R=√20²+40²+2.20.40 cos 50
R=55 N
R/sin β = F/sin α
55/sin 50 = 40/sin α
α = 33°
Which of the following statements is false?
A Heat is a form of energy while temperature is a measure of degree of hotness
B Heart and temperature are linearly related
C Heat can be measured by physical changes due to change in temperature
D Temperature can be measured by physical changes due to change in heat
d. is wrong...the temperature cannot be measured due to physical changes
Most of the bending of light in the eye is done at the air-cornea interface. By what angle (θcornea) is the beam of light shown in Figure deviated as it passes from air to the cornea if the incident angle is θi = 23.6°? The refractive index of air is nair = 1.00, the refractive index of the cornea is ncornea = 1.38. Explain why θcornea< θi?
The angle (θcornea) when light passes from air to cornea is 16.86°
What is Snell's law?It states that the ratio of sine of angle of incidence and angle of refraction is equal to the refractive index of second medium to the first medium.
sini/sinr =n₂ / n₁
Most of the bending of light in the eye is done at the air-cornea interface. The beam of light deviated as it passes from air to the cornea if the incident angle is θi = 23.6°.
Given the angle of incidence i = 23.6°, refractive index of air n₁ =1, refractive index of cornea n₂ = 1.38, then the angle of refraction at cornea is
sinr = sini x (n₁/n₂)
Plug the values, we get
sinr = sin23.6 x (1/1.38)
sinr = 16.86°
The angle of refraction is less than angle of incidence due to refraction.
Thus, the angle (θcornea) when light passes from air to cornea is 16.86°
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In a recent study of how mice negotiate turns, the mice ran around a circular 90∘ turn on a track with a radius of 0.10 m. The maximum speed measured for a mouse (mass = 18.5 g) running around this turn was 1.39 m/s. Part A What is the minimum coefficient of friction between the track and the mouse's feet that would allow a turn at this speed?
The minimum coefficient of friction between the track and the mouse's feet that would allow a turn at this speed without sleeping is 1.97.
Minimum coefficient of frictionThe minimum coefficient of friction is calculated as follows;
F = μmg = mac
μmg = mac
where;
ac is centripetal accelerationμg = ac
μg = v²/r
μ = v²/rg
where;
μ is the minimum coefficient of frictionv is velocityr is radius of the pathg is acceleration due to gravityμ = (1.39²)/(0.1 x 9.8)
μ = 1.97
Thus, the minimum coefficient of friction between the track and the mouse's feet that would allow a turn at this speed without sleeping is 1.97.
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What is matter ?
.......................
Answer:
Something which occupies space and have mass.
The following equation shows the position of a particle in time t, x=at2i + btj where t is in second and x is in meter. A=2m/s2, b=1m/s.
Find
A, the average velocity of the particle in the time interval t₁=2sec and t₂=3sec
B, the velocity and acceleration at any time t.
C, the average acceleration in the time interval given in part (a)
(a) The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 10 m/s.
(b) The velocity and acceleration at any time t is v = (4ti + j) m/s and a = a = 4i m/s²
(c) The average acceleration in the time interval given in part (a) is 3.98 m/s².
Position of the particlex = at²i + btj
x = 2t²i + tj
Average velocity, at t₁=2sec and t₂=3secΔv = Δx/Δt
x(2) = 2(2)²i + 2j
x(2) = 8i + 2j
|x(2)| = √(8² + 2²) = 8.246
x(3) = 2(3)²i + 3j
x(3) = 18i + 3j
|x(3)| = √(18² + 3²) = 18.248
Δv = (18.248 - 8.246)/(3 - 2)
Δv = 10 m/s
Velocity and acceleration at any time, tv = dx/dt
v = (4ti + j) m/s
a = dv/dt
a = 4i m/s²
Average accelerationv(2) = 4(2)i + j
v(2) = 8i + j
|v(2)| = 8.06 m/s
v(3) = 4(3)i + j
v(3) = 12i + j
|v(3)| = 12.04 m/s
a = (12.04 - 8.06)/(3 - 2)
a = 3.98 m/s²
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A 0.15-kilogram baseball moving at 43 meters per second was stopped by the catcher’s glove in 0.050 seconds. What was the average force exerted on the ball by the glove? Round your answer to two significant figures.
The average force exerted on the ball by the glove will be 129 N.
What is force?Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.
Given data;
Mass,(m)=0.15-kilogram
Initial speed,u=43 meters per second
Time period,t= 0.050 seconds
Average force exerted,F=?
The average force exerted on the ball by the glove is;
[tex]\rm F = m\frac{v-u}{t} \\\\ F=0.15( \frac{43-0}{0.050} )\\\\ F=129 N[/tex]
Hence, the average force exerted on the ball by the glove will be 129 N.
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Honey bees beat their wings, making a buzzing sound at a frequency of 2.3 × 102 hertz. What is the period of a bee's wing beat?
Name the inertia in the following cases.
A passenger jumping out of a moving bus falls forward.
Answer:
inertia of motion
Explanation:
it's because when a passenger is jumping from a bus his/her body is in motion after falling in a road he/she remains or tends to remain in the state of motion that is the reason
A mass of (200 g) of hot water at (75.0°C) is mixed with cold water of mass M at (5.0°C). The final temperature of the mixture is (25.0°C). What is the mass of the cold water (M)?
Answer:
500 g
Explanation:
Specific heat of water = 1 j/g-c
Heat given up by hot water = 200(75-25)(1) = 10 000 j
this is the heat GAINED by the cold water
10000 j = x ( 25 -5)(1)
x =500g
A 2100-W hair dryer is operated on a 120-V
circuit for 12 min. If electricity
costs $0.25/kWh, what was the cost (in
cents) of using the blow dryer? Round final
answer to the nearest cent.
Answer:
cost=$15
Explanation:
given;
P= 2100 W
t= 12'= 720 sec=0.2h
V= 120 V
required;
Energy?
cost?
solution;
Energy(kWh) = power*time(in hour)
E=2100*0.2= 420 kWh
cost= 420 kWh* $0.25/kWh
cost= $15
since blow dryer use 120-V
A cannonball is shot horizontally off a high castle wall at 47.4 m/s. What is the magnitude of the cannonball's velocity after 1.23 s? (Ignore direction)
The magnitude of the cannonball's velocity after 1.23 s will be 59.46 m/sec.
What is velocity?The change of distance with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.
The given data in the problem is
u is the initial velocity of canonball= 47.4 m/sec
g is the acceleration of free fall = 9.81 m/sec²
v is the velocity after 1.23 s
According to Newton's first equation of motion,
[tex]\rm v=u +gt \\\\ v= 47.4 \ m/sec + 9.81 \ m/sec^2 \times 1.23 sec \\\\\ v=59.46 \ m/sec[/tex]
Hence, the magnitude of the cannonball's velocity after 1.23 s will be 59.46 m/sec.
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A 0.6 kg ball moving to the right at 12 m/s makes a head on elastic collision with a 0.3 kg ball traveling to the left at 3 m/s.
The velocity of the 0.6 kg ball initially after the collision is
As the pressure on a sample of gas increases, the volume of the sample
Decrease
Stays the same
Increase
Answer:
decreases
Explanation:
because all the particles are wanting to say together and hit each other in a small area
what is the frequency of the photon emitted by a hydrogen atom when its electron drops from the n = 6 to n = 4 energy level?
The frequency of the photon emitted by a hydrogen atom is [tex]26.2*10^-^4 hz[/tex]
What are Photons?A particle representing a quantum of light or other electromagnetic radiation. A photon carries energy proportional to the radiation frequency but has zero rest mass.
In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ:
v = c/λ
Since the wavelength λ is in the bottom of the fraction, the frequency is inversely proportional to the wavelength.
v = c/λ
v= [tex]\frac{3*10^8}{434*10^-^9} = 6.91*10^1^4 Hz[/tex]
By using Rydberg's formula,
1/λ [tex]= Rz^2(\frac{1}{n_1^2} - \frac{1}{n_2^2})[/tex]
1/λ = [tex]109677 *(\frac{1}{4^2} - \frac{1}{6^2}) = 3808.22 cm^-^1[/tex]
λ = [tex]26.2*10^-^4 hz[/tex]
[tex]26.2*10^-^4 hz[/tex] is frequency of the photon emitted by a hydrogen atom.
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Jason while driving on Kukum highway at 70 m.s – 1 seeing the traffic light turn red, he applies the brake and comes to rest in a time of 2 seconds. What is his deceleration?
Answer:
35 m/s^2
Explanation:
Decceleration = change in velocity / change in time
= ( 70 m/s ) / 2 seconds = 35 m/s^2
DEcceleration = 35 m/s^2
Jason's speed changes by - 35 m/s^2
Compare/Contrast the Jovian planets in terms of their size (vs. Earth), composition (elemental), location (relative to the Sun), major moons (name a few), orbital period (Earth years), and rotational period (Earth time).
a) Jupiter
b) Saturn
c) Uranus
d) Neptune
Jupiter is the largest. the closest Jovian planet to the sun is Jupiter and most farthest is Neptune. moons of Jupiter are Europa, lo, Ganymede, etc. Saturn has an orbital period equal to 29 earth years. Uranus's rotational period is equal to 17h 14m.
In terms of size-
Earth- 6,371 kmJupiter- it is 11 times larger than the earth in terms of diameterSaturn- it is the next largest planet. Saturn is 9 times bigger than the earth. Uranus- it is roughly 4 times larger than the earth. Neptune-it is roughly 4 times larger than the earth same as Uranus.In terms of location-
Jovian planets are generally farther from the sun while terrestrial plants are closer to the sun. therefore Jupiter, Saturn, Uranus, and Neptune are away from the sun whole earth is closer to the sun.
In terms of moons-
Jovian planets have more moons as compared to earth. Jupiter has 53 moon, Uranus has 27 Miranda, ariel ,Oberon) while the earth has one moon.
In terms of the orbital period-
Jovian planets have a longer orbital period than earth as they are further from the sun.
In terms of the rotational period-
The rotational period of the Jovian planet is approximately 10 to 17 hours.
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Can you put this image back together? Type the correct order of letters below.
Answer:
CABD
.....................
The image is cut and jumbled and placed into different places, so the correct order of the image that it can be back together is CABD.
What is an image?A specific piece of something is an image. It can provide information to the optical system in two dimensions, three components, or in another way. An item that mimics a subject, such as a picture or other two-dimensional image, might be considered an image. An image in the context of signal analysis is a dispersed color amplitude.
A graphical image need not make use of the complete visual system. A common illustration of this is a grayscale image, which does not employ color, but instead relies on the visual game's sensitivity to brightness across all wavelengths. Even if it doesn't make proper use of the visual system, a black-and-white and white visual depiction of something is nonetheless an image.
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Two very large charged parallel metal plates are 13.0 cm c m apart and produce a uniform electric field of 3.40×106 N/C N / C between them. A proton is fired perpendicular to these plates with an initial speed 5.20 km/s k m / s , starting at the middle of the negative plate and going toward the positive plate.
The work done by the electric field on the proton when it reaches the positive plate willl be 9.1 ×10⁻¹⁵ J.
What is an electric field?A physical field that surrounds electrically charged particles and exerts a force on all other charged particles in the field, either attracting or repelling them, is referred to as an electric field,
The electric field formula is as follows:
E = F /Q
Where,
The electric field is denoted by the letter E.
F is a powerful letter.
The charge is Q.
The potential difference between the plate;
[tex]\rm V = E d \\\\ V = 3.40 \times 10^6 \times 0.13 \ m \\\\ V= 442000 \\\\ V = 4.42 \times 10^5 \ v[/tex]
Force on the charged particle ;
[tex]\rm F = qV \\\\ F= 1.6 \times 10^{-19} \times 4.42 \times 10^ 5 \\\\\ F = 7.0 \times 10^{-14} \ N[/tex]
Work done in order to move the charge;
[tex]\rm W = F \times d \\\\ W= 7.0 \times 10^{-14} \ N \times 0.13 m \\\\ W=9.1 \times 10^{-15} \ J[/tex]
Hence, the work done by the electric field on the proton when it reaches the positive plate willl be 9.1 ×10⁻¹⁵ J.
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How much heat is required to convert 12.0 g of ice at -10.0°C to steam at 100.0°C. Express your answer in joules, calories, and Btu.
A snowboarder on a slope starts from rest and reaches a speed of 4.2 m/s after 7.3 s
The car's acceleration will be 0.575 m/s².The unit of acceleration is m/sec².
What is acceleration?The rate of velocity change concerning time is known as acceleration.
Given data;
Initial velocity, u= 0 m/s
Final velocity, v= 4.2 m/s
Time elapsed, t = 7.3 seconds.
To find ;
Acceleration, a
The acceleration when the change in velocity is observed by the formula as:
a= (v-u)/(t)
Substitute the given values:
a= (4.2-0)/(7.3)
a=(4.2)/(7.3)
a= 0.575 m/s²
Hence, the car's acceleration will be 0.575 m/s².
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The value of acceleration due to gravity (g) on a point 10,000 kilometers above sea level is about 1.49 meters/second2. How much will an object, which weighs 98 newtons on the surface of Earth, weigh on this point? The value of acceleration due to gravity on Earth is 9.8 meters/second2.
An object, which weighs 98 N on the surface of Earth, weigh on this point is 2.23 x 10²⁴ kg.
What is gravity?The force of attraction felt by a person at the center of a planet or Earth is called as the gravity.
Given, the Earth has the acceleration due to gravity, g = 9.81 m/s².
Force of gravity W = mass x acceleration due to gravity
98N = m x 9.8m/s²
m = 10 kg
The value of acceleration due to gravity (g) on a point 10,000 km above sea level is about 1.49 m/s².
The acceleration due to gravity and mass is related as
g = GM/R²
where G = gravitational constant = 6.67 x 10⁻¹¹ N.m²/kg² and R is the distance between two masses.
Substituting the values, we get
1.49 m/s² = 6.67 x 10⁻¹¹ N.m²/kg² x M/ (10000 x 10³ m)²
M = 2.23 x 10²⁴ kg
Therefore, an object will weigh on this point is 2.23 x 10²⁴ kg
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The half-life of Iodine-131 is 8.0252 days. If 14.2 grams of I-131 is released in Japan and takes 31.8 days to travel across the Pacific, how much I-131 will be left by the time it reaches California?
Answer:
Explanation:
Half-life problems are modeled as exponential equations. The half-life formula is [tex]P=P_o\left (\dfrac{1}{2} \right)^{\frac{t}{k}}[/tex] where [tex]P_o[/tex] is the initial amount, [tex]k[/tex] is the length of the half-life, [tex]t[/tex] is the amount of time that has elapsed since the initial measurement was taken, and [tex]P[/tex] is the amount that remains at time [tex]t[/tex].
[tex]P=14.2\left (\dfrac{1}{2} \right)^{\frac{t}{8.0252}}[/tex]
Deriving the half-life formula
If one forgets the half-life formula, one can derive an equivalent equation by recalling the basic an exponential equation, [tex]y=a b^{t}[/tex], where [tex]t[/tex] is still the amount of time, and [tex]y[/tex] is the amount remaining at time [tex]t[/tex]. The constants a and b can be solved for as follows:
Knowing that amount initially is 14.2g, we let this be time zero:
[tex]y=a b^{t}[/tex]
[tex](14.2)=ab^{(0)}[/tex]
[tex]14.2=a *1[/tex]
[tex]14.2=a[/tex]
So, [tex]a=14.2[/tex], which represents out initial amount of the substance, and our equation becomes: [tex]y=14.2 b^{t}[/tex]
Knowing that the "half-life" is 8.0252 days (note that the unit here is "days", so times for all future uses of this equation must be in "days"), we know that the amount remaining after that time will be one-half of what we started with:
[tex]\left(\frac{1}{2} *14.2 \right)=14.2 b^{(8.0252)}[/tex]
[tex]\dfrac{7.1}{14.2}=\dfrac{14.2 b^{8.0252}}{14.2}[/tex]
[tex]0.5=b^{8.0252}[/tex]
[tex]\sqrt[8.0252]{\frac{1}{2}}=\sqrt[8.0252]{b^{8.0252}}[/tex]
[tex]\sqrt[8.0252]{\frac{1}{2}}=b[/tex]
Recalling exponent properties, one could find that [tex]\left ( \frac{1}{2} \right )^{\frac{1}{8.0252}}=b[/tex], which will give the equation identical to the half-life formula. However, recalling this trivia about exponent properties is not necessary to solve this problem. One can just evaluate the radical in a calculator:
[tex]b=0.9172535661...[/tex]
Using this decimal approximation has advantages (don't have to remember the half-life formula & don't have to remember as many exponent properties), but one minor disadvantage (need to keep more decimal places to reduce rounding error).
So, our general equation derived from the basic exponential function is:
[tex]y=14.2* (0.9172535661)^t[/tex] or [tex]y=14.2*(0.5)^{\frac{t}{8.0252}}[/tex] where y represents the amount remaining at time t.
Solving for the amount remaining
With the equation set up, substitute the amount of time it takes to cross the Pacific to solve for the amount remaining:
[tex]y=14.2* (0.9172535661)^{(31.8)}[/tex] [tex]y=14.2*(0.5)^{\frac{(31.8)}{8.0252}}[/tex]
[tex]y=14.2* 0.0641450581[/tex] [tex]y=14.2*(0.5)^{3.962518068}[/tex]
[tex]y=0.9108598257[/tex] [tex]y=14.2* 0.0641450581[/tex]
[tex]y=0.9108598257[/tex]
Since both the initial amount of Iodine, and the amount of time were given to 3 significant figures, the amount remaining after 31.8days is 0.911g.
Find the magnitude of this
vector:
The magnitude of the vector is 34.092 N
What is resultant?The resultant is the square root of sum of square of the vector component of x and y direction.
R =√ [(Nx)² +(Ny)²]
Given is the vector with horizontal length of the vector = -28.7 m and the vertical length of the vector = 18.4 m
The resultant will be
R =√ [(-28.7)² +(18.4)²]
R = 34.092 N
Thus, the magnitude of the vector is 34.092 N.
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Places rich in limestone and gypsum have hard water . why ??
Answer:
Hard water is formed when water percolates through deposits of limestone, chalk or gypsum which are largely made up of calcium and magnesium carbonates, bicarbonates and sulfates.
Explanation:
Hard water is formed when water percolates through deposits of limestone, chalk or gypsum which are largely made up of calcium and magnesium carbonates, bicarbonates and sulfates.
Answer:
Hard water indicates a high amount of minerals.
Explanation:
This most often occurs when natural water sources pass through mineral deposits such as limestone or chalk. The process leads to a relatively high level of calcium, iron, and magnesium.
Grains (pounds)
Nonfat/1% milk (gallons)
Poultry (pounds)
Seafood (pounds)
12
Vegetables (pounds)
271
1
Yogurt (pounds)
Fats and oils (pounds)
55
24
52
Soft drinks (gallons)
123
150
Sugars (pounds)
Source: U.S. Department of Agriculture, Hope Health Letter, April 1999
135
2
34
More people are:
What assumption can be made about the eating habits over the years?
6
63
15
320
4
67
O
A. becoming vegetarians
OB. eating more beef than chicken
OC. consuming whole milk dairy products
D. trying to eat healthier foods
E. eliminating soft drinks from their diets
Answer:
D. trying to eat healthier foods
Explanation:
What is the spring constant if 85.0J of energy is stored when a spring is compressed 0.400m?
A.1060N/m
B.212N/m
C.531N/m
D.425N/m
Answer:
212N/m
Explanation:
First of all, what is spring constant
As per Hooke's law, The restoring force applied by the spring is proportional to the change in length, and restoring force is directed towards the equilibrium position. The proportionality constant is called the spring constant and it is a measure of the stiffness of the spring. So as Hooke's law
F = -Kx
Where
F -> Restoring force
K-> Spring constant
x -> change in length
the negative sign indicates it is acting toward the center
Rearranging this for the Spring constant, Spring constant formula is given by
k = Fx
Unit of Spring Constant is Newton/meter
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Imagine that a single cell below goes through four cell divisions.
How many cells are produced? To find out, draw the parent cell
and cells present after each division. Then write the number of
cells in the space below each drawing. (Hint: the number of cells
doubles with each division.)
Two, four, eight and sixteen cells are produced from first, second, third and fourth cell division respectively.
How many cells are produced?When the body cell passes through cell division process, it divides into two daughter cells. In the second cell division, two cells divides into four cells. In the third cell division, the four cells divides into eight cells. In the fourth cell division, the eight cells divides and sixteen cells are produced.
So we can conclude that two, four, eight and sixteen cells are produced from first, second, third and fourth cell division respectively.
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The pressure of a gas (relative to vacuum) inside a rigid container at 0 °C is:
A) The same as at 25 °C.
B) Not zero, but somewhat less than it would be at 25 °C.
C) zero
The pressure of a gas inside a rigid container at 0 °C will not be zero, but will somewhat be less than it would be at 25 °C.
Temperature and pressure of gasesAccording to Charle's law of gases, the pressure of a gas is directly proportional to its temperature. This is based on the condition that the volume of the gas does not change.
Thus, for a gas inside a rigid container, the pressure at 0 °C may not be zero. However, the pressure will be less than it would be if the temperature were to be 25 °C.
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It takes a minimum distance of 76.50 m to stop a car moving at 15.0 m/s by applying the brakes (without locking the wheels). Assume that the same frictional forces apply and find the minimum stopping distance when the car is moving at 32.0 m/s.
The minimum stopping distance when the car is moving at 32.0 m/s is 348.3 m.
Acceleration of the car
The acceleration of the car before stopping at the given distance is calculated as follows;
v² = u² + 2as
when the car stops, v = 0
0 = u² + 2as
0 = 15² + 2(76.5)a
0 = 225 + 153a
-a = 225/153
a = - 1.47 m/s²
Distance traveled when the speed is 32 m/sIf the same force is applied, then acceleration is constant.
v² = u² + 2as
0 = 32² + 2(-1.47)s
2.94s = 1024
s = 348.3 m
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Need help with this question!
Answer:(note that values will be on top in small)
cobalt :- 60Co
potassium :- 40K
neon :- 24Ne
lead :- 208Pb
