In this problem, you will apply kinematic equations to a jumping flea. Take the magnitude of free-fall acceleration to be 9.80m/s2 . Ignore air resistance. A flea jumps straight up to a maximum height of 0.460m . What is its initial velocity v0 as it leaves the ground?
Answers
When the flea reaches its maximum height, its speed is zero.
(That's why it doesn't go any higher than that.)
Its average speed all the way up is
(1/2) (V₀ + 0) = V₀ / 2 .
The time it takes for the original speed to dribble down to zero is
V₀/g = V₀/9.8 .
Distance covered = (Average speed) x (time in motion)
0.46 m = (V₀/2) x (V₀/9.8)
0.46 = V₀² / 19.6
V₀² = (0.46 x 19.6) = 9.016
V₀ = √9.016 = 3 m/s (rounded)
xf = xi + vi(t) + 1/2(a)t^2.
0 = 0 + 2.62(t) + 1/2(-9.81)t^2
0 = 2.62t - 4.905t^2
4.905t = 2.62
t = 2.62/4.905
t = 0.5341488277268093781855249745158
time in three significant figures:
t = 0.534.
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In your own words, explain why we see a rainbow or colorful sunset. Explain the properties and interactions that make this display possible.
Answers
Data;
- Power = 1200W
- Time/day = 10 mins
Power
The is the rate of energy used to time. It is the measure of expedience of energy.
a). How many minutes is the dryer used in a month.
Assuming there 30 days in a month;
This shows that the dryer is used 300 minutes in a month.
b). How many hours is the dryer used in a month.
To solve this problem, we simply need to convert the value of (a) from minutes to hours.
The dryer was used for a total of 5 hours in a month.
c). The power of the dryer in kilowatt.
To convert the power in watt to kilowatt, we divide by 1000.
The power in kilowatt is 1.2kw
d). How many kilowatt/hr of electricity used in a month.
The dryer consumes 6kw/h in a month.
e). If the town charges $0.15/kwh, the cost in a month
The cost of the dryer in a month is $0.9.
Learn more on power here;
5 hours
1.2 killowatt
6 killowatt hour
6*0.15=0.9
$0.9
photon?
(1) 1.86 × 10^22 J (3) 4.14 × 10^−19 J
(2) 1.44 × 10^2 J (4) 3.18 × 10^−26 J
Answers
Energy = （6.626 x 10^-34*3.00 x 10^8)/（4.80 × 10^−7）= 4.14*10^-19 J, which is 3.
Normally, when solving these equations, don't forget to check the units are correct (eg. wavelength is in meters) and dont forget to include the units in the calculation.
Taking into account the definition of photon, energy of a photon, wavelength, frecuency and propagation speed, the correct answer is the option (3): The energy of a photon with aa wavelength of 4.80×10⁻⁷ meter is 4.14×10⁻¹⁹ J.
What is a photon and energy of a photon
You have to know that electromagnetic radiation carries energy, which can be absorbed or emitted. To explain the processes of emission and absorption, Plank and Einstein proposed that the energy of radiation is composed of indivisible units (quanta). In each elemental process only a quantum of light can be emitted or absorbed. Each of these quanta was called a "photon".
The exchanges of energy between matter and radiation take place not continuously, but by discrete and indivisible quantities or quanta of energy. The quantum of energy is proportional to the frequency of radiation.
The relationship between the amount of energy (E) transported by the photon and its frequency (f) is determined by the following expression, where the energy of a photon is obtained by multiplying Planck's constant h by the frequency f of electromagnetic radiation:
E=h×f
What is wavelength, frecuency and propagation speed
Wavelength is the minimum distance between two successive points on the wave that are in the same state of vibration. It is expressed in units of length (m).
On the other side, frequency is the number of vibrations that occur in a unit of time. Its unit is s⁻¹ or hertz (Hz).
Finally, the propagation speed is the speed with which the wave propagates in the medium, that is, it is the magnitude that measures the speed at which the wave disturbance propagates along its displacement.
The propagation speed relate the wavelength (λ) and the frequency (f) inversely proportional using the following equation:
v = f×λ
All electromagnetic waves propagate in a vacuum at a constant speed of 3×10⁸ m/s, the speed of light.
What is the energy of the photon in this case
In this case, you know:
- h= 6.63*10⁻³⁴ Js
- f= v÷λ where v= 3×10⁸ m/s and λ=4.80×10⁻⁷ m
Replacing in the definition of energy of a photon:
E=h× (v÷λ)
E= 6.63×10⁻³⁴ Js× (3×10⁸ m/s ÷4.80×10⁻⁷ m)
Solving:
E= 4.14×10⁻¹⁹ J
Finally, the correct answer is the option (3): The energy of a photon with aa wavelength of 4.80×10⁻⁷ meter is 4.14×10⁻¹⁹ J.
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A. It will be 2.54 g/cm².
B. It will be different from the other chemicals.
C. It will be 1.67 g/cm3.
D. It will be the same as the other reactant.
Answers
Answers
Use the formula:
F = kq1q2/r^2
F = force = 8.3x10^-4N
q1, q2 = charges
r = separatioon
k = constant = 9x10^9 in MKS units
so we have
r = sqrt[k q1 q2/F]
r = sqrt[9x10^9*(-14)x10^-9 * (-6)x10^-9 / 8.3x10^-4 ]
r = 0.0302 m
So the distance between spheres is 0.0302 m
Answers
Answer:
To estimate the final error on the density of the cube, we can consider the errors introduced by both the measurement of its volume and its weight.
1. Volume Measurement:
- The side length of the cube is given as 10 centimeters, and your ruler can measure to 1 mm accuracy.
- So, the error in measuring the side length is ±0.05 cm (half of the smallest measurement unit).
- To calculate volume, you need to cube the side length: Volume = (10 cm)^3 = 1000 cm^3.
- Using the error propagation rule, the relative error in volume is ±0.05 cm / 10 cm = ±0.005.
2. Weight Measurement:
- The weight is given as 1 kg nominally, which is equivalent to 1000 g.
- Your scale has a precision down to 0.1 g.
- So, the error in measuring the weight is ±0.1 g / 1000 g = ±0.0001 (0.01%) relative error.
Now, to calculate the final error in density, you need to consider both errors in volume and weight:
Density = Weight / Volume
Relative Error in Density = (Relative Error in Weight) + (Relative Error in Volume)
Relative Error in Density = (0.0001) + (0.005) = 0.0051 or 0.51%
So, the final estimated error on the density of the cube is approximately ±0.0051 g/cm^3 or ±0.51%.
Final answer:
The density of the cube is calculated using its mass and volume, with potential errors from the measurements of these quantities leading to a total estimated density error of approximately ±3.01%.
Explanation:
The density of an object is given by the formula density = mass/volume. In this case, the mass of the cube is given as 1 kg (or 1000 g for consistency with the scale's precision), and the volume of the cube can be calculated from the given side length using the formula for the volume of a cube, volume = side³, which equals 1000 cm³.
However, there are measurement errors associated with both the ruler and scale. The ruler can measure to the nearest mm (or 0.1 cm), so the error is ±0.1 cm on each measurement of the cube's sides, leading to a volume error of about ±3%. The scale can measure to the nearest 0.1 g, which gives a mass error of about ±0.01%. The total error in the density, obtained by summing these errors, is therefore approximately ±3.01%.
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