Answer:
[tex]F_4=\frac{4}{b}F_1[/tex]
Explanation:
Centripetal force is the net force acting on a body which makes it move along a curved path. This force is always towards the center of curvature.
The centripetal force is given by:
F = mv² / r
where m is the mass of the body, v is the velocity of the body, r is the radius, F is the centripetal force and v²/r is the centripetal acceleration.
Given that:
[tex]\frac{v_4}{v_1}=2\\\\v_4=2v_1\\\\ Also, radius\ of\ lane\ 4(r_4)=2*radius\ of\ lane\ 1\\\\Let\ r_1\ be\ radius\ of\ lane\ 1,m=mass\ of\ runner\ in\ lane\ 1=mass\ of\ runner\ in\ lane\ 4\ \\and\ v_4=velocity\ of\ runner\ in\ lane\ 4.\ Hence:\\\\r_4=b*r_1=br_1\\\\The\ centripetal\ force\ for\ lane\ 4(F_4)\ is:\\\\F_4=\frac{mv_4^2}{r_4}\\\\ F_4=\frac{m(2v_1)^2}{br_1}\\\\F_4= \frac{4mv_1^2}{br_1} \\\\But\ F_1=\frac{mv_1^2}{r_1}\\\\Hence\ F_4=\frac{4}{b}F_1[/tex]
F4 is equal to 4/b F1. A further explanation is provided below.
According to the question,
[tex]\frac{v_4}{v_1} =2[/tex][tex]\frac{r_4}{r_1} = b[/tex]The net force of the object in uniform circular motion will be:
→ [tex]F = \frac{mv^2}{r}[/tex]
∴ [tex]F_1 = \frac{m_1 v_1^2}{r_1}[/tex]
[tex]F_4 = \frac{m_4 v_4^2}{r_4}[/tex]
Now,
→ [tex]\frac{F_1}{F_4} = \frac{m_1}{m_4}\times (\frac{v_1}{v_4} )^2\times \frac{r_4}{r_1}[/tex]
[tex]\frac{F_1}{F_4} = \frac{1}{4}\times b[/tex]
[tex]F_1 = \frac{b}{4} F_4[/tex]
[tex]F_4 = \frac{4}{b} F_1[/tex]
Thus the above response i.e., "option b" is correct.
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Does the KE of a car change more when it accelerates from 22 km/h to 32 km/h or when it accelerates from 32 km/h to 42 km/h
Answer:
The change in kinetic energy (KE) of the car is more in the second case.
Explanation:
Let the mass of the car = m
initial velocity of the first case, u = 22 km/h = 6.11 m/s
final velocity of the first case, v = 32 km/h = 8.89 m/s
change in kinetic energy (K.E) = ¹/₂m(v² - u²)
ΔK.E = ¹/₂m(8.89² - 6.11²)
= 20.85m J
initial velocity of the second case, u = 32 km/h = 8.89 m/s
final velocity of the second case, v = 42 km/h = 11.67 m/s
change in kinetic energy (K.E) = ¹/₂m(v² - u²)
ΔK.E = ¹/₂m(11.67² - 8.89²)
= 28.58m J
The change in kinetic energy (KE) of the car is more in the second case.
A pitcher throws a 0.143-kg baseball toward the batter so that it crosses home plate horizontally and has a speed of 42 m/s just before it makes contact with the bat. The batter then hits the ball straight back at the pitcher with a speed of 49 m/s. Assume the ball travels along the same line leaving the bat as it followed before contacting the bat. If the ball is in contact with the bat for 0.005 0 s, what is the magnitude of the average force exerted by the bat on the ball?
Answer:
200N appox
Explanation:
Step one:
Given data
mass of ball= 0.143kg
initial velocity of ball u= 42m/s
final velocity of the ball= 49m/s
time of impact= 0.005s
Step two
From the relation Ft=mΔv
we can find the average force as
F=mΔv/t
substitute
F=0.143*(49-42)/0.005
F=0.143*7/0.005
F=1.001/0.005
F=200.2
F= 200N appox
The average force is 200N
A 235 kg crate is pulled across a horizontal surface with a force of 760 N applied at an
angle of 30° above the horizontal. Determine the horizontal component of the applied
force
Answer:
658.16N
Explanation:
Step one:
given data
mass m= 235kg
Force F= 760N
angle= 30 degrees
Required
The horizontal component of the force
Step two:
The horizontal component of the force
Fh= 760cos∅
Fh=760cos30
Fh=760*0.8660
Fh=658.16N
17. Calculate the amount of gravitational potential energy at the top of one 4 points hill. The mass of the coaster is 500 kg. The height from the hill to the valley is 59.6 m. Use 9.81 m/s^2 as the acceleration due to gravity. Record your calculations in joules. (Hint: Gravitational PE = mgh)
A. 292.338 m/s^2
B. 3037 J
C. 82.3 kg
D. 292,338 J
Answer: D. 292,338 J
This is the correct answer :)
A generator transforms?
A woman of mass 50 kg is swimming with a velocity of 1.6 m/s. If she stops stroking and glides to a stop in the water, what is the impulse of the force that stops her?
Answer:
– 80 Ns.
Explanation:
From the question given above, the following data were obtained:
Mass (m) = 50 kg
Initial velocity (u) = 1.6 m/s
Final velocity (v) = 0 m/s
Impulse (I) =?
Impulse is simply defined by the following equation:
I = Ft = m(v – u)
I = 50 (0 – 1.6)
I = 50 (–1.6)
I = – 80 Ns
Thus, the impulse of the force that stopped her is – 80 Ns.
NOTE: The negative sign indicates that the net force is in opposite direction to her movement.
NEED HELP ASAP!!!!
A car drives around a racetrack for 30 seconds. What do you need to know to
calculate the average velocity of the car?
O A. The slope of the car's velocity-time graph
O B. The total displacement of the car
O C. The area under the position-time graph
O D. The slope of the car's position-time graph
A car drives around a racetrack for 30 seconds. To calculate the average velocity of the car we need to know about distance. from option B and D we can calculate velocity. Therefore option B and D is correct.
What is velocity ?Velocity is "rate of change of displacement with respect to time".
i.e. v= dx/dt. it is also defined as displacement over time.
i.e. v=Displacement/Time. Velocity shows how much distance can be covered in unit time. It's SI unit m/s. Dimension of velocity is [M⁰ L¹ T⁻¹].
Option A) The slope of the car's velocity-time graph.
it gives Velocity/time. we can not find average velocity with this data.
Option B) The total displacement of the car.
when we know displacement and time, we can calculate velocity. therefore this option is correct.
Option C) The area under the position-time graph.
This gives position×time, which is useless to find velocity.
Option D) The slope of the car's position-time graph.
this gives velocity of the car. Therefore this option is correct.
Hence option B and D is correct, we can calculate average velocity from them.
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Amateur radio operators in the United States can transmit on several bands. One of those bands consists of radio waves with a wavelength near 15.m. Calculate the frequency of these radio waves. Round your answer to 2 significant digits.
Answer:
20 MHz
Explanation:
Since speed of radio waves = speed of light = c and for a wave, v = fλ where v = speed of wave, f = frequency and λ = wavelength.
Given that λ = 15 m and v = c = 3 × 10⁸ m/s
f = v/λ
substituting the values of the variables into the equation, we have
f = v/λ = 3 × 10⁸ m/s ÷ 15 m
= 0.2 × 10⁸ Hz
= 2 × 10⁷ Hz
= 20 × 10⁶ Hz
= 20 MHz
Which type of reaction does this chemical equation represent? 2Na + MgCl2 - 2NaCl + Mg
A. Synthesis
B. Decomposition
C. Single-replacement
D. Double-replacement
The answer is in fact c
The type of reaction the chemical equation represent is a decomposition reaction.
What is decomposition reaction?Decomposition reaction is a type of chemical reaction in which a large compound is broken down or degraded into simpler substances.
Therefore, type of reaction the chemical equation represent is a decomposition reaction.
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A wave is described by y(x,t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimeters and t is in seconds. The angular wave number is:
Answer: 3 radians/meter.
Explanation:
The general sinusoidal function will be something like:
y = A*sin(k*x - ω*t) + C
Where:
A is the amplitude.
k is the wave number.
x is the spatial variable
ω is the angular frequency
t is the time variable.
C is the mid-value.
The rule that we can use to solve this problem, is that the argument of the sin( ) function must be in radians (or in degrees)
Then if x is in meters, the wave-number must be in radians/meters, so when these numbers multiply the "meters" part is canceled.
Then for the case of the function:
y(x,t) = 0.1 sin(3x + 10t)
Where x is in meters, the units of the wave number (the 3) must be in radians/meters. Then the angular wave number is 3 radians/meter.
Angular wave number is measured in rad/s. the angular wave number in the given equation is 10 rad/s.
Angular wave number:
It is the number of wavelengths per unit distance. It is also known as angular frequency. It is measured in rad/s.
For given equation,
[tex]\bold{y(x,t) = 0.1 sin(3x + 10t)}[/tex]
Angular wave number is the parameter which is multiplied by time (t). So, it is the number 10, this will be measured in rad/s.
Therefore, the angular wave number in the given equation is 10 rad/s.
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a tool for studying motion is called?
Answer:
phytochemical
Explanation:phytochemical is a tool for studying motion
Activity
Many characters portrayed in the media suffer from psychological disorders. For example, piglet from Winnie the Pooh has generalized anxiety
disorder and Elsa from the movie Frozen has agoraphobla. Similarly, Identify at least four characters from movies or television shows and
describe the disorders the characters suffer from in the stories.
Answer:
Explanation:
Belle from beauty and the beast has what they call Stockholm syndrome.
Spongebob from Spongebob square pants has what is called Williams-Beuren syndrome
Ariel from the Little Mermaid has what they call Disposophobia.
Alice from Alice in the wonderland has what is called schizophrenia
Scar from the Lion King has what is known as anti social personality disorder.
Like the question suggested, many characters suffer different types of disorder, and I've just listed out a few
A string has its 4th harmonic at 31.5 Hz. What is the fundamental frequency?
Unit= Hz
Answer:
7.9Hz
Explanation:
Step one:
given data
We are told that the fourth harmonic is at 31.5 Hz
We know that harmonics are a multiple of the fundamental frequency, such that if the fundamental frequency is 25Hz, then the second harmonic is
2nd= 2*25= 50Hz
3rd= 3*25= 75Hz........and so on
Step two:
In this problem, we are told that the 4th harmonic is 31.5Hz, that is
4th= 4*f= 31.5
Divide both sides by 4 to get f
f= 31.5/4
f= 7.9 Hz
Hence the first/fundamental frequency is 7.9Hz
Answer:
its 7.9 tried it on acellus
Explanation:
27. The pressure at A is 9.5 atm and the water velocity is 10 m/s. What is the water velocity at point C
Answer:
10 m/s
Explanation:
An airplane normally flying 80km/h north encounters a wind from the west of 10km/h at a right angle to its forward motion a crosswind what will it's resultant velocity be?
Answer:
Resultant velocity of the airplane = 80.62 km/h
Explanation:
Given that,
An airplane normally flying at 80 km/h north encounters a wind from the west of 10km/h at right angle to its forward motion a crosswind.
We need to find the resultant velocity of the airplane. It can be calculated as follows :
[tex]v=\sqrt{80^2+10^2} \\\\v=80.62\ km/h[/tex]
So, the required velocity is 80.62 km/h.
If the melanin lines on the wing are spaced 2.0 μm apart, what is the first-order diffraction angle for green light (λ = 550 nm)?
This question is incomplete, the complete question is;
The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing.
If the melanin lines on the wing are spaced 2.0 μm apart, what is the first-order diffraction angle for green light (λ = 550 nm)?
Answer:
the first-order diffraction angle for green light is 15.96°
Explanation:
Given the data in the question;
from diffraction theory;
nλ = dsin∅
where n is the diffraction order ( 1st order = 1 )
λ is the wavelength ( 550 nm = 550 × 10⁻⁹ m)
d is the grating spacing ( 2.0 μm = 2.0 × 10⁻⁶ m )
∅ is the diffraction angle ( ? )
so we substitute
nλ = dsin∅
sin∅ = nλ / d
sin∅ = (1 × 550 × 10⁻⁹ m) / 2.0 × 10⁻⁶ m
sin∅ = 0.275
∅ = sin⁻¹(0.275)
∅ = 15.96°
Therefore, the first-order diffraction angle for green light is 15.96°
Tim, with mass 73.1 kg, climbs a gymnasium rope a distance of 4.6 m. The acceleration of gravity is 9.8 m/s 2 . How much potential energy does Tim gain? Answer in units of J.
Answer:
3,295.348Joules
Explanation:
Potential Energy = mass * acceleration due to gravity * height
Given the following
Mass = 73.1kg
Acceleration due to gravity = 9.8m/s²
Distance (Height) = 4.6m
Substitute into the formula;
Potential Energy = 73.1 * 9.8 * 4.6
Potential Energy = 3,295.348Joules
Hence Tim gain 3,295.348Joules of energy
Drag the tiles to the correct boxes to complete the pairs.
Identify the type of potential energy described.
Tiles
gravitational
chemical
magnetic
elastic
electric
Answer:
those are all correct. The arrows are matched correctly
A marksman holds a rifle with a mass of 2.57 kg loosely, so it can recoil freely. He fires a bullet with a mass of 3.65 g horizontally with a velocity relative to the ground of 318.4 m/s. What is the final kinetic energy in J of the rifle
Answer:
KE = 0.262 J
Explanation:
given data
rifle with mass Mr = 2.57 kg
bullet with mass Mb = 3.65 g
velocity relative to the ground Vb = 318.4 m/s
solution
we get here final KE of rifle that is express as
KE = 0.5 × Mr × (Vr)² ..............1
here Vr is
Mb × Vb = Mr × Vr .........2
put here value
3.65 × [tex]10^{-3}[/tex] × 318.4 = 2.57 × Vr
Vr = 0.452 m/s
now put value in eq 1 we get
KE = 0.5 × 2.57 × (0.452)²
KE = 0.262 J
1. The directional movement of ions by facilitated diffusion through protein channels is determined by
Answer:
The electrochemical gradient of the ion that is being transported.
Explanation:
Facilitated diffusion through protein is defined as a form of facilitated transport whereby passive movement of ions along concentration gradients are guided by the presence of other ions.
Thus, the electrochemical gradient of the ion being transported is what facilitates it
g 2. _______The property(ies) of a thermal system is (are)(A) temperature or (B) internal energy or (C) work.
Answer:
(A) temperature
Explanation:
Given that thermal properties of a material are those properties that can be observed or felt when the heat is added to the material.
Hence, in this case, the correct answer is "Temperature."
On the other hand, the internal energy is not a thermal property but rather an extensive property that cannot be assessed directly.
Also, work is not a thermal property but rather a process quantity.
Two firefighters are trying to break through a door. One firefighter is heavy, and the other is light. If they run at the same speed, which one is more likely to break through? Explain.
Answer:
The Heavier Firefighter
Explanation:
Generally, more massive objects will have more intertia than less massive objects. As such it takes more force to halt a more massive object if its moving at the same speed as a smaller object. This can also be thought of in the context of Newton's second law. The more force needed to accelerate an object means the more force the object will have.
At equal speed, the firefighter with more weight will have more momentum and exact more force which will cause breakthrough.
According to Newton's second law of motion, the force applied to an object is directly proportional to the product of mass and acceleration of the object.
F = ma
Acceleration is the change in velocity per change in time of motion.
The law can also be written as;
[tex]F = ma = \frac{mv}{t}[/tex]
Also, momentum is given as the product of mass and velocity.
P = mv
Thus, at equal speed, the firefighter with more weight will have more momentum and exact more force which will cause breakthrough.
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Calculate the work needed to lift a block weighing 4 Newton’s a distance of 10 meters. Help me please.
Answer:
W = 40 J
Explanation:
The work done by a force is defined as the dot product of the force and displacement of the object. Therefore, the following formula can be used to find the work done:
[tex]W = F.d = Fd Cos\theta\\[/tex]
where,
W = Work Done = ?
F = Force = Weight of Block = 4 N
d = distance lifted = 10 m
θ = angle between force and displacement = 0°
Therefore,
[tex]W = (4\ N)(10\ m)(Cos\ 0^{0})[/tex]
W = 40 J
What is the electric field inside a hollow sphere with total charge Q distributed evenly along the surface of the sphere
Answer:
0 N/C
Explanation:
Using Gauss' law ∫εE.dA = Q. where E = electric field, dA = differential area and Q = charge enclosed.
Since for r < r₀ where r₀ = radius of the sphere, Q = 0. and ∫εE.dA = ∫εEdAcos180 (since the electric field is directed radially inward opposite to the normal area vector)
∫-εEdA = 0
-εE∫dA = 0
-εEA = 0
E = 0/-εA
E = 0 N/C
Eating 2500 Cal every day a friend of mine maintains a stable weight of 70 kg. One day, after eating 3500 Cal, he decided to do extra exercise to avoid gaining weight. He was doing jumps: he leaves the ground with a speed of 3.3m/s at every jump. Assuming that his body turns energy to mechanical work with a 25 % efficiency, how many jumps he will have to make
Answer:
2721
Explanation:
First, we find the change in calories
E = E(taken) - E(daily)
E = 3500 - 2500
E = 1000 cal
Next, we use the efficiency to find the available metabolic energy
E' = n.E, where n = efficiency
E' = 0.25 * 1000
E' = 250 cal
Converting this cal to J, we have
1 cal = 4.18 J
250 cal = 250 * 4.18 J
250 cal = 1045 kJ
Given that the final velocity is 0, we use equation of motion to find the height, h attained
u² = 2gh
h = u²/2g
h = 3.3² / 2 * 9.81
h = 10.89 / 19.62
h = 0.56 m
Potential energy, E = mgh
E = 70 * 9.8 * 0.56
E = 384 J
Total number of jumps, n =
n = 1045 / 384
n = 2721 jumps
Choose all the answers that apply.
Which of the following characteristics are found in flowering plants?
1. seeds
2. cones
3. reproduction by spores
4. vascular tissue
5. fruit
Answer:
Seeds And Reproduction By Spores
Explanation:
Did on Odyssey
A satellite is launched to orbit the Earth at an altitude of 2.25*107 m for use in the Global Positioning System (GPS). Take the mass of the Earth to be 5.97*1024 kg and its radius 6.38*106 m.
What is the orbital period of this GPS satellite?
Answer:orbital period of this GPS satellite, T= 48,874.4 s
Explanation:
Altitude (h)= 2.25 X 10^7 m
Radius of the Earth ( r)=6.38 X 10^6 m
The distance from center of the Earth to the point is given as
R = r +h
6.38 x 10^6 m+ 2.25 x 10^7 m
=28,880,000=2.888 x 10^7m
Also, Mass of the Earth =5.97 x 10^24 kg
and Gravitational Universal Constant
= 6.67 x 10^-11N.m2/kg2
Orbital period T
= 2π
=2 X 3.142[tex]\sqrt{ (2.888 x 10^7m)^3 /6.67 x 10^-11N.m2/kg2 X 5.97 x 10^24 kg}[/tex]
2X 3.142 [tex]\sqrt{60,491088.9}[/tex]
= 2X 3.142 X 7,777.60
T= 48,874.4 s
I need help, please.
Answer:
sorry I don't know it
Explanation:
Describe a grand challenge in today's society?
how many times can the earth revolve around the sun in the time it takes Jupiter to revolve around the sun once?????????
Answer:
Jupiter fully revolves around the sun in about 11.9 Earth years, where as Earth fully revolves around it in a year.
Explanation:
