex]F = 423.04 \ N[/tex]
Explanation:
From the question we are told that
The weight is [tex]W = 35 .0 \ N[/tex]
The force constant is [tex]k = 220 \ N/m[/tex]
The frequency is [tex]f = 10.5 \ Hz[/tex]
The amplitude is [tex]A = 3.00 \ cm = 0.03 \ m[/tex]
Generally the maximum driving force is mathematically represented as
[tex]F = m * w^2 A[/tex]
Here m is the mass of the weight which is mathematically represented as
[tex]m = \frac{ W }{g}[/tex]
=> [tex]m = \frac{ 35 }{9.8 }[/tex]
=> [tex]m = 3.571 \ kg[/tex]
Also [tex]w[/tex] is the angular frequency of the weight which is mathematically represented as
[tex]w = 2 \pi * f[/tex]
[tex]w = 2* 3.142 * 10[/tex]
=> [tex]w = 62.84 \ rad/s[/tex]
So
[tex]F = 3.571 * 62.84^2 * 0.03[/tex]
[tex]F = 423.04 \ N[/tex]
A spinning top spinning at 16rad/s takes 88.9s to come to a complete stop. Find the angular acceleration of the top.
Answer:
The angular acceleration of the top is 0.18 rad/s²
Explanation:
Given;
angular velocity of the top, ω = 16 rad/s
time it takes to come to a complete stop, t = 88.9s
The angular acceleration of the top, is calculated as;
[tex]\alpha = \frac{\omega}{t}[/tex]
α is the angular acceleration
ω is angular acceleration
t is the time
[tex]\alpha = \frac{\omega}{t}\\\\\alpha = \frac{16}{88.9}\\\\\alpha =0.18 \ rad/s^2[/tex]
Therefore, the angular acceleration of the top is 0.18 rad/s²
If white light illuminates a diffraction grating having 710 lines/mmlines/mm , over what range of angles does the visible mm
Complete Question
The human eye can readily detect wavelengths from about 400 nm to 700 nm. If white light illuminates a diffraction grating having 710 lines/mm, over what range of angles does the visible m = 1 spectrum extend
Answer:
The value [tex]\theta = 16.5 ^ o[/tex]
Explanation:
From the question we are told that
The diffraction grating haves [tex]a = 710 \ lines /mm[/tex]
Generally the separation of the slit is mathematically represented as
[tex]d = \frac{1}{710} \ mm =0.001408 \ mm = 1.408 *10^{-6} \ m[/tex]
Generally the condition for constructive interference is mathematically represented as
[tex]dsin(\theta ) = n \lambda[/tex]
So
[tex]\theta = sin ^{-1} [\frac{n * \lambda }{d} ][/tex]
=> [tex]\theta = sin^{-1}[\frac{1 * 400 *10^{-9}}{ 1.408*10^{-6}} ][/tex]
=> [tex]\theta = 16.5 ^ o[/tex]
Marisol drives north at 64.3 km/h. How far does Marisol travel after 5.8 h?
Answer:
372.94 km
d= st
= (64.3 km/h)(5.8h)
=372.94 km
a wave is described by where x is in meters, y is in centimeters and t is in seconds. The angular frequency is
Complete Question
A wave is described by y(x,t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimetres and t is in seconds. The angular wave frequency is
Answer:
The value is [tex]w = 10 \ rad /s[/tex]
Explanation:
From the question we are told that
The equation describing the wave is y(x,t) = 0.1 sin(3x + 10t)
Generally the sinusoidal equation representing the motion of a wave is mathematically represented as
[tex]y(x,t) = Asin(kx + wt )[/tex]
Where w is the angular frequency
Now comparing this equation with that given we see that
[tex]w = 10 \ rad /s[/tex]
in a young's double-slit experiment the center of a bright fringe occurs wherever waves from the slits differ in the distance they travel by a multiple of
Answer:
Zero
Explanation:
Because using
Deta X= dsinစ x n(lambda)
But we know that for central maxima
n is zero
So after substituting
Deta x = 0
Radio waves are readily diffracted around buildings, whereas light waves are negligibly diffracted around buildings. This is because radio waves
Answer:
Radio waves have longer wavelength
Explanation:
Radio wave is an electromagnetic frequency that has the ability to travel through long distance. They have frequencies shuttling been the range of 10^4 hz and a frequency of 10^12 hz
Light wave is also called visible light. This is because it is visible to the naked eye, despite it being in the electromagnetic spectrum. It's frequency is usually between 4*10^-7 hz and a frequency of 7*10^-7 hz.
As can be seen from both, the radio waves length are quite far stronger than that of the light waves.
A sinewave has a period (duration of one cycle) of 35 μs. What is its corresponding frequency (no of completed cycles in a second), in kHz, expressed to 3 significant figures?
If the frequency of this sinewave is now reduced by a factor of 2.5, using the value calculated above to 3 significant figures, what will be the new period?
Express your answer in μs, to 3 significant figures
Answer:
We know that the relation between period and frequency is:
T = period.
f = frequency.
T = 1/f.
Then, if the period is 35 μs = 35x10^-9 seconds.
The frequency will be:
f = (1/ 35x10^-9 s) = (1/35s)*10^9
now, 1Hz = 1/s
1KHz = 1/1000s = 10^-3 s
f = (10^9/35)*10^-3 KHz = 10^6/35 KHz = 28,571.429 KHz.
Now we must divide this by 2.5:
28,571.429 KHz/2.5 = 11,428.572 KHz
Now we can use the relation:
T = 1/f
T = 1/11,428.572 KHz = (1/11,428.572 Hz)*10^-3
T = 8.750x10^-8 seconds.
And we want this expressed in μs = 10`-9 seconds, we have:
T = 8.750x10^-8 s = (10/10)8.750x10^-8 s = 87.50x10`-9s = 87.50 μs
So as expected, if the frequency is reduced by a factor of 2.5, the period will increase by a factor of 2.5
As the initial period was 35 μs, and:
2.5*35 μs = 87.5 μs
A π_ ("pi-minus") particle, which has charge _e, is at location ‹ 4.00 10-9, -5.00 10-9, -2.00 10-9 › m. What is the electric field at location < -2.00 10-9, 4.00 10-9, 3.00 10-9 > m, due to the π_ particle?
Answer:
The electric field due to charge at distance r is [tex](-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]
Explanation:
Given that,
Initial position of particle [tex]r_{1}=4.00\times10^{-9}i-5.00\times10^{-9}j-2.00\times10^{-9}k\ m[/tex]
Final position of particle [tex]r_{2}=-2.00\times10^{-9}i+4.00\times10^{-9}j+ 3.00\times10^{-9}k\ m[/tex]
We need to calculate the magnitude of the position vector
Using formula of position vector
[tex]\vec{r}=\vec{r_{2}}-\vec{r_{1}}[/tex]
Put the value into the formula
[tex]\vec{r}=-2.00\times10^{-9}i+4.00\times10^{-9}j+ 3.00\times10^{-9}k-(4.00\times10^{-9}i-5.00\times10^{-9}j-2.00\times10^{-9}k)[/tex]
[tex]\vec{r}=-9\times10^{-9}i+9\times10^{-9}j+5\times10^{-9}k[/tex]
[tex]\vec{|r|}=\sqrt{(9^2+9^2+5^2)\times10^{-18}}[/tex]
[tex]\vec{|r|}=13.6\times10^{-9}\ m[/tex]
We need to calculate the unit vector along electric field direction
Using formula of unit vector
[tex]\hat{r}=\dfrac{\vec{r}}{|\vec{r}|}[/tex]
Put the value into the formula
[tex]\hat{r}=\dfrac{-9\times10^{-9}i+9\times10^{-9}j+5\times10^{-9}k}{13.6\times10^{-9}}[/tex]
[tex]\hat{r}=-0.66i+0.66j+0.36k[/tex]
We need to calculate the electric field due to charge at distance r
Using formula of electric field
[tex]E=\dfrac{kq}{r^2}\hat{r}[/tex]
Put the value into the formula
[tex]E=\dfrac{9\times10^{9}\times1.6\times10^{-19}}{(13.6\times10^{-9})^2}\times(-0.66i+0.66j+0.36k)[/tex]
[tex]E=7.78\times10^{6}\times(-0.66i+0.66j+0.36k)[/tex]
[tex]E=-0.8169\times10^{6}i+0.8169\times10^{6}j+2.800\times10^{6}k\ N/C[/tex]
[tex]E=(-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]
Hence, The electric field due to charge at distance r is [tex](-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]
Four students measured the same line with a ruler like the one shown below. The results were as follows: 5.52 cm, 6.63 cm, 5.5, and 5.93. Even though you cannot see the line they actually measured, which of the recorded measurements are possible valid measurements for this instrument, according to its precision? Select all that apply. 1. 5.52 2. 6.63 3. 5.5 4. 5.93
Answer:
1) 5.52 cm , C) 5.5 cm
Explanation:
When a measurement is carried out, in addition to the value of the magnitude, the error or uncertainty of the measurement must occur, in a direct measurement with an instrument the uncertainty is equal to the appreciation of the instrument.
Uniform see the errors by the number of significant figures days, in this cases they are two decimals for which the appreciation of the instrument ± - 0.01
now we can analyze the measurements made
1) 5.52 cm. Validate. It is a valid measurement is within the uncertainty range
2) 6.63 cm. It does not validate. It is out of the error range
3) 5.5 cm Valid. It is within the given error range,
4) 5.93 cm Not Valid. It is out of the error range.
Answer:
6.63 and 5.93
Explanation:
Waves with a wavelength of 10 meters will begin to touch bottom when the depth of water is _______ meters.
Answer:
When the depth is less than 0.5 m
Explanation:
Waves will begin to touch bottom when depth of the water is less than 1/20 of the wavelength. This type of wave is known as a shallow wave.
wavelength = 10 m
It will begin to touch bottom when its depth is less than
1/20 x 10 = 0.5 m
11. A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side
Answer:
≈159.15
Explanation:
So displacment is the fastest, or shortest way to get somewhere
Youd take your circumference (500) and find the diameter from that using the 2 formulas
C=2πr
d=2r
your answer would be ≈159.15
If im incorrect please correct me! Im only just relearning this stuff (im a freshman)
Suppose you wanted to break a meter stick over your knee. The cross-section of a meter stick is rectangular. Will it be easier to break with the long side against your knee or with the short side against your knee? Cross-section of a meter stick : (i.e. looking down the end of a meter stick)
Answer:
It will be easier to break the meter rule with the long side against my knee.
Explanation:
To break the meter rule involves the principle of bending moment. The long side will require less force to generate the same amount of bending moment that will have to be generated to break the meter rule. The short side on the other hand will require more force to generate this mount of bending moment. This is because the shorter has a very small surface area, which concentrates the force on your knee. The pressure is then dissipated as more pressure to your knee. Th longer side has a lesser surface area so, most of the force is used in breaking the meter rule.
A rock is dropped from a tall building. You can ignore air resistance. Determine its final speed and distance traveled after 4 seconds.
(A) speed = 20 m/s, distance = 80 m
(B) speed = 40 m/s, distance = 20 m
(C) speed = 40 m/s, distance = 80 m
(D) speed = 80 m/s, distance = 40 m
(E) speed = 20 m/s, distance = 40 m
Answer:
(C) speed = 40 m/s, distance = 80 m
Explanation:
According to Newton law of motion for a falling body:
v = u + gt
Where v is the final velocity, u is the initial velocity, t is the time taken to fall and g is the acceleration due to gravity.
Given that: t = 4 s, g = 10 m/s², u = 0 m/s(at top of building). Therefore substituting values:
v = 0 + 10(4)
v = 40 m/s
To find the distance h, we use the formula:
v² = u² + 2gh
Substituting values:
40² = 0² + 2(10)h
20h = 40² - 0²
20h = 1600
h = 1600 / 20
h = 80 m
The speed = 40 m/s, distance = 80 m
Nina and Jon are practicing an ice skating routine. Nina is standing still. Jon, who is twice as heavy as Nina, skates toward her, pushing Nina away with force f. Assuming the system is closed, which statement is correct about this system? A. Nina experiences a force equal to f. B. Nina experiences a force equal to f/2.
If the system is closed, Nina will experience only a force equal to F exerted by Jon.
According to Newton's third law of motion, action and reaction is equal and opposite. That is the force applied to a stationary object is equal to the reaction exerted by the stationary object.
Applying this law, the force Jon applied on Nina is equal to the reaction Nina exerts on Jon.
If Jon exerts a force of F magnitude on Nina, consequently, Nina will experience the force of equal magnitude and exert equal reaction in opposite direction towards Jon.Also, if the system is closed, no additional force will be experienced by Nina, except the force applied by Jon.Thus, assuming the system is closed, Nina will experience only a force equal to F exerted by Jon.
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Rigid-body mechanics is divided into two areas: ________deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity; whereas________ is concerned with the accelerated motion of bodies.
Answer:
Statics and dynamics
Explanation:
Rigid-body mechanics is divided into two areas: statics deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity; whereas dynamic is concerned with the accelerated motion of bodies.
In rigid-body mechanics, there are two various branches: statics and dynamics. Statics studies the stability of bodies, i.e., those that are at rest or move at a constant speed, whereas dynamics studies the accelerated movement of bodies.
What is equilibrium?Even if neither a system's energy state nor its phase of motion tends to change over time, the system is said to be in equilibrium.
A simple mechanical body is considered to have been in equilibrium if it neither suffers accelerometers nor angular acceleration. Unless an external force disrupts this state, it will remain in equilibrium indefinitely.
When all forces acting on a single particle are added together and equal to zero, equilibrium results. In addition to the conditions outlined in the article above, a rigid body is said to be in equilibrium if the vector sum of any torques operating on it equals zero, maintaining the body's steady state of rotational motion.
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Identify two types of motion where an object's speed remains the same while it continues to change direction
Answer:
motion in which acceleration is orthogonal to travel directionmotion in which speed is constantExplanation:
1) Any motion in which the acceleration is orthogonal to the direction of travel will have this characteristic:
circular motion in a plane
motion of a charged particle in a magnetic field perpendicular to the direction of travel
__
2) Motion in which the speed is constant, regardless:
motion of a photon through a varying gravitational field
You and a friend each drive 58 km. You travel at 89. km/h, your friend at 94 km/h. How long will your friend wait for you at the end of the trip?
Answer:
2.1 minutes/ 126 seconds
Explanation:
Distance = speed x time
We can rearrange this equation for time:
Time = Distance/Speed
For you (89km/h):
Distance = 58km, Speed = 89km/h
Therefore time = 58/89 = 0.652 (3dp) hours
For friend:
Distance = 58km, Speed = 94km/h
Therefore time = 58/94 = 0.617 (3dp) hours
Difference in time = 0.652 - 0.617 = 0.035 hours.
Convert to minutes: 0.035 x 60 (because 60 min in hour) = 2.1
Your friend will be waiting for 2.1 minutes, or 126 seconds (2.1 x 60).
Hope this helped!
How could you test the hypothesis that elephants interpreted the ground signal as being farther away than the air signal?
Answer:
One way to test the hypothesis is to create two waves, one in the air and one on the ground at the same time. One of them for the elephant to get closer and another for the elephants to move away. Observe the reaction of the animal and with this we know which sound came first.
Explanation:
This hypothesis is based on the fact that the speed of sound in air is v = 343 m / s with a small variation with temperature.
The speed of sound in solid soil is an average of the speed of its constituent media, giving values between
wood 3900 m / s
concrete 4000 m / s
fabrics 1540 m / s
earth 5000 m / s wave S
ground 7000 m / s P wave
we can see that the speed on solid earth is an order of magnitude greater than in air.
One way to test the hypothesis is to create two waves, one in the air and one on the ground at the same time. One of them for the elephant to get closer and another for the elephants to move away. Observe the reaction of the animal and with this we know which sound came first.
From the initial information, the wave going through the ground should arrive first.
To test the hypothesis that elephants interpreted the ground signal as being farther away the air signal is to see how fast they react by high and low frequency sounds. This however can be done by creating two waves, one in the air and one on the ground at the same time. One of them for the elephant to get closer and another for the elephants to move away. The reaction of the animal is then observed and via the first sound from one of them
HypothesisA hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
In non-scientific use, hypothesis and theory are often used interchangeably.
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What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 84.0 kg?
Complete question:
The length of nylon rope from which a mountain climber is suspended has an effective force constant of 1.40 ×10⁴ N/m.
What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 84.0 kg?
Answer:
The frequency (in Hz) at which he bounce is 2.054 Hz
Explanation:
Given;
effective force constant, K = 1.40 ×10⁴ N/m.
The total mass = his mass plus the mass of his equipment, m = 84 kg
The frequency (in Hz) at which he bounce is given by;
[tex]f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}\\\\f = \frac{1}{2\pi} \sqrt{\frac{1.4*10^4}{84}}\\\\f = 2.054 \ Hz[/tex]
Therefore, the frequency (in Hz) at which he bounce is 2.054 Hz
Does the distance between diffraction minima increase or decrease when the slit width is increased? Explain with reference to your data (observation) and theory
Answer:
the width of the slit is dividing therefore the distance to the minimums increases as the width of the slit decreases
Explanation:
In the diffraction phenomenon the intensity minima are described by
a sin θ = (m + ½) λ
without using trigonometry we can find an expression for the sine
tan θ = y / L
for small angles
Tan θ = sin θ/ cos θ = sin θ = y / L
a y / L = (m + ½) lam
y = (m + ½) λ L / a
we see that the width of the slit is dividing therefore the distance to the minimums increases as the width of the slit decreases
In the observation of the experiment the length of the pattern increases with the decrease in the width of the slit
True or False: The study of the motion of objects is a foundational part of Physics
Answer:
True
Explanation:
In the foundational topics of physics mechanics consists of motion, energy and forces, theses areas are core concerns in the study of physics hence they are the foundational topics and are often times treated first in all matters.
What is motion?
Simply put, it is alternating from points to points.
the areas of study that involves motion and force together is call dynamics.
while the area of study of motion without any applied force is call statics.
A substance is soluble in water. It is added into the water and dissolves. More solute continues being added until it reaches a point where the newly added solute begins to sit on the bottom of the container without dissolving. What has happened? A. The solute has become a solvent. B. The solute was not actually soluble to begin with. C. The solute has become saturated. D. The solution has become saturated.
Answer:
option D
Explanation:
also to add.... there exists a solubility equilibrium between solid solute and the solution.
The newly added solute begins to sit on the bottom of the container without dissolving this represents that the solution has become saturated, Therefore the correct answer is D.
What is a Saturated Solution?It is a type of solution in which no more amount of solute can be dissolved any further, The saturated solution already contains the maximum amount of solute that can be dissolved within it.
The solution reached a point where the newly added solute starts to sit on the bottom this means the solution has become saturated.
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3. Why does a cyclist bend cycle at the time of making circular
turn?
A cyclist must lean into a turn to prevent tipping over in the other direction.The frictional force provides the centripetal force necessary to turn the cyclist to the left.But the frictional force also produces a clockwise torque that will cause the rider and the bicycle to tip clockwise to the right.The force is provided by the friction of the tires.
Answer:
to become stable
Explanation:
when it bends it body, it moves closer to the center of gravity which makes the bicycle stable and hence the turn can be taken easily
A hiker caught in a rainstorm absorbs 1.00 L of water in her clothing. If it is windy so that the water evaporates quickly at 20 ∘C, how much heat is required for this process?
Answer:
2260000 J
Explanation:
From the question,
Q = ml.................... Equation 1.
Where Q = Heat, m = mass of water, l = specific latent heat of vaporization.
But we can get the mass o water using the formula of density.
D = m/v........... Equation 2
Where D = density of water, v = volume of water.
make m the subject of the formula in equation 2
m = D×v............ Equation 3
Substitute equation 3 into equation 1
Q = D×v×l................. Equation 4
Given: v = 1.00 L = 0.001 m³.
Constant: l = 226000 J/kg, D = 1000 kg/m³
Substitute these values into equation 4
Q = 0.001(2260000)(1000)
Q = 2260000 J
What is the maximum speed with which a 1200-kg car can round a turn of radius 90.0 m on a flat road if the coefficient of static friction between tires and road is 0.70?
2. Is this result independent of the mass of the car?
Answer:
78.6m/s
Explanation:
We know that frictional force also contributes to the centripetal force that keeps the car in circular motion in the turn
And is given as
F= mv²/r
But the frictional force is
F= ugm
= = 0.7*1200*9.8= 8232N
To find maximum velocity v we say
V= √F x r/m
= √ 8232* 90 /1200
= 78.6m/s
2. Yes it is independent of mass of car
Answer:
The value is [tex]v = 24.85 \ m/s[/tex]
Yes
Explanation:
From the question we are told that
The mass of the car is [tex]m= 1200 \ kg[/tex]
The radius is [tex]r = 90 \ m[/tex]
The coefficient of static friction is [tex]\mu_s = 0.70[/tex]
Generally at maximum speed the centripetal force acting on the car is equal to the friction force on the car
So
[tex]F_c = F_f[/tex]
[tex]\frac{m v^2}{r} = \mu_s * m * g[/tex]
=> [tex]v = \sqrt{\mu_s * g * r }[/tex]
=> [tex]v = \sqrt{ 0.70 * 9.8 * 90 }[/tex]
=> [tex]v = 24.85 \ m/s[/tex]
Yes the value is independent of the mass because from the equation above we see that v is independent of mass
A typical cell has a membrane potential of -70 , meaning that the potential inside the cell is 70 less than the potential outside due to a layer of negative charge on the inner surface of the cell wall and a layer of positive charge on the outer surface. This effectively makes the cell wall a charged capacitor. Because a cell's diameter is much larger than the wall thickness, it is reasonable to ignore the curvature of the cell and think of it as a parallel-plate capacitor. How much energy is stored in the electric field of a 50--diameter cell with a 7.0--thick cell wall whose dielectric constant is 9.0?
Answer:
energy is stored is 2.2 × 10⁻¹³ J
Explanation:
The capacitance of the cell is given with the expression
C = (KE₀A) / d
k is the dielectric constant, A is the area of the cell, d is the thickness of the cell.
Now given that; the diameter is 50,
Area A = 4πR²
A = 4π × ( 25 × 10⁻⁶ m)²
A = 7850×10⁻¹² m²
our capacitance C = (KE₀A) / d
C = [9 ( 8.85 × 10⁻¹² C²/N.m² × 7850×10⁻¹² m² )] / 7×10⁻⁹ m
C = 8.93 × 10⁻¹¹ F
Now Energy stored
E = 1/2 × CV²
E = 1/2 × (8.93 × 10⁻¹¹ F) × ( 70 × 10⁻³ V)²
E = 2.2 × 10⁻¹³ J
Therefore energy is stored is 2.2 × 10⁻¹³ J
The energy that should be stored in the electric field should be 2.2 × 10⁻¹³ J.
Calculation of the energy:Since
The capacitance of the cell should be
C = (KE₀A) / d
Here,
k is the dielectric constant,
A is the area of the cell,
d is the thickness of the cell.
Now the diameter is 50,
So,
Area A = 4πR²
A = 4π × ( 25 × 10⁻⁶ m)²
A = 7850×10⁻¹² m²
Now
our capacitance C = (KE₀A) / d
C = [9 ( 8.85 × 10⁻¹² C²/N.m² × 7850×10⁻¹² m² )] / 7×10⁻⁹ m
C = 8.93 × 10⁻¹¹ F
Now Energy stored should be
E = 1/2 × CV²
E = 1/2 × (8.93 × 10⁻¹¹ F) × ( 70 × 10⁻³ V)²
E = 2.2 × 10⁻¹³ J
Therefore energy is stored is 2.2 × 10⁻¹³ J.
Learn more about cell here: https://brainly.com/question/22268502
If a proton is traveling north directly above the wire, what is the direction of the magnetic force on the proton due to the wire?
Answer:
Direction is downwards
Explanation:
This is by employing Flemings Right hand rule which says If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge.