Answer:
24.132 m/s
Explanation:
Note
[tex]U[/tex] = Initial Velocity
[tex]U_x[/tex] = Initial Horizontal Velocity
[tex]U_y[/tex] = Initial Vertical Velocity
[tex]V[/tex] = Final Velocity
[tex]V_x[/tex] = Final Horizontal Velocity
[tex]V_y[/tex] = Final Vertical Velocity
[tex]B[/tex] = launch angle
[tex]g[/tex] = gravity
[tex]t[/tex] = time
[tex]U_x=U*cos(B)[/tex]
[tex]U_y=U*sin(B)[/tex]
The horizontal component of the velocity is constant throughout the flight. So [tex]U_x=V_x[/tex] It can be defined as
[tex]V_x=U*cos(B)[/tex]
We can use the kinematics equation
[tex]V=U+at[/tex]
Gravity is acting downwards; gravity would be negative
[tex]V_y=U_y-gt[/tex]
The magnitude of the velocity can be defined as
[tex]V=\sqrt{V_x^2+V_y^2}[/tex]
Inserting some of the other equations gives us an equation at a given time (t).
[tex]V=\sqrt{(U*cos(B))^2+(U*sin(B)-gt)^2}[/tex]
[tex]V=\sqrt{(UcosB)^2+(UsinB)^2+(gt)^2-2gtU*sinB[/tex]
[tex]V=\sqrt{U^2+g^2*t^2-2*t*g*U*sinB}[/tex]
[tex]V(t)=\sqrt{U^2+g^2t^2-2tgUsinB}[/tex]
We are given
[tex]U=34.6[/tex]
[tex]B=80.2[/tex]
[tex]t=1.09[/tex]
[tex]g=9.81[/tex]
[tex]V(1.09)=\sqrt{34.6^2+9.81^2*1.09^2-2*1.09*9.81*34.6*sin80.2}[/tex]
[tex]V(1.09)=\sqrt{34.6^2+114.338-2*1.09*9.81*34.6*sin80.2}[/tex]
[tex]V(1.09)=\sqrt{34.6^2+114.338-739.94868*sin80.2}[/tex]
[tex]V(1.09)=\sqrt{34.6^2+114.338-729.151}[/tex]
[tex]V(1.09)=\sqrt{1197.16+114.338-729.151}[/tex]
[tex]V(1.09)=\sqrt{582.347}[/tex]
[tex]V(1.09)=24.132[/tex]
A rating/review would be much appreciated. Hope this helps!
Let me know if you have any questions about my work
Photo used to help with the question is below!! Please answer! Will mark BRAINLIEST!
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Chose the correct answer:
-reflection
-refraction
-absorption
-none of the above
What keeps planets in our solar system?
A. The elliptical motion of the planets around the sun
B. The gravitational force between the Earth and Sun
C. The magnetic field surrounding the Sun
D. The electromagnetic radiation from the sun
Answer:C
Explanation:
Which statement correctly characterizes the relationship between water vapor and air
Answer:
A
Explanation:
may i be marked brainliest?
Statement A correctly characterizes the relationship between water vapor and air. Colder air can hold more water vapor.
What is dew point temperature?
Under constant air pressure and water content, the dew point is the temperature at which air must be chilled to become saturated with water vapor.
When temperatures fall below the dew point, moisture capacity decreases and airborne water vapor condenses to create liquid water known as dew.
As the temperature of the air increases the vapor become more and dry. So that older air can hold more water vapor.
Hence,statement A correctly characterizes the relationship between water vapor and air.
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Р.
Use the information to answer the following question.
The information shows the masses after the compounds are balanced.
2 LiCl + Na,o
-
Li,O +2 NaCl
84
+
62
=
X +
118
If the following materials are used during the reaction of Lithium, Oxygen, Sodium, and Chlorine, what mass of Lithium Oxide would we
expect to see after the reaction and why?
O A. 28g of Li,O, because all mass must be conserved, it would be half of the compound LiCl in the products
O
B. 44g of Li,O, because all mass must be conserved, it would be half of the compound LiCl in the products
o
C. 28g of Li_0, because all mass must be conserved
D. 44g of Li2O, because all mass must be conserved
Answer:
C. 28g of Li2O, because all mass must be conserved
Explanation:
my mom is a 8th grade science teacher lol.
Determine the speed of the 50-kg cylinder after it has descended a distance of 2 m, starting from rest. Gear A has a mass of 10 kg and a radius of gyration of 125 mm about its center of mass. Gear B and drum C have a combined mass of 30 kg and a radius of gyration about their center of mass of 150 mm
This question is incomplete, the missing image is uploaded along this answer below.
Answer:
the speed of the 50-kg cylinder after it has descended is 3.67 m/s
Explanation:
Given the data in the question and the image below;
relation between velocity of cylinder and velocity of the drum is;
V[tex]_D[/tex] = ω[tex]_c[/tex] × r[tex]_c[/tex] ----- let this be equ 1
where V[tex]_D[/tex] is velocity of cylinder, ω[tex]_c[/tex] is the angular velocity of drum C and r[tex]_c[/tex] is the radius of drum C
Now, Angular velocity of gear B is;
ω[tex]_B[/tex] = ω[tex]_C[/tex]
ω[tex]_B[/tex] = V[tex]_D[/tex] / r[tex]_c[/tex] -------- let this equ 2
so;
V[tex]_D[/tex] / 0.1 m = 10V[tex]_D[/tex]
Next, we determine the angular velocity of gear A;
from the diagram;
ω[tex]_A[/tex]( 0.15 m ) = ω[tex]_B[/tex]( 0.2 m )
from equation 2; ω[tex]_B[/tex] = V[tex]_D[/tex] / r[tex]_c[/tex]
so
ω[tex]_A[/tex]( 0.15 m ) = (V[tex]_D[/tex] / r[tex]_c[/tex] ) 0.2 m
substitutive in value of radius r[tex]_c[/tex] (0.1 m)
ω[tex]_A[/tex]( 0.15 m ) = (V[tex]_D[/tex] / 0.1 m ) 0.2 m
ω[tex]_A[/tex]( 0.15 ) = 0.2V[tex]_D[/tex] / 0.1
ω[tex]_A[/tex] = 2V[tex]_D[/tex] / 0.15
ω[tex]_A[/tex] = 13.333V[tex]_D[/tex] ----- let this be equation 3
To get the speed of the cylinder, we use energy conversation;
assuming that the final position is;
T₁ + ∑[tex]U_{1-2[/tex] = T₂
0 + m[tex]_D[/tex]gh = [tex]\frac{1}{2}[/tex]m[tex]_D[/tex]V²[tex]_D[/tex] + [tex]\frac{1}{2}I_A[/tex]ω²[tex]_A[/tex] + [tex]\frac{1}{2}I_B[/tex]ω²[tex]_B[/tex]
so
m[tex]_D[/tex]gh = [tex]\frac{1}{2}[/tex]m[tex]_D[/tex]V²[tex]_D[/tex] + [tex]\frac{1}{2}[/tex](m[tex]_A[/tex]k[tex]_A[/tex]²)(13.333V[tex]_D[/tex])² + [tex]\frac{1}{2}[/tex](m[tex]_B[/tex]k[tex]_B[/tex]²)(10V[tex]_D[/tex])²
we given that; m[tex]_D[/tex] = 50 kg, h = 2 m, m[tex]_A[/tex] = 10 kg, k[tex]_A[/tex] 125 mm = 0.125 m, m[tex]_B[/tex] = 30 kg, k[tex]_B[/tex] = 150 mm = 0.15 m.
we know that; g = 9.81 m/s²
so we substitute
50 × 9.81 × 2 = ( [tex]\frac{1}{2}[/tex] × 50 × V[tex]_D[/tex]²) + [tex]\frac{1}{2}[/tex]( 10 × (0.125)² )(13.333V[tex]_D[/tex])² + [tex]\frac{1}{2}[/tex]( 30 × (0.15)²)(10V[tex]_D[/tex])²
981 = 25V[tex]_D[/tex]² + 13.888V[tex]_D[/tex]² + 33.75V[tex]_D[/tex]²
981 = 72.638V[tex]_D[/tex]²
V[tex]_D[/tex]² = 981 / 72.638
V[tex]_D[/tex]² = 13.5053
V[tex]_D[/tex] = √13.5053
V[tex]_D[/tex] = 3.674955 ≈ 3.67 m/s
Therefore, the speed of the 50-kg cylinder after it has descended is 3.67 m/s
An astronomy class is so excited by the discovery of planets around other stars that they decide to do a library exhibit on the subject so that everyone in the school can learn about it. In this exhibit they want to pay tribute to both the astronomers of today who have done the work AND some of the scientists of the past whose work was essential to making the discoveries possible (and directly related to the techniques involved). Which of the following scientists of the past should definitely be included in the exhibit?
a. George Herbigâ
b. Ejnar Hertzsprungâ
c. Ptolemyâ
d. Gerard Kuiperâ
e. Christian Dopplerâ
Answer: e. Christian Dopplerâ
Explanation:
Based on the information given, the scientist of the past that should definitely be included in the exhibit is Christian Dopplera.
He described how the frequency of sound waves and light is being affected by the relative speed of both the source and also the observer. This was referred to as the Doppler effect.
In this scenario, the Doppler effect can be used to show how the universe is expanding. Therefore, the correct option is E.
which of the following changes will increase the frequency of an oscillating pendulum?
a. an increase in the mass of the pendulum.
b. an increase in the initial height of release.
c. an increase in the length of the rope.
d. more than one of the above
e. none of the above
explain your answer.
NO LINKS.
Answer:
b because we apply Hooke's law
Explanation:
Hooke's law
brandon buys a new seadoo. he goes 12km north from the beach he jumps wakes for 6km to the east what distance did he cover what was his displacement
Total distance covered by Brandon is 18 km and total displacement covered by him is 13.41 km.
Displacement: What is it?The definition of displacement is the changing of an object's position. It has a magnitude and direction and is a vector quantity. It is shown as an arrowhead that travels from the initial location to the end. An object's position changes, for instance, if it moves from position A to position B.
Distance covered by Brandon is-
12 + 6 = 18 km
Displacement covered by Brandon is-
d²= 12² + 6²
= 144 + 36
d²= 180
d = √180
d = 13.41 km.
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You are assigned the design of a pressurized water tank for a future colony on Mars, where the acceleration due to gravity is 3.71 m/s^2. The pressure at the surface of the water will be 100 kPa, and the depth of the water will be 14.5 m . The pressure of the air outside the tank, which is elevated above the ground, will be 89.0 kPa . The tank's flat bottom has an area of 1.65 m^2, and the density of water is 1000 kg/m^3.
Required:
Find the net downward force on the tank's flat bottom, of area 2.15 m^2, exerted by the water and air inside the tank and the air outside the tank.
The function of the ossicles in the middle ear is to transmit the vibrations of the tympanic membrane caused by sound waves propagated in air to the fluid-filled cochlea. In doing so, the ossicles change the nature of the vibrations. The ear tries to conserve the energy in the wave I,
where v is the wave speed, cramster-equation-2010731130406341613664 is the density of the medium, cramster-equation-2010731131286341613668 is the frequency of the wave and A is the amplitude of the wave.
Calculate the magnitude of the change in A that occurs. The density of air and water is 1.3x10–3g/cm3 and 1.0g/cm3, respectively, and the velocity of sound is 331 m/s in air and 1410 m/s in water. The frequency of the wave remains constant as the wave propagates. (Hint: Begin with to find .)
The frequency of the wave which remains constant as the wave propagates and the magnitude of change in amplitude is 57.2.
What is Density?
Density can be defined as how much matter is contained within a particular volume of a substance. A dense object is the one which weighs more than a less dense object which is the same size. An object which is less dense than that of water will float on it, whereas an object with greater density will sink. The density equation is: D = M / V.
density: dair = 1.3 x 10⁻³ g/cm³, dwater = 1.0 g/cm³,
velocity: vair = 331 m/s, vwater = 1410 m/s
v×d×A² = constant
vair×dair×Aair² = vwater×dwater×Awater²
so,
Aair/Awater = sqrt[(vwater/vair)×(dwater/dair)] = 57.2
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A man lifts various loads with the same lever. The distance of the applied force from the fulcrum is 2.00 m and the distance from the fulcrum to the load is 0.500 m. A graph of resistance force vs. effort force is shown. What is the mechanical advantage of the lever? What is the ideal mechanical advantage of the lever? What is the efficiency of the lever? Show your work.
The mechanical advantage of the lever is 3.5.
The ideal mechanical advantage of the lever is 4
The efficiency of the lever is 87.5 %.
What is the mechanical advantage of the lever?The mechanical advantage of the lever is the ratio of the load overcame by the lever to the effort applied by the lever.
M.A = Load / Effort
From the graph we will find the change in load to change in effort is calculated as;
M.A = ( 160 N - 20 N ) / ( 50 N - 10 N )
M.A = 3.5
The ideal mechanical advantage of the lever is calculated as follows;
I.M.A = distance travelled by effort / distance travelled by load
I.M.A = ( 2 m ) / ( 0. 5 m )
I.M.A = 4
The efficiency of the lever is calculated as follows;
E = M.A / I.M.A x 100%
E = ( 3.5 / 4 ) x 100%
E = 87.5 %
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Anna litic and Noah formula how place a 1.50 kg brick on a wooden board and incline the board at 34.4* above the horziontal. The coefficient of friction between the brick and the board is 0.350. determine the force of gravity, parallel component of gravity and the perpendicular component of gravity. Please also find net force and acceleration
The force due to gravity here is 14.7 N. The net force acting on the brick is 9.5 N and the acceleration of the brick is then 6.3 m/s².
What is frictional force?Friction is a resistive force which opposes the motion of an object. The product of normal force by gravity and frictional coefficient gives the frictional force.
Given that, mass = 1.50 Kg
force by gravity = mg = 1.50 × 9.8 m/s² = 14.7 N
parallel component = 14.7 cos 34.4 = 12.12 N
perpendicular component = 14.7 sin 34.4 = 8.30 N
The frictional force = mg × coefficient of friction
= 14.7 × 0.35 = 5.14 N
then net force = 14.7 - 5.14 = 9.5 N
Acceleration of the brick = net force/mass
a = 9.5 N/1.50 Kg = 6.30 m/s²
Hence, acceleration on the brick is 6.30 m/s².
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Sarah and Devon are involved in an egg catching contest. They stand a fixed distance apart and toss a raw egg back and forth to each other. The goal is to catch the egg without it breaking. Which of the following would be the best strategy for Devon to employ as he attempts to catch the egg tossed by Sarah? Devon should…
A
Decrease the time it takes to stop the egg once it hits his hand.
B
Increase the time it takes to stop the egg once it hits his hand.
C
Tell Sarah to toss the egg at a very small angle to decrease the time the egg is in the air.
D
Tell Sarah to toss the egg at a rather large angle to increase the time the egg is in the air.
E
Use only one hand to catch the egg so that less mass is involved in stopping the egg.
Answer:
The correct answer is - B. Increase the time it takes to stop the egg once it hits his hand.
Explanation:
In order to catch the egg the force and time makes an impulse to the egg to change its momentum and bring it to rest. In order to change the momentum, one needs to decrease the force exerted onto the egg and increase the time it takes to make it rest.
Less force can be given to the egg by increasing the time to bring it to rest stop the egg once it hits his hand. Other than this it should be caught to the sides.
The rectangular coordinates of a point are (5.00, y) and the polar coordinates of
this point are (r, 67.4°).
a. What is the value of the polar coordinate r in this case?
b. In what quadrant are both the sine and tangent negative?
Answer:
Explanation:
Polar coordinates formula
Summary. To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) : x = r × cos( θ ) y = r × sin( θ )
A jug containing water at 26° C while another contains water at 82°C,if a patient wish to bath with water 40°C , the ratio of the mass of hot water to that of cold water is_
Answer:2:7
Explanation:
Quantity of heat energy before mixing= Quantity of heat energy after mixing
M1. S1.T1+ M2.S2.T2= M.S3.T3
Let, .
M1 = mass of cold water
M2 = mass of hot water
S1=S2=S3=S
M=M1+M2
T1=28,T2=82,T3= 40
M1.28 + M2.82= (M1+M2)40
M1.28 + M2.82= M1 40+M2.40
M2.82 -M2.40= M2.40–M1.28
M2.42= M1. 12
M2/M1= 12/42= 2/7
Or
M2: M1= 2:7
A 30kg metal ball is dropped from a height of 12.5 m.
a. Find the final velocity when the ball hits the ground.
b. Find the time it takes for the ball to hit the ground.
From conservation of linear momentum, the final velocity is 15.7 m/s and the time taken is 1.6 s
What is Velocity ?Velocity can be defined as a distance travel in a specific direction per time taken. It is a vector quantity.
Given that 30kg metal ball is dropped from a height of 12.5 m.
a. Find the final velocity when the ball hits the ground.
The maximum K.E of the ball at it final velocity will be equal to its maximum P.E at height 12.5 m. That is,
K.E = P.E
1/2mv² = mgh
Where
m = 30 Kgg = 9.8 m/s²h = 12.5 mv = ?Substitute all the parameters
1/2 × 30 × v² = 30 × 9.8 × 12.5
v² = 245
v = √245
v = 15.65 m/s
b. The time it takes for the ball to hit the ground can be found through
h = ut + 1/2gt²
but u = 0
h = 1/2gt²
Substitute all the necessary parameters
12.5 = 1/2 × 9.8 × t²
12.5 = 4.9t²
t² = 12.5/4.9
t² = 2.55
t = √2.55
t = 1.6 s
Therefore, the final velocity when the ball hits the ground is 15.65 m/s and the time it takes for the ball to hit the ground is 1.6 s
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A student conducts an experiment to test how the temperature affects the amount of salt that can dissolve in water. In the experiment, she uses 150 milliliters of water in each trial and stirs for five minutes each time.
The independent variable that we have in the experiment is the temperature. Option B
What is an experiment?We know that if we are talking about an experiment, what we have to look at is that we must consider the interplay of the variables that is taking place in the process. As we change one of the variables in the experiment, there would be a change in another variable in the experiment also.
Now, the variable that we usually beging to alter is the one that we call the independent variable. As we change the value of this particular variable, there would be a change in the independent variable.
We have been told that; a student conducts an experiment to test how the temperature affects the amount of salt that can dissolve in water.
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A monkey (mass m) is swinging on a vine of length L while carrying a bunch of bananas (a large bunch, mass m/2). His swinging motion has period T and reaches maximum height during the swing h (measured from the bottom of his arc of motion). He accidentally lets go of his bananas when he is at a height of h/2. What happens to the amplitude and period of his oscillation as a result? Explain.
Answer:
Explanation:
The period of oscillation will remain unchanged because the period of oscillation of a pendulum does not depend upon the mass of the bob . Here monkey along with bunch of banana represents bob .
When the monkey and banana were at height h /2 , they have potential energy as well as kinetic energy . banana is separated from the system . It carried its total energy along with it . But the energy of monkey remained intact with it . So it will keep on moving as usual . So it will attain the same maximum height as before .
Hence the amplitude of oscillation too will remain unchanged .
The figure below shows a cylinder filled with an ideal gas, which has a moveable piston resting on it. The cylinder's volume is initially 5.50 L, when a force on the piston of F = 14.5 kN pushes the piston downward a distance d = 0.140 m, until the volume of the cylinder is 3.00 L. The process occurs while the cylinder is in thermal contact with a large energy reservoir at a temperature of 295 K.
(A) How much work (in kJ) is done on the gas by the piston during the process?
(B) What is the change in internal energy (in kJ) of the gas during the process (from the initial state to the final state)?
(C) What is the energy transfer (in kJ) by the gas as heat during the process? (Treat the gas as the system and let the sign of your answer indicate the direction of energy flow.)
(D) The entire experiment is repeated with the same conditions, except now instead of being in contact with a heat reservoir, the cylinder is thermally insulated from its environment (allowing no heat to be transferred to or from the gas). In this case, what happens to the temperature of the gas during the process?
I uploaded the answer to[tex]^{}[/tex] a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3gVQKw3
what are you made of
Answer:
Body stuff
Explanation:
:) <3
a stage light uses a white lamp wgat color of light will be seen when
a yellow filter is used
an orange filter is used
Answer:
Explanation:
When a yellow filter is used, the stage light will appear yellow because the filter absorbs all colors of light except for yellow, which it allows through. When an orange filter is used, the stage light will appear orange for the same reason.
It is important to note that the color of the lamp itself will not change, but the light that is seen by the observer will appear to be the color of the filter due to the absorption and transmission properties of the filte
What will be the linear expansion of a piece of wrought iron 8 feet long if it’s temp is raised 70 degrees F?
The linear expansion of the wrought iron is 0.0038 feet.
What is the linear expansion of the wrought iron?
The linear expansion of the wrought iron is the increase in length of the wrought iron due to change or increase in temperature.
Mathematically, the formula for the linear expansion of metals is given as;
ΔL = αLΔθ
where;
ΔL is the linear expansion of the metalα is the coefficient of thermal expansion of the metalL is the original length of the metalΔθ is the change in temperature of the metalThe coefficient of thermal expansion of wrought iron = 0.0000067 / ⁰F
The linear expansion of the wrought iron is calculated as follows;
ΔL = αLΔθ
ΔL = ( 0.0000067/ ⁰F x 8 ft x 70 ⁰F )
ΔL = 0.0038 ft
Thus, the linear expansion of the wrought iron is a function of the increase in temperature of the iron and the original length of the iron.
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What does a step-down transformer change in an alternating current?
Answer: A step-down transformer changes the magnitude of the voltage in an alternating current (AC) electrical signal. It reduces the voltage of the AC signal by using a winding ratio between the primary (input) and secondary (output) coils that is less than 1:1.
Explanation: For example, if the winding ratio of a step-down transformer is 1:0.5, the output voltage of the secondary coil will be half the magnitude of the input voltage of the primary coil. In this case, the transformer would change the AC voltage from a higher value to a lower value.
The transformer does not change the frequency of the AC signal, which is determined by the source of the electrical power. The transformer also does not change the waveform of the AC signal, which is typically a sinusoidal wave.
You can see things outside of a beam of light because of? I NEED HELP ASAP
Answer:
Reflected light bounces off of materials that for whatever reason cannot absorb the light. The reflected light is always whatever color it was originally. We do not see things from light that is reflected. We see things from the light that they EMIT.
A resistor with a resistance of 2 MΩ is connected in series with a 5 µF capacitor and a battery with emf 10 V. The capacitor has originally a charge of 5 µC and then discharged. At what time will the charge be equal to 1µC?
A. 16 sec
B. 1.6 sec
C. 3.2 sec
D. 8 sec
8:11
GCSE Science - Physics
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14 67%
A cat accelerates from rest to 10 m/s
when it sees a dog. This takes 2
the cat?
seconds What is the acceleration of the cat ?
the acceleration of the cat is 5m/s square
Your friend Christy has always been good at making schedules-she plans her days out to the minute and
loves helping others be more productive in this way too. Which career in astronomy might she be suited for?
Ground Control
CAPCOM
Flight Controller
Flight Director
She might be best suited for a profession as an astronomy flight controller. The target speed for every one of the 4 motors is determined by the flight controller using the information acquired by the sensors.
Why study astronomy?The goal of astronomy is to explain whatever we see within the universe, including the planets and comets inside our own solar system, far-off galaxies, and echoes of something like the Big Bang.
Is math required for astronomy?Math is constantly used by astronomers. When using a telescope to see celestial objects, one application of it is this. The camera that is mounted on the telescope essentially captures a series of numbers, which could represent the amount of light that various celestial objects emit.
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In transverse waves, the movement of the particles is _________
O in a circle
O left to right
O diagonal
O up and down
Answer:
the correct answer is up and down
Explain how waves and their interactions with matter are used in the operation of technical devices. (i.e. solar cells, scanners, and medical imaging)
Explain energy transformations
Explain how electromagnetic induction is used in a simple motor
Relate any other terms like, speed, acceleration, momentum, friction, forces, gravity will affect the motion of the device.
Understand the 3 basic attributes of a PV cell. (Absorption of light, separation of charge carriers, and extraction of charge carriers to an external circuit.)
I know it's a lot but I really need to pass this class and I have zero passion for physics, they forced me to take this class. If I had biology I would have loved it. but you know anyone who loves Physics is welcome :)
Answer:
Examples of electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet, x-rays, and gamma rays. ... Microwaves are used to cook your food. Infrared waves are used in remote controls and are emitted from all warm objects, allowing them to be used to create heat-sensitive cameras.
Explanation:
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A 7.600 kg box is resting on a horizontal surface and attached to a 2.400 kg box by a thin, light wire that passes over a frictionless pulley. The coefficient of kinetic friction between the box and the surface is 0.1500. The pulley has the shape of a hollow sphere of mass 1.200 kg and diameter 0.2800 m. The system is released from rest and allowed to move. The hanging box falls 0.6100 m before it hits the ground. What is the speed of the hanging block just before it hits the ground
Answer:
v = 1.98 m / s
Explanation:
Let's analyze this exercise a bit, initially the hanging box is at a height h, which is why it has gravitational power energy, as the system is removing the kinetic energy is zero and just when the box reaches the floor its potential energy has dropped to zero and the three bodies have kinetic energy, also between the box and the horizontal surface there is friction, so there is work. Let's use the relationship between work and energy
starting point. Before starting the movement
Em₀ = U = m g h
final point. Just before the block hit the floor
Em_f = K = ½ M v² + ½ I w² + ½ m v²
the speed of the two blocks must be the same to maintain the tension of the rope
The work of the friction force
the friction force opposes the movement so its work is negative
W = - fr x
the law of equilibrium is the largest block
N-W = 0
N = W = Mg
we substitute
W = - μ M g x
the relationship between the work of the non-conservative force (friction) and the energy is
W = Em_f - Em₀
- μ Mg x = ½ M v² + ½ I w² + ½ m v² - mg h
the moment of inertia of a hollow sphere is
I = ⅔ m_s r²
angular and linear velocity are related
v = w r
w = v / r
the distance the horizontal block travels must be the same as the distance the vertical block travels
x = h
let's substitute
- μ M g h = ½ (M + m) v² + ½ (⅔ m_s r²) (v/r) ² - m g h
(- μ M + m) g h = ½ (M + m + ⅔ m_s) v²
v² = [tex]\frac{2(\mu \ M + m ) \ g h }{ M +m + \frac{2}{3} m_s}[/tex]
let's calculate
v² = 2 (-0.15 7.6 +2.4) 9.8 0.61 / (7.6 + 2.4 + 2/3 1.2)
v = [tex]\sqrt{\frac{42.32}{ 10.8} }[/tex]
v = 1.98 m / s