Answer:
The value is [tex]p = - 2.63 \ Diopters[/tex]
Explanation:
From the question we are told that
The value of the far point is [tex]a = 40 \ cm = 0.4 \ m[/tex]
The distance of the lens to the eye is [tex]b = 2 \ cm = 0.02[/tex]
Generally
[tex]1 Diopter = > 1 m^{-1}[/tex]
Generally the power spectacle lens needed is mathematically represented as
[tex]p = \frac{1}{d_o } + \frac{1}{d_i}[/tex]
Here [tex]d_o[/tex] is the object distance which for a near sighted person is [tex]d_o = \infty[/tex]
And [tex]d_i[/tex] is the image distance which is evaluated as
[tex]d_i = b - a[/tex]
=> [tex]d_i = 0.02 - 0.4[/tex]
=> [tex]d_i = -0.38 \ m[/tex]
So
[tex]p = \frac{1}{\infty } + \frac{1}{-0.38}[/tex]
=> [tex]p = 0 - 2.63[/tex]
=> [tex]p = - 2.63 \ Diopters[/tex]
calculate the load placed 10m from the fulcrum that can be balanced by an effort of 5 N applied at a distance of 4 m from the fulcrum in a lever
Answer:
A = 2 m from fulcrum
Explanation:
Product of anti clockwise = Product of clockwise moment
5 × 4 = 10 × A
20 = 10 x A
A = 20 / 10
A = 2 m from fulcrum
If the object of mass 30 kg is accelerating at 3 m/s2, What is the net force acting on the object?
3 N
10 N
30 N
900 N
Answer:
Force = Mass × Acceleration
F = MA
F = 30kg × 3ms^-2
F = 90 N
The greater the change in the speed of light in different media
the greater the angle of
Answer:
the angle at which light bends when it enters a different medium depends on its change in speed. The greater the change in speed, the greater the angle of refraction is. For example, light refracts more when it passes from Air to Diamond then it does when it passes from Air to wate.
Answer: Refraction
Explanation:
a half meter ruler is pivoted at its midpoint and balances whaen a weight of 20N is placed at the 10 cm mark and a weight W is placed at the 45 cm mark on the ruleer. Calculate the weight W
The weight W palced at a distance of 45 cm on a half meter ruler pivote at its midpoint is 15 N.
To calculate the weight W, we use the principle of moment.
Principle of moment?It states that, if a body is at equilibrium, the sum of clockwise moment is equal to the sum of anticlockwise moment.
From the question,
Clockwise moment (F×d ) = Anticlockwise moment (W×D).......... Equation1
Make W the subject of the equation
W = Fd/D............. Equation 2Given:
F = 20 Nd = (25-10) = 15 cm = 0.15 mD = (45-25) = 20 cm = 0.2 mSubstitute these values into equation 2
W = 20×0.15/0.2W = 15 NHence, the weight W is 15 N
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A large bagel spins with angular speed w about its center. A smaller bagel spins with triple the angular speed.
How does the period Tlarge of the large bagel compare with the period Tsmall of the small bagel?
Answer:
T large = 3T small
Explanation:
It's just 3 times larger
The activity of mining has direct negative effects on
a. atmosphere
b.hydrosphere
c.biosphere
d.geosphere
Answer:
A
Explanation:
When coal is burned it releases many harmful chemicals into the air, such as methane (greenhouse gas) and contributes to global warming
Plz help
Fill in the blank with the correct observation from the simulation.
As the days go on, the distance that the moon is from the sun in the night sky
A. Stays the same
B. Decreases
C. Increases
Starting at New Moon, The visual distance increases for about 2 weeks, then decreases for about the next 2weeks, until the next New Moon.
On the average, it changes by about 12° per day.
How much force is required to accelerate a 5 kg mass at 20 m/s^2
Hello!
[tex]\large\boxed{F = 100N}[/tex]
Use the equation F = m · a (Newton's Second Law) to solve. Substitute in the given values:
F = 5 · 20
F = 100N
A block of iron at 33.0°C has mass 2.30 kg. If 3.50×104 J of heat are transferred to the block, what is its resulting temperature?
Answer:
66.8°C
Explanation:
dQ = m*cp*dT where:
m = mass of block
cp = specific heat of iron
dT = temperature change
-------
dQ = 3.5 10^4 J
cp = 0.45 Kj / Kg = 450 J / Kg
3.5 10^4 = 2.3 * 450 * dt-----dt = 35000 / 450 * 2.3 = 33.8 °
-------
Final temperature = 33 + 33.8 = 66.8 °C
7. A monkey freefalls for 17.5 seconds. (a) What was the velocity after this time? (b) How far did it fall?
Answer:
a ) Vf = 171.7 [m/s]
b) y = 1502.6[m]
Explanation:
a) To solve this problem we must use the following equation of kinematics.
[tex]v_{f}=v_{o}+g*t[/tex]
where:
Vf = final velocity [m/s]
Vo = initial velocity = 0 (freefall, without initial velocity)
g = gravity acceleration = 9.81 [m/s²]
t = time = 17.5 [s]
Now replacing:
[tex]v_{f} = 0 + 9.81*17.5\\v_{f} = 171.7[m/s][/tex]
Note: The gravity acceleration is positive, since the monkey is moving in the direction of the gravity acceleration.
b)
Now using another equation of kinematics we can calculate the distance traveled.
[tex]v_{f}^{2}=v_{o}^{2}+2*g*y[/tex]
where:
y = distance traveled [m]
[tex]171.7^{2}=0 +2*9.81*y\\y=29480.9/(2*9.81)\\y=1502.6[m][/tex]
A woman starts at the origin and walks 7m along the x-axis. She then turns 90° and walks parallel to the y-axis for 6m. How far is she from the origin? Express your answer in m to the nearest tenth.
Answer:
9.2m
Explanation:
Think of the woman's path as a triangle. She walks 7m horizontally and 6m vertically. These are the two legs of a triangle. In order to find her distance from the origin, we can use pythagorean theorem to find the hypotenuse of the triangle. The hypotenuse will give us the direct measurement from the origin (0,0) to her current point (7,6).
a²+b²=c²
(7)²+(6)²=c²
49+36=c²
85=c²
Find the square roots of both sides to get c=9.21954...
Round your answer to the nearest 10th:
c=9.2m
The woman is approximately 9.2m from the origin.
Solve this question
The density formula is d =
m
V
.
A cylinder of lead has a
diameter of 3 cm and a height of 8 cm. The density of lead is
3
11.4 g/cm³. What is the mass of the cylinder?
The mass of the cylinder made of lead is 644.33 kg.
What is mass?Mass can be defiend as the quantity of matter a contained in a body. The S.I unit of mass is kilogram (kg).
To calculate the mass of the cylindrical lead, we use the formula below.
Formula:
m = πr²hd........... Equation 1Where:
m = Mass of the cylindrical leadh = Height of the cylindrical leadd = Density of the leadr = Radius of the cylindrical leadπ = PieFrom the question,
Given:
r = 3/2 = 1.5 cmd = 11.4 g/cm³h = 8 cm π = 3.14Substitute the values above into equation 1
m = 11.4×3.14×1.5²×8m = 644.33 kgHence, the mass of the cylinder made of lead is 644.33 kg.
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You witness the birth of a littler of puppies.Where were the atoms that make up these puppies come from? How did these atoms form?
Answer:
The atoms come from the mother; it can be comprimised of its diet, nutrience within, and other enzymes within the canine body. According to the law of conservation of matter, they are transformed by never destroyed or created so they must have come from inside or outside in the kother's environment.
Hope this helps.
What happens to the pressure of a gas in a closed container if you double its volume while its temperature is held constant?
Answer:
This question lacks options, the options are:
A) It would increase by a factor of four.
B) It would decrease by a factor of four.
C) It would be halved.
D) It would be doubled.
E) It would not change.
The answer is C
Explanation:
The relationship between the pressure and volume has been explained by BOYLE in his law. Boyle's law states that, at a constant temperature, the volume is inversely proportional to the pressure of a gas. This means that as the VOLUME INCREASES, the PRESSURE DECREASES and vice versa.
P ∝ 1/V or V ∝ 1/P
Hence, based on this explanation, when the volume of a gas in a closed container is doubleb, its pressure will be reduced by half i.e. 1/2. In other words, the pressure will be HALVED.
A cross-country runner runs 10 miles in 40 minutes. What is their average speed?
Answer:
15mil/hr
Explanation:
To make the average speed in mph, we need to get the 40 minutes to an hour. We multiply 40 minutes by 3/2 to get 60 minutes or an hour.
40 x (3/2) = 60
This means that we need to multiply 10 miles by 3/2:
10 x (3/2) = 15 (we get 15 miles)
Average speed is equal to distance over time.
Average speed is 15mil/hr.
Hope this helps!
Light travels about 180 million kilometers in 10 minutes. How far does it travel in 1 minute? How far does it travel in 1 second? Show your reasoning
I need help
Explanation:
180 million km = 10 min
? = 1 min
180 million x 10 = 1,800,000,000 km
180 million km = 600s
? = l s
108,000,000,000km
A rock is at the top og a 20 meter tall hill. The rock has a mass of 10 kg. How much potential energy does it have
Answer:
1962 joules
Explanation:
m = 10 kg
h = 20 m
g = 9.81 ms^-2
PE = ?
PE = MGH
PE = 10 x 9.81 x 20
PE = 1962 joules
Comparing infrared and ultraviolet, we can say that __________. Comparing infrared and ultraviolet, we can say that __________.
Answer:
The appropriate response will be "Infrared has a longer wavelength and lower photon energy".
Explanation:
This same Infrared emission falls between some of the observable but rather microwave components of the electric spectrum. Infrared rays have quite a wavelength longer than ultraviolet light. And indeed the frequency of radiation remains smaller, unlike UV rays. Even before we recognize that the energy (photon) of the visible region has always been equal to the total of waves. Infrared thus has smaller photon intensity versus ultraviolet.If a marble is dropped from a cliff, how fast is the marble going after falling for 3.6 seconds?
PLEEEEAAASSSEEEEEE HELPPPP MEEEE>
Answer:
35.28m/s
Explanation:
Given
Time t = 3.6secs
Required
Final speed v
Using the equation of motion;
v = u + gt
Substitute;
v = 0 + 9.8(3.6)
v = 0 + 35.28
v = 35.28m/s
Hence the speed of the marble is 35.28m/s
A box of mass mis pulled by force Fp at an angle along a frictionless surface. The box accelerates to the night
חס
m
What is the magnitude of the horizontal acceleration?
Answer:
ma / cos theta is the answer you are looking for
A box of mass m is pulled by force Fp at an angle along a frictionless surface and the box accelerates to the right with a magnitude of the horizontal acceleration Fpcosθ/m, therefore the correct option is D.
What is friction?Friction is a type of force that resists or prevents the relative motion of two physical objects when their surfaces come in contact.
The friction force prevents any two surfaces of objects from easily sliding over each other or slipping across one another. It depends upon the force applied to the object.
A box of mass m is pulled by force Fp at an angle along a frictionless surface. The box accelerates to the right
The only horizontal force responsible for the movement of the box is the horizontal component of the force Fp which is Fpcosθ
By using equilibrium of horizontal forces
ΣFh =0
ma= Fpcosθ
a =Fpcosθ/m
The magnitude of the horizontal acceleration is Fpcosθ/m,therefore the correct option is D.
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a car is initially at rest. ten seconds later it is moving 30 m/s. what is the car's acceleration
Answer:
The car's acceleration is [tex]3\ m/s^2[/tex]
Explanation:
Constant Acceleration Motion
It's a type of motion in which the velocity of an object changes uniformly over time.
The final speed is given by:
[tex]v_f=v_o+at[/tex]
Where a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:
Using the equation above we can solve for a:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
The car is initially at rest (vo=0) and t=10 seconds later it's moving at vf=30 m/s, thus its acceleration is:
[tex]\displaystyle a=\frac{30-0}{10}[/tex]
[tex]\displaystyle a=\frac{30}{10}=3[/tex]
[tex]a = 3\ m/s^2[/tex]
The car's acceleration is [tex]3\ m/s^2[/tex]
A light wave passes through an aperture (that is, a narrow slit). When it does so, the degree to which the wave spreads out will be...
Explanation:
Single slit diffraction
Diffraction is the phenomenon of spreading out of waves as they pass through an aperture or around objects. Diffraction occurs when the size of the aperture or obstacle is of the same order of magnitude as the wavelength of the incident wave. For very small aperture sizes, the vast majority of the wave is blocked. in case of large apertures the wave passes by or through the obstacle without any significant diffraction.
weight of Ali is 500andN.he is standing on the ground with an area of 0.025 m^2 area .we can find pressure under his feet. what is it?
Answer:
20000 Pa
Explanation:
Pressure is defined as the force per unit area.
Mathematically : P =F/A where F is force and A is area
Force = 500 N
Area= 0.025 m²
P= 500/0.025
P= 20000 Pa
Total internal reflection at the air liquid surface is observed for an unknown liquid when the angle of incidence is 43 degrees. What is the index of refraction of this unknown liquid?
a. 0.68
b. 1.0
c. 1.47
d. 1.59
Answer:
c. 1.47
Explanation:
Snell's law states that there exists always a fixed relationship between the index of refraction of two transparent media, and the sines of the incident and refraction angles, as follows:[tex]\frac{n_{i} }{n_{r} } = \frac{sin_{\theta r} }{sin_{\theta i} } (1)[/tex]
When there is a total internal reflection, this means that light can't go across the border between two media, i.e., the refraction angle is 90º, which means that sin θr = 1Since the refraction index for air is 1, i.e. nr =1, this means that (1) , for total internal reflection becomes:[tex]n_{i} = \frac{1}{sin_{\theta i} } = \frac{1}{sin 43} = 1.47 (2)[/tex]
A small plane starts from rest and accelerates uniformly to the east to a takeoff velocity of 70 m/s in 5 seconds. What is the plane’s acceleration?
Please help!
The acceleration of the plane after 5 seconds will be 14 m/s².
What is acceleration?The rate of change of velocity with respect to time is called acceleration. Mathematically -
a = Δv/Δt
Given is a small plane that starts from rest and accelerates uniformly to the east to a takeoff velocity of 70 m/s in 5 seconds.
The acceleration of the body can be calculated as follows -
a = Δv/Δt
a = (70 - 0)/(5 - 0)
a = 70/5
a = 14 m/s²
Therefore, the acceleration of the plane after 5 seconds will be 14 m/s².
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The half-life for radioactive decay (a first-order process) is 24,000 years. How many years does it take for one mole of this radioactive material to decay so that just one atom remains?
Answer: it will take 1.9 × 10⁶ yrs for one mole of the radioactive material to decay so that just one atom remains
Explanation:
Given that;
Half life t_1/2 = 24,000 years
initial amount of radio active element = 1 mole
now one mole of a substance has Avagadro number of atoms which is initially 6.023 × 10²³ which are present and finally only 1 atom is left
using the formula
t_1/2 = 0.693/k
In[ N₀/N_t] = kt
N₀ is the initial amount, N_t is the amount left after t time, t is the time, k is the rate constant.
now we substitute
t_1/2 = 0.693/k
k = 0.693/ t_1/2
k = 0.693 / 24,000 years
k = 0.000028875 yr⁻¹
so
In[ N₀/N_t] = kt
t = 1/0.000028875 yr⁻¹ In [ 6.023 × 10²³ / 1 ]
= 34632.0346 In[6.023 × 10²³]
= 34632.0346 × 54.7550
= 1896277.0545 yrs ≈ 1.9 × 10⁶ yrs
Therefore it will take 1.9 × 10⁶ yrs for one mole of the radioactive material to decay so that just one atom remains
If a vehicle is traveling at constant velocity and then comes to a sudden stop, has it undergone negative acceleration or positive acceleration? Explain your answer
Answer:
Negative acceleration
Explanation:
Let us assume a vehicle is moving with a constant velocity u and then it comes to a sudden stop.
The initial velocity of the vehicle is u and finally it comes to rest, it means final velocity is 0.
As we know that,
Acceleration is equal to change in velocity divided by time taken.
[tex]a=\dfrac{v-u}{t}\\\\\text{Put v=0}\\\\a=\dfrac{-u}{t}[/tex]
We can see that the value of acceleration is negative. Hence, it leads to negative acceleration.
A 0.50 mº gas tank holds 3.0 moles of ideal monatomic Helium gas at a temperature of 250 K. What is the mms speed of the molecules? (The Boltzmann constant is 1.38 x 10-23 J/K, NA = 6.022 x 1023 molecules/mol.)
Answer:
v = 1247.92 m/s
Explanation:
The formula for kinetic energy is given as follows:
[tex]K.E = \frac{1}{2}mv^2[/tex]
Another formula that is used for Kinetic Energy is given as:
[tex]K.E = \frac{3}{2}KT[/tex]
Comparing both formulae for K.E:
[tex]\frac{1}{2}mv^2 = \frac{3}{2}KT\\\\mv^2 = 3KT\\v = \sqrt{ \frac{3KT}{m}}[/tex]
where,
v = rms speed of helium molecule = ?
K = Boltzmann Constant = 1.38 x 10⁻²³ J/k
T = Absolute Temperature = 250 K
m = mass of helium molecule = 6.646 x 10⁻²⁷ kg
Therefore,
[tex]v = \sqrt{\frac{(3)(1.38\ x\ 10^{-23}\ J/k)(250\ k)}{6.646\ x\ 10^{-27}\ kg}} \\\\[/tex]
v = 1247.92 m/s
If the amplitude of a simple harmonic oscillator is doubled, by what multiplicative factor does the angular frequency change?
Answer:
No change
Explanation:
In a simple harmonic motion, we have that
y = A sin(wt), where
w is the said angular frequency
The angular frequency w, is given as √(k/m)
If the amplitude, A is doubled it will have no corresponding effect on the angular frequency, w, because they do not depend on each other. A is independent of w, and w is independent of A. And as such, no matter the change in either, it doesn't affect the other