Answer:
Momentum(P) = 1336kgm/s
Explanation:
Momentum is the product of the mass and velocity, therefore Momentum(P) is = mass*velocity. since the mass is given 800kg, all we are left with is the displacement 500m and the time 300s which can be used to find the velocity. so velocity is the displacement divided by the time, ie 500/300 which will give us the velocity 1.67m\s. hence we multiply the mass and the velocity and we'll get 1336kgm/s.
What range of the electromagnetic spectrum does this wave belong to?
Answer:
please give me brainlist and follow
Explanation:
Infrared radiation
The infrared part of the electromagnetic spectrum covers the range from roughly 300 GHz to 400 THz (1 mm – 750 nm). It can be divided into three parts: Far-infrared, from 300 GHz to 30 THz (1 mm – 10 μm). The lower part of this range may also be called microwaves or terahertz waves.
For a particular scientific experiment, it is important to be completely isolated from any magnetic field, including the earth's field. The earth's field is approximately 50 μT, but at any particular location it may be a bit more or less than this. A 1.00-mm-diameter current loop with 200 turns of wire is adjusted to carry a current of 0.199 A ; at this current, the coil's field at the center is exactly equal to the earth's field in magnitude but opposite in direction, so that the total field at the center of the coil is zero.
Required:
What is the strength of the earth's magnetic field at this location?
Answer:
50000 μT
Explanation:
From the given information:
the diameter of the loop = 1.0 mm = 0.001 m
no of turns (N) = 200
current (I) = 0.199 A
radius = d/2 = 0.001/2
= 5 × 10⁻⁴ m
Recall that;
the magnetic field at the centre of circular wire is:
[tex]= \dfrac{\mu I N}{2R}[/tex]
[tex]= \dfrac{4 \pi \times 10^{-7} \times 200 \times0.199}{2\times 5\times 10^{-4}}[/tex]
= 0.05 T
= 50000 μT
Since the centre of the earth's magnetic field is given to be equal to the magnetic field produced by the wire, then:
the earth's magnetic field = 50000 μT
Which sentence in the passage can be used to conclude that Eris is a dwarf planet and not a planet?
Erls takes about 557 Earth years to orbit the Sun. It has a mean surface temperature of about 40 Kelvin. It has a nearly spherical shape. It has
several other objects in its orbit, though
few are as massive as itself. Eris is too far away and small to be clearly visible from the Earth. Scientists
used its moon, Dysnomla, to measure it Qris is believed to be slightly more massive than Pluto. However, both of them are smaller than Earth's
Moon. Eris orbits the Sun directly, it is not a satellite of another planet or dwarf planet.
I
think
Answer:
is.......
it has several other objects in its original, though few are as massive as itself........
Answer:
my teachers have always taught me that a dwarf planet cannot have other objects in its orbit seeing that the gravitational force will make it collide with the planet or push it out of the orbit. hope it helps xx
Q1. Which statement is correct
a) Distance and Displacement are the same thing
b) Distance is displacement with direction added
c) Displacement is distance with direction added
Q2. Which statement is true
a) The magnitude of distance and direction must always be the same
b) Distance can be less than displacement
c) Displacement is always the shortest distance between two points
d) Distance follows the exact path while displacement is the straight line distance between starting and ending position
Answer:
C
D
Explanation:
Hydrogen gas is maintained at 3 bars and 1 bar on opposite sides of a plastic membrane which is .3 mm thick. The temperature is 25C, and the diffusion coefficient of hydrogen in the plastic at 25C is 9x10-8 m2/s. The solubility of hydrogen in the plastic membrane is 1.5x10-3 kmol/m3. What is the mass diffusive flux (in kg/m2.s) of hydrogen on the membrane
Answer:
[tex]N_a=1.8*10^{-6}kg/sm^2[/tex]
Explanation:
From the question we are told that:
Thickness of plastic membrane [tex]L_t=0.3mm[/tex]
The temperature of hydrogen [tex]T_h=25 \textdegree C[/tex]
Diffusion coefficient of hydrogen in the plastic [tex]25 \textdegree C \mu=9*10-8m2/s[/tex]
The solubility of hydrogen in the plastic membrane [tex]\+x=1.5*10{-3} kmol/m3[/tex]
Generally the equation for molar conc is mathematically given by
[tex]CA_1=x*bar[/tex]
3bars
[tex]CA_1=1.5*10^{-3}*3[/tex]
[tex]CA_1=4.5*10^{-3}kmol/m^3[/tex]
1bar
[tex]CA_1=1.5*10^{-3}*1[/tex]
[tex]CA_1=1.5*10^{-3}kmol/m^3[/tex]
Generally the equation for molar diffusion flux of Hydrogen N_a is mathematically given by
[tex]N_a=\frac{D{AB}}{\L}(CA_1-CA_2)[/tex]
[tex]N_a=\frac{9*10^{-8}}{0.3*10^-^3} (4.5*10^{-3}-1.5*10^{-3})kmoi/m^-3[/tex]
[tex]N_a=9.*10^{-7}kmol/sm^2*2kh/kmole[/tex]
[tex]N_a=1.8*10^{-6}kg/sm^2[/tex]
A disk with mass 1.64 kg and radius 0.61 meters is spinning counter-clockwise with an angular velocity of 17.6 rad/s. A rod of mass 1.51 kg and length 1.79 meters spinning clockwise with an angular velocity of 5.12 rad/s is dropped on the spinning disk and stuck to it (the centers of the disk and the rod coincide). The combined system continues to spin with a common final angular velocity. Calculate the magnitude of the loss in rotational kinetic energy due to the collision
Answer:
The loss in rotational kinetic energy due to the collision is 36.585 J.
Explanation:
Given;
mass of the disk, m₁ = 1.64 kg
radius of the disk, r = 0. 61 m
angular velocity of the disk, ω₁ = 17.6 rad/s
mass of the rod, m₂ = 1.51 kg
length of the rod, L = 1.79 m
angular velocity of the rod, ω₂ = 5.12 rad/s (clock-wise)
let the counter-clockwise be the positive direction
let the clock-wise be the negative direction
The common final velocity of the two systems after the collision is calculated by applying principle of conservation of angular momentum ;
m₁ω₁ + m₂ω₂ = ωf(m₁ + m₂)
where;
ωf is the common final angular velocity
1.64 x 17.6 + 1.51(-5.12) = ωf(1.64 + 1.51)
21.1328 = ωf(3.15)
ωf = 21.1328 / 3.15
ωf = 6.709 rad/s
The moment of inertia of the disk is calculated as follows;
[tex]I_{disk} = \frac{1}{2} mr^2\\\\I_{disk} = \frac{1}{2} (1.64)(0.61)^2\\\\I_{disk} = 0.305 \ kgm^2[/tex]
The moment of inertia of the rod about its center is calculated as follows;
[tex]I_{rod} = \frac{1}{12} mL^2\\\\I_{rod} = \frac{1}{12} \times 1.51 \times 1.79^2\\\\I _{rod }= 0.4032\ kgm^2[/tex]
The initial rotational kinetic energy of the disk and rod;
[tex]K.E_i = \frac{1}{2} I_{disk}\omega _1 ^2 \ \ + \ \ \frac{1}{2} I_{rod}\omega _2 ^2 \\\\K.E_i= \frac{1}{2} (0.305)(17.6) ^2 \ \ + \ \ \frac{1}{2} (0.4032)(-5.12) ^2\\\\K.E_i = 52.523 \ J[/tex]
The final rotational kinetic energy of the disk-rod system is calculated as follows;
[tex]K.E_f = \frac{1}{2} I_{disk}\omega _f ^2 \ \ + \ \ \frac{1}{2} I_{rod}\omega _f ^2\\\\K.E_f = \frac{1}{2} \omega _f ^2(I_{disk} + I_{rod})\\\\K.E_f = \frac{1}{2} (6.709) ^2(0.305+ 0.4032)\\\\K.E_f = 15.938 \ J[/tex]
The loss in rotational kinetic energy due to the collision is calculated as follows;
[tex]\Delta K.E = K.E_f \ - \ K.E_i\\\\\Delta K.E = 15.938 J \ - \ 52.523 J\\\\\Delta K.E = - 36.585 \ J[/tex]
Therefore, the loss in rotational kinetic energy due to the collision is 36.585 J.
Spiral fracture of bone: Spiral fracture of bone occurs due to twisting of the limb, and is a very common skiing accident. The fracture plane is helical, and is very difficult to heal. Mechanically, it occurs due to an applied torsion load on the bone. Recall that a state of pure shear occurs within the material when torsion is applied on a cylinder, and the bone can be idealized as a cylinder. Let a femur bone be subjected to a torque of T 50 N-m. Assume body weight of the person to be W- 80 Kgs, while each leg is subjected to half of that weight. Given radius of the bone r 10 mm. Compute the principal stresses and shear stresses, as well as orientation of planes on which these stresses are realized.
Answer:
principal stresses :б1 = 32.62mPa б2 = 31.38mPa
Max Shear stress : 16.31 mPa
Orientation of max principle plane = 44.43°
Orientation of minimum principal plane = 134.43°
Explanation:
Given data:
Torque = 50 N-m
weight = 80 kgs
half of weight is subjected to each leg
radius of bone = 10 mm = 0.010 m
a) Determine the principal stresses and shear stress
first calculate the max shear stress ( this will occur in the outermost element
= 16T / π*d^3 where : T = 50 , d = 0.020 m
hence max shear stress = 32 mPa
next determine compressive stress
= ( 40*g) / π/4*d^2 . where : d = 0.020 m , g = 9.81
hence compressive stress = 1.24 mPa
draw and calculate the radius of Mohr's circle
radius of Mohr's circle = 32.0060
Hence principal stresses = 32.0060 ± 0.62
б1 = 32.62mPa
б2 = 31.38mPa
attached below is the remaining part of the solution
A car has a mass of 1.00x10 to the 3rd power kilograms, it has an acceleration of 4.5 meters/seconds, what is the net force on the car?
Explanation:
Net force on the car= mass of the car × acceleration
F=1×10^3×4.5
=4.5×10^3 N
state the Newton 2nd law of motion and also prove that F= ma
Explanation:
F = ma is the formula of Newton's Second Law of Motion. Newton's Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
...
BRAINLIEST DO NOT ANSWER UNLESS YOU KNOW OR I WILL REPORT YOU!!!! I HAVE ALREADY REPORTED TWO PEOPLE
1. Suppose a hammer claw moves a distance of .01 meters to remove a nail. If an output force of 1,500 N is exerted by the claw of the hammer, and you move the handle of the hammer .05 meters, what is the input force.
2. What is the mechanical advantage of a hammer if the input force is 125 N and the output force is 2,000 N?
3. Find the efficiency of a machine that does 800 J of work if the input work is 2,400 J.
4. Find the force needed to lift a 2,000 N weight using a machine with a mechanical advantage of 15.
Answer:
1) 0.01(1500) = 0.05F
F = 300 N
2) 2000/125 = 16
3) 100(800/2400) = 33.3%
4) 2000/15 = 133 N
Explanation:
A musical note has a frequency of 512 Hz. If the wavelength of the note is 0.685 m, what is the speed of the sound of that note?
F. O 0.00120 m/s
G.O 351 m/s
H
345 m/s
J.
841 m/s
Answer:351
Explanation:trust
A musical note has a frequency and the wavelength of the note. The speed of the sound of that note will be 351m/s. The correct option is G.
What is frequency?The frequency is the number of cycle per second.
The wavelength is related to frequency and speed as
f = v/λ
Given is the frequency f = 512Hz and wavelength λ= 0.685m, then the speed of note will be
v =512 Hz x 0.685m
v =350.72 m/s
Speed is approximately 35 m/s.
Thus, the correct option is G.
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Biologists use optical tweezers to manipulate micron-sized objects using a beam of light. In this technique, a laser beam is focused to a very small-diameter spot. Because small particles are attracted to regions of high light intensity, the focused beam can be used to "grab" onto particles and manipulate them for various experiments. In one experiment, a 10 mW laser beam is focused to a spot that has a diameter of 0.62 μm.
a. What is the intensity of the light in this spot?
b. What is the amplitude of the electric field?
Answer:
The correct answer is:
(a) [tex]3.31\times 10^{10} \ \omega/m^2[/tex]
(b) [tex]5\times 10^6 \ N/C[/tex]
Explanation:
The given values are:
Power of Laser beam,
= 10 mW
on converting it, we get
= [tex]10\times 10^{-3} \ \omega[/tex]
= [tex]10^{-2} \ \omega[/tex]
Spot's diameter,
= 0.62 μm
= [tex]0.62\times 10^{-6} \ m[/tex]
Now,
(a)
The intensity of light will be:
⇒ [tex]I=\frac{P}{\pi r^2}[/tex]
or,
⇒ [tex]=\frac{4P}{\pi d^2}[/tex]
On substituting the values, we get
⇒ [tex]=\frac{4\times 10^{-2}}{\pi(0.62)^2\times 10^{-12}}[/tex]
⇒ [tex]=3.31\times 10^{10} \ \omega/m^2[/tex]
(b)
The amplitude of electric field will be:
⇒ [tex]I=\frac{1}{2}\epsilon_0E_0.C[/tex]
or,
⇒ [tex]E_0=\sqrt{\frac{2I}{CE_0} }[/tex]
On substituting the values, we get
⇒ [tex]=\sqrt{\frac{3.31\times 10^{10}\times 2}{3\times 10^8\times 8.85\times 10^{-12}} }[/tex]
⇒ [tex]=5\times 10^6 \ V/m[/tex]
A wave travels at a constant speed.How does the frequency change if the wavelength is reduced by a factor of 3 The frequency decreases by a factor of 3 the frequency increases by a factor of 3 the frequency increases by a factor of 9 the frequency does not change
Answer:
The frequency increases by a factor of 3.
Explanation:
The relation between speed, wavelength and frequency of a wave is given by :
[tex]v=f\lambda[/tex]
or
[tex]f\propto \dfrac{1}{\lambda}[/tex]
A wave travels at a constant speed. If the wavelength is reduced by a factor of 3, it would mean that the frequency increases by a factor of 3 because there is an inverse relationship between wavelength and frequency.
A string with a length of 7.25 m is fixed at both ends. If the string is plucked so that there are five nodes along the string in addition to those at either end, what is the wavelength of the interfering waves for this mode?
Answer:
the wavelength of the interfering waves for this mode is 2.4168
Explanation:
The computation of the wavelength of the interfering waves for this mode is shown below:
Given that
The length is 7.25m
And, the number of nodes is 6
So, the wavelength should be
= 2 × 7.25m ÷ 6
= 2.4168 m
Hence, the wavelength of the interfering waves for this mode is 2.4168
The same would be considered
A 125-g coin is placed 8.0 cm from the axis of rotation of a horizontally rotating turntable as shown. The coefficient of static friction between the coin and the turntable is μs . The turntable makes exactly 1.0 revolution per second and the coin remains in place without slipping. [a] (8 pts) Draw a free-body force diagram for the coin. [b] (10pts)What is the frictional force acting on the coin? [c] (12pts)When the rotational speed is increased to 1.2 revolutions per second, the coin starts to slip. Calculate the coefficient of static friction μs between the coin and the turntable?
Answer:
zhvshshisvdiscdoscd if vdidg
A box slides to the right across a horizontal floor. A person called Ted exerts a force T to the right on the box. A person called Mario exerts a force M to the left, which is half as large as the force T. Given that there is friction f and the box accelerates to the right, rank the sizes of these three forces exerted on the box.
a. f < M < T
b. M < f < T
c. M < T < f
d. f = M < T
e. It cannot be determined.
Answer:
a. f < M < T
Explanation:
Let us take the right direction as positive.
Since Ted exerts a force T to the right his force is +T, Mario exerts a force M to the left, his force is -M. It is also given that Mario's force is half of Ted's force, so M = T/2. Finally, the frictional force , f is to the left, so it is -f. Let the net force be F and it is to the right since the box moves to the right.
So, +T - M - f = +F
Substituting M = T/2, we have
+ T -T/2 - f = F
+ T/2 - f = F
+T/2 = F + f
So, T = 2(F + f) and
M = T/2 = F + f
Since T = 2(F +f) = 2M, It follows that T > M
Also, since M = F + f, it follows that M > f
So, T > M > f ⇒ f < M < T
So, the answer is a.
State five uses of bases.
Answer:
Sodium hydroxide is used in the manufacture of soap. It is used in petroleum refining; in making medicines, paper, pulp, etc. It is used in making rayon. Calcium hydroxide is also known as slaked lime. It is used to neutralize acid in water supplies; in the manufacture of bleaching powder; as a dressing material for acid burns; as an antidote for food poisoning.Ammonium hydroxide is used to remove ink spots from clothes and to remove grease from window-panes. It is used in the cosmetic industry. Alkalis are used in alkaline batteries. Generally, potassium hydroxide is used in such batteries.Strontium hydroxide(Sr(OH)2) is used in the food industry for the refining of beet sugar.The molecules in the rods and cones in the eye are turned to absorb photons of particular energies. The retinal molecule, like many molecules, is a long chain. Electrons can freely move along one stretch of the chain but are reflected at the ends, thus behaving like a particle in a one-dimensional box. The absorption of a photon lifts an electron from the ground state into the first excited state. Do the molecules in a red cone (which are turned to absorb red light) or the molecules in a blue cone (tuned to absorb blue light) have a longer "box"?
Answer:
The answer "[tex]E_{red1} < E_{blue1}[/tex] can include that is [tex]L_{red} > L_{blue}[/tex]".
Explanation:
In this scenario, when we take the expression [tex]E_n =\frac{1}{2m}(\frac{hn}{2L})^2[/tex] that is the energy of the inversely proportional to the length of the box. because[tex]E_{red1} < E_{blue1}[/tex] it could be include that is [tex]E_{red1} < E_{blue1}[/tex] because [tex]E_{red1} < E_{blue1}[/tex] which can include [tex]E_{red1} < E_{blue1}[/tex].
- A certain mass is suspended at one end of a spring of spring-constant of 32,000gm/s2. The
time taken to execute 10 oscillations is 15 second.
(a) What is the time period?
(b) What is the value of mass suspended at the end of the spring.
Answer: I am pretty sure it is (b) what is the value of mass suspended at the end of the spring.
Explanation:
How does mass differ from weight? List 2 differences.
weight is vector vary from place to place
Answer:
The difference between mass and weight is that mass is the amount of matter in a material, while weight is a measure of how the force of gravity acts upon that mass.
Explanation:
Mass is the measure of the amount of matter in a body. Mass is denoted using m or M. ... Weight is mass multiplied by the acceleration of gravity (g).
Scientists have measured the distance between the Earth and the Moon by reflecting a beam of laser
light off the Moon. They measure the time taken for light to travel to the Moon and back.
a) What other piece of information is needed to calculate the Earth-Moon distance?
b) How would the distance be calculated?
Answer:
a)speed of light.
a)speed of light×time=distance.
Explanation:
light has a constant speed of 299,792,458m/s
This distance is analyzed quantitatively by LIDAR (Light Detection And Ranging) stations, which bounce laser pulses off the retroreflecting mirrors installed on the Moon by the Apollo astronauts.
What is LIDAR?
Lidar is a method of determining ranges that involves using a laser to target an object or a surface and measuring the time it takes for the reflected light to return to the receiver.
LiDAR is a type of remote sensing technology. LiDAR technology collects measurements by using a laser pulse. These are employed in the production of 3D models and maps of objects and environments.
Lidar, which stands for light detection and ranging, has been around for quite some time. It employs lasers to ping off objects and return to the laser source, measuring distance by timing the travel, or flight, of a light pulse.
LIDAR (Light Detection And Ranging) stations analyze this distance quantitatively by bouncing laser pulses off the retroreflecting mirrors installed on the Moon by the Apollo astronauts.
Thus, this way, the distance can be calculated.
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1. Compared to sadness, depression:
a. Is more common
b. Lests longer
c. Has fewer symptoms
d. Is easier to recognize
Protons have
_electric charge. Electrons have
_electric charge. Neutrons have
electric charge. Most atoms are electrically
because the number of protons
equals the number of electrons. Atoms with an electric charge become charged by gaining or losing
When this charge becomes built up on an object, we call that build up
Answer:
Protons have positive charge
Electrons have negative charge
Neutrons have no charge
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SOMEONE HELP PLEASE I ASKED THIS TWICE LAST NIGHT I MEAN DAM!! You drop a water balloon from a second-story window. Which formula would you use to calculate the velocity of the water balloon just before it hits the ground, assuming it is in free fall?
A. v=g/t B. v=get C. g=vt D. t=vg
Answer:
I think it would be V=g/t
A ball falls down 30 meters from the top of a building. If the ball weighed 1.2 kg, what is the gravitational potential energy lost by the ball? Estimate g as 9.81.
One way to conserve energy is to replace incandescent light bulbs with compact fluorescent bulbs. The fluorescent bulb typically uses 25% of the energy of an incandescent bulb of comparable brightness typically lasts about 12 times longer. a)How much would you save by replacing a 100-watt incandescent bulb with a compact fluorescent bulb over the 12,000 hour lifetime of the bulb if the electricity cost 0.08$ per kwh (kilowatt hour)
Answer:
cos to = $ 24
Explanation:
When replacing the bulb only 25% of the energy is used, therefore
W = 0.25 100
W = 25 W
Let's look for the energy in the life of the bulb
E = 25 10⁻³ 12000
E = 300 Kwh
now we can calculate the cost using a direct proportion rule.
Cost = 0.08 300
cos to = $ 24
Mu
wann-A
Very Short Answer Type Questions
1. Name the nutrients present in our food which give mainly energy to our body.
2. Name the nutrient which is needed for the growth and repair of our body. Proteins
3. Name the main carbohydrate which we eat in our food. I heat Rica maizes Pearl Potato
4. Which carbohydrate is present in wheat, rice and potatoes ? Plants
5. Name two foods each rich in (a) fats, and (b) starch. Batterheen
6. Name the major nutrients in our food.Combshed soles Fats Rooten mineral water Vitamin
7. Name the vitamin which is required for maintaining good eyesight Witamin A
8. Name the vitamin which keeps the teeth, gums and joints healthy, and helps fight diseases. 14
9. Name the vitamin which is necessary for the normal growth of bones and teeth Wermico
10. Which vitamin is produced in the human body when skin is exposed to sunlight ? uamu-D
11. Name the main vitamin present in (a) oranges, and (b) carrots. Worthing
12 Name an important mineral present in (a) apple, and (b) sea-fish.
13. Which mineral is needed to make haemoglobin present in our red blood cells.
14. In addition to calcium, which other mineral is needed for making bones and teeth ? (chum, Pha
15. Name a mineral which is needed for keeping bones and teeth healthy.
16. Which mineral is needed for the proper functioning of thyroid gland ?
17. Name two food materials which contain a lot of water. Fresh forest
18. Name the component of our food which helps prevent constipation. bulk oftend, wollte man
Vegetable
19. What is the other name of roughage? Dletary Abu
29Which component of food is mainly made of indigestible carbohydrate 'cellulose'?
21. The examples of carbohydrates are : sugar, cellulose, glucose and starch. Which of these carbohydrate
provides roughage in our food ?
22. Name two components of food which do not provide any nutrients.Cellulog
23. Fill in the following blank with a suitable word :
Iron is an important constituent of.........present in our blood. Hemoglobin
Short Answer Type Questions
24. What is the function of fats in our body? Name
Type of bacteria that attacks the throat- causing fever sore throat rash
Answer:
Streptococcus Pyogenes
Explanation:
Strep throat!
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Answer:
1. k
2. t
3. k
4. k
5. k
6. k
7. k
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9. k
10. k
I'm not sure but hope it helps:)
A pendulum consists of a 2.0-kg block hanging on a 1.5-m length string. A 10-g bullet moving with a horizontal velocity of 900 m/s strikes, passes through, and emerges from the block (initially at rest) with a horizontal velocity of 300 m/s. To what maximum height above its initial position will the block swing
Answer:
The maximum height above its initial position is:
[tex]h_{max}=1.53\: m[/tex]
Explanation:
Using momentum conservation:
[tex]m_{b}v_{ib}=m_{B}v_{fB}+m_{b}v_{fb}[/tex] (1)
Where:
m(b) is the mass of the bulletm(B) is the mass of the blockv(ib) is the initial velocity of the bulletv(fb) is the final velocity of the bulletv(fB) is the final velocity of the blockLet's find v(fb) using equation (1)
[tex]m_{b}(v_{ib}-v_{fb})=m_{B}v_{fB}[/tex]
[tex]v_{fB}=\frac{m_{b}(v_{ib}-v_{fb})}{m_{B}}[/tex]
[tex]v_{fB}=\frac{0.1(900-300)}{2}[/tex]
[tex]v_{fB}=30\: m/s[/tex]
We need to find the maximum height, it means that all kinetic energy converts into gravitational potential energy.
[tex]\frac{1}{2}m_{B}v_{fB}=m_{B}gh_{max}[/tex]
[tex]h_{max}=\frac{1}{2g}v_{fB}[/tex]
[tex]h_{max}=\frac{1}{2(9.81)}30[/tex]
[tex]h_{max}=1.53\: m[/tex]
I hope it helps you!
The maximum height above its initial position is: [tex]h_{max}[/tex]=1.53m
What is simple harmonic motion?Simple harmonic motion is the periodic motion or back and forth motion of any object with respect to its equilibrium or mean position. The restoring force is always acting on the object which try to bring it to the equilibrium.
Using momentum conservation:
[tex]m_bv_{1b}=m_Bv_{fB}+m_bv_{fb}[/tex]
Where:
m(b) is the mass of the bullet
m(B) is the mass of the block
v(ib) is the initial velocity of the bullet
v(fb) is the final velocity of the bullet
v(fB) is the final velocity of the block
Now for finding the value of final velocity VfB
[tex]m_b(v_{1b}-v_{fb})=m_Bv_{fB}[/tex]
[tex]v_{fB}=\dfrac{m_b(v_{1b}-v_{fb})}{m_B}[/tex]
[tex]v_{fB}=\dfrac{0.1(900-{300})}{2}[/tex]
[tex]v_{fB}=30\ \frac{m}{s}[/tex]
We need to find the maximum height, it means that all kinetic energy converts into gravitational potential energy.
[tex]\dfrac{1}{2}m_Bv_{fB}=m_Bv_{fB}[/tex]
[tex]h_{max}=\dfrac{v_{fB}}{2g}[/tex]
[tex]h_{max}=\dfrac{30}{2\times 9.81}[/tex]
[tex]h_{max}=1.53\ m[/tex]
Thus the maximum height above its initial position is: [tex]h_{max}[/tex]=1.53m
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