A yoyo with a mass of m = 150 g is released from rest as shown in the figure.
The inner radius of the yoyo is r = 2.14 cm, and the outer radius is R = 4.00 cm, and the moment of inertia about the axis perpendicular to the plane of the yoyo and passing through the center of mass is ICM = 1.01×10-4 kgm2.
1. Determine the linear acceleration of the yoyo.
2. Determine the angular acceleration of the yoyo.
3. What is the weight of the yoyo?
4. What is the tension in the rope?
5. If a 1.27 m long section of the rope unwinds from the yoyo, then what will be the angular speed of the yoyo?
Answers
(1) The linear acceleration of the yoyo is 3.21 m/s².
(2) The angular acceleration of the yoyo is 80.25 rad/s²
(3) The weight of the yoyo is 1.47 N
(4) The tension in the rope is 1.47 N.
(5) The angular speed of the yoyo is 71.385 rad/s.
Linear acceleration of the yoyoThe linear acceleration of the yoyo is calculated by applying the principle of conservation of angular momentum.
∑τ = Iα
rT - Rf = Iα
where;
I is moment of inertiaα is angular accelerationT is tension in the roper is inner radiusR is outer radiusf is frictional forcerT - Rf = Iα ----- (1)
T - f = Ma -------- (2)
a = Rα
where;
a is the linear acceleration of the yoyoTorque equation for frictional force;
[tex]f = (\frac{r}{R} T) - (\frac{I}{R^2} )a[/tex]
solve (1) and (2)
[tex]a = \frac{TR(R - r)}{I + MR^2}[/tex]
since the yoyo is pulled in vertical direction, T = mg [tex]a = \frac{mgR(R - r)}{I + MR^2} \\\\a = \frac{(0.15\times 9.8 \times 0.04)(0.04 - 0.0214)}{1.01 \times 10^{-4} \ + \ (0.15 \times 0.04^2)} \\\\a = 3.21 \ m/s^2[/tex]
Angular acceleration of the yoyoα = a/R
α = 3.21/0.04
α = 80.25 rad/s²
Weight of the yoyoW = mg
W = 0.15 x 9.8 = 1.47 N
Tension in the ropeT = mg = 1.47 N
Angular speed of the yoyov² = u² + 2as
v² = 0 + 2(3.21)(1.27)
v² = 8.1534
v = √8.1534
v = 2.855 m/s
ω = v/R
ω = 2.855/0.04
ω = 71.385 rad/s
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Related Questions
A crate with a mass of M = 60.5 kg is suspended by a rope from the midpoint of a uniform boom. The boom has a mass of m = 119 kg and a length of l = 9.64 m. The end of the boom is supported by another rope which is horizontal and is attached to the wall as shown in the figure.
1. The boom makes an angle of θ = 60.2° with the vertical wall. Calculate the tension in the vertical rope.
2. What is the tension in the horizontal rope?
Answers
The boom makes an angle of θ = 60.2° with the vertical wall and the tension in the horizontal rope is mathematically given as
[tex]T_1=730.85 \mathrm{~N}[/tex]
[tex]T_1'=\frac{1980.51 \mathrm{~N}}{}[/tex]
What is the tension in the vertical rope.?Generally, the equation for is mathematically given as
1) Tension in vertical rope,
[tex]T_{1}=74.5 \times 9.81\\T_1=730.85 \mathrm{~N}[/tex]
2) Tension in horizontal rope,
[tex]\sum{Mg} =0\\Mg\frac{l}{2} \sin \theta+T_{1} \frac{l}{2} \sin \theta &=T_{2} l \cos \theta \\[/tex]
[tex]T_{2} &=\frac{M g(l / 2) \sin \theta+T_{1}(l / 2) \sin \theta}{l \cos \theta} \\\\&=\frac{M g \tan \theta}{2}+\frac{T_{1} \tan \theta}{2} \\\\T_{2} &=\frac{142 \times 9.81 \tan 61.8}{2}+\frac{730.85 \times \tan 61.8}{2} \\\\=& 1299+681.51[/tex]
[tex]T_1=\frac{1980.51 \mathrm{~N}}{}[/tex]
In conclusion, the tension in the horizontal rope is
[tex]T_1=\frac{1980.51 \mathrm{~N}}{}[/tex]
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I need help on a question
As we know that the three most common household fuse values are 3A,5A and 13A. Make a list of yourhousehold electrical appliances. Divide them into 3 groups according to their power consumption to decide what fuse should be fitted in the plug for each of them.
Answers
Some household appliances and their fuse ratings are given below:
3A fuse - Table lamp, television, mixer, blender, fridge, freezer,5A fuse - floor lamps, coffee maker, dish washer13A fuse - Washing machine, dishwasher, microwave, toaster, iron.What is a fuse?A fuse is a device which is designed to protect an appliance by cutting off the electric circuit when current greater than its rating flows through it.
Some household appliances and their fuse ratings are given below:
3A fuse - Table lamp, television, mixer, blender, fridge, freezer,5A fuse - floor lamps, coffee maker, dish washer13A fuse - Washing machine, dishwasher, microwave, toaster, iron.In conclusion, a fuse is designed to protect an electrical appliance from excess current.
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A treasure chest full of silver and gold coins is being lifted from a pirate ship to the shore using two ropes as shown in the figure. The mass of the treasure chest is 75.6 kg.
If the tension in rope A is 7.42x10^2 N and the tension rope B carries is 7.52x10^2 N, what is the tension in rope C?
Answers
The tension in rope C is determined as 122.23 N.
Tension in rope CThe tension in rope C is calculated as follows;
B² = A² + C²
C² = B² - A²
where;
C is tension in rope CA is tension in rope AB is tension in rope BC² = (752²) - (742²)
C² = 14,940
C = √14,940
C = 122.23 N
Thus, the tension in rope C is determined as 122.23 N.
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By what percent does the braking distance of a car decrease, when the speed of the car is reduced by 10.3 percent? Braking distance is the distance a car travels from the point when the brakes are applied to when the car comes to a complete stop.
Answers
The braking distance is the distance traveled by a car experiencing a braking force until it comes to rest.
Our initial energy is solely kinetic:
[tex]E_i = \frac{1}{2}mv^2[/tex]
And, since the car goes to rest, it is no longer in motion. It will have no kinetic energy.
[tex]E_f = 0[/tex]
Therefore, there was work done by the braking force.
[tex]W_B = E_f - E_i = -\frac{1}{2}mv^2[/tex]
Recall the definition of work:
[tex]W = F\cdot \Delta x[/tex]
Or in this case, since the displacement and breaking force are antiparallel:
[tex]W = -F_B\Delta x[/tex]
This is equivalent to the dissipation of kinetic energy:
[tex]W = -F_B\Delta x = -\frac{1}{2}mv^2[/tex]
Now, to visualize this, let's rearrange the equation to solve for displacement.
[tex]\Delta x =\frac{mv^2}{2F_B}[/tex]
There is a direct, SQUARE relationship between necessary braking distance speed.
If the speed was reduced by 10.3 percent, its new speed is only 89.7% percent of the original, so:
[tex]\Delta x' =\frac{m(0.897v)^2}{2F_B}[/tex]
[tex]\Delta x' = 0.8046\Delta x[/tex]
The reduction by a percentage is:
[tex]1 - 0.8046 = 0.1954 \\\\\boxed{= 19.54\%}[/tex]
While buying a hot plate you notice the resistance of the hot
plate is 22.02. When connected to a 120. V source, how
much current will the hot plate carry? How much power does
it consume?
Answers
Answer:
Current = 5.45amps
Power = 654 watts
Explanation:
E =120V
I =?
R = 22.02 Ohms
I= E/R
I= 120/22.02
I = 5.45AmPs
P = ? P= E x R
E = 120V P= 120x5.45
I = 5.45 AmPs P= 654W
When working with two-dimensional motion, choose the direction of _________________ to be a positive direction.
Answers
Rightward and upward
What is One-dimensional motion and two-Dimensional Motion?Whenever any object moves in one direction only, the motion is known as one-dimensional motion.
Two-dimensional motion is the movement of the object in two directions simultaneously.
Example: A ball thrown at an angle is a two-dimensional motion.
In two-dimensional motion, there are two axes used, generally the x-axis and the y-axis.
Generally, the x-axis is positive towards the rightward direction and negative towards the leftward direction.
Similarly, the y- axis is positive towards the upward direction and negative toward the downward direction.
So, the rightward and upward directions are chosen as positive.
Therefore:
When working with two-dimensional motion, choose the direction of , the rightward and upward to be a positive direction.
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Three small objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA = 1.09 kg, mB = 2.83 kg, mC = 3.39 kg.
What is the moment of inertia of this set of objects with respect to the axis perpendicular to the the x-y plane passing through location x = 4.00 m and y = 3.00 m? The objects are small in size, their moments of inertia about their own centers of mass are negligibly small.
Answers
The moment of inertia of this set of objects with respect to the axis perpendicular to the the x-y plane passing through location x = 4.00 m and y = 3.00 m is 144.97 Kg.m^2.
What is moment of inertia?The moment of inertia is the amount of rotation obtained by an object when it is in state of motion or rest.
Three small objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA = 1.09 kg, mB = 2.83 kg, mC = 3.39 kg.
The coordinates of Ball A :(2,1) Ball B :(8,2) and Ball C: (5,8) and axis is at (4,3)
Here, for the moment of inertia of each ball
For ball A
IA = 1.09 x ((4 - 2)^2 + (3-1)^2)
IA = 8.72 Kg.m^2
for the ball B
IB = 2.83 * ((4 - 8)^2 + (3 - 2)^2)
IB = 48.11 Kg.m^2
for the ball C
IC = 3.39 * ((4 - 5)^2 + (3 - 8)^2)
IC = 88.14 Kg.m^2
Total moment of inertia = 8.72 + 48.11 + 88.14
Total moment of inertia = 144.97 Kg.m^2
Thus, the moment of inertia of this set of objects with respect to the axis perpendicular to the the x-y plane passing through location x = 4.00 m and y = 3.00 m is 144.97 Kg.m^2.
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What is resistance force?
A. The force opposing the effort
B. The force exerted by the machine
C. The work put into a machine
D. A force that improved on your effort?
Answer asap
Answers
Answer:
A is the correct answer
Explanation:
resistance force is the force that opposing to effort
The displacement at any given time of an object is x = 6 sin 98t , where the symbols have their usual meanings. i). Proof that this object is executing simple harmonic motion.
Answers
A simple harmonic motion is defined by the amplitude and angular frequency of the oscillation, which are represented in the given function as 6 units and 98 rad/s respectively.
General wave equation for simple harmonic motiony = A sinωt
where;
A is amplitude of the motionω is angular frequencyAmplitude of the oscillationA = 6 units
Angular frequency of the waveω = 98 rad/s
A simple harmonic motion is defined by the amplitude and angular frequency of the oscillation. Thus, the wave is executing simple harmonic motion.
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A shell is launched with an initial velocity at an angle of 40.0° above horizontal
from ground level. The shell needs to hit 1.5 km away. There is no appreciable air resistance,
and g = 9.80 m/s2
.
a. What should the initial velocity be?
b. What are the components of the shell’s velocity when it hits the ground? (horizontal
and vertical components)
Answers
Answer:
122.17 m/s
Explanation:
x cos 40 = horizontal velocity
1500 m / x cos 40 = time in the air = 1958.11 / x
x sin 40 = vertical velocity
find when shell vertical velocity = 0 (this is max height....1/2 way through its flight) , the time when it hits the ground will be twice this...
0 = x sin 40 - 9.8 t
t = x sin40 / 9.8 time in the air is twice this = .13118 x
Equate the two times from above to solve for x
1958.11/ x = .13118 x
x = 122.17 m/s
A uniform rod with a mass of m = 1.94 kg and a length of l = 2.10 m is attached to a horizontal surface with a hi=nge. The rod can rotate around the hi=nge without friction. (See figure.)
Initially the rod is held at rest at an angle of θ = 70.4° with respect to the horizontal surface. Then the rod is released.
1. What is the angular speed of the rod, when it lands on the horizontal surface?
2. What is the angular acceleration of the rod, just before it touches the horizontal surface?
Answers
Answer:
H = L sin θ / 2 height of center of mass
E = m g H = m g L sin θ / 2
I = m L^2 / 3 moment of inertia about end of rod
1/2 I ω^2 = m g L sin θ / 2 KE of rod when it hits surface
1/2 m L^2 / 3 ω^2 = m g L sin θ / 2
ω^2 = 3 g sin θ / L
ω = (3 g sin θ / L)^1/2 angular speed of rod striking surface
P = I α if P = torque
α = m g L/2 / (m L^2 / 3) = 3 g / (2 L) angular acceleration of rod
Three strings, attached to the sides of a rectangular frame, are tied together by a knot as shown in the figure. The magnitude of the tension in the string labeled C is 56.3 N. Calculate the magnitude of the tension in the string marked A.
Answers
The tension in the string marked A is determined as 331.35 N.
Angle made by A with respect to verticaltanθ = Δy/Δx
tanθ = (6 - 1)/(7 - 1) = 0.8333
θ = arc tan(0.8333) = 39.81⁰
with respect to horizontal = 90 - 39.81 = 50.19⁰
Angle made by B with respect to horizontaltanθ = Δy/Δx
tanθ = (9 - 6)/(7 - 5) = 1.5
θ = arc tan(1.5) = 56.31 ⁰
Angle made by C with respect to horizontaltanθ = Δy/Δx
tanθ = (6 - 4)/(14 - 7) = 0.2857
θ = arc tan(0.2857) = 15.95 ⁰
Bcosθ + Aosθ = Ccosθ
Bcos(56.31) + A[cos(50.19)] = 56.3cos(15.95)
0.55B + 0.64A = 54.13 ----- (1)
Bsinθ + Asinθ = Csinθ
Bsin(56.31) + A[sin(50.19)] = 56.3sin(15.95)
0.832B + 0.77A = 15.47---- (2)
Solve (1) and (2)
0.2A = 66.27
A = 66.27/0.2
A = 331.35 N
Thus, the tension in the string marked A is determined as 331.35 N.
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A bowling ball of mass 7 kg is dropped from the top of a tall building. It safely lands on the ground 4.7 seconds later. Neglecting air friction, what is the height of the building in meters? (Give the answer without a unit and round it to the nearest whole number)
Answers
The height of the building in meters, given the data is 108 m
Data obtained from the questionMass (m) = 7 KgTime (t) = 4.7 sAcceleration due to gravity (g) = 9.8 m/s²Height (h) = ?How to determine the height of the buildingThe height of the building can be obtained as illustrated below:
h = ½gt²
h = ½ × 9.8 × 4.7²
h = 108 m
Thus, the height of the building is 108 m
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what are beats
a. periodic fluctuations in the velocity of sound waves
b. periodic fluctuations in the wavelength of sound waves
c. periodic fluctuations in the intensity of sound waves
d. periodic fluctuations in the frequency of sound waves
Answers
Beats can be defined as the periodic fluctuations in the frequency of sound waves. That is option D
What are sound waves?Sound waves are those waves that are produced by the vibration of an object whose energy is usually propagated through a medium.
When two sound waves of different frequencies meets, a periodic variation that occurs is called beats.
Therefore, Beats can be defined as the periodic fluctuations in the frequency of sound waves.
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By what percent does the braking distance of a car decrease, when the speed of the car is reduced by 10.3 percent? Braking distance is the distance a car travels from the point when the brakes are applied to when the car comes to a complete stop. (Hint: it's not 10.3%)
91.5% is incorrect.
Answers
The percentage decrease in the braking distance of the car is 19.5%.
Distance traveled by the carv² = u² + 2as
where;
v is final velocity when brake is appliedu is initial velocitys is distance traveleds = (v² - u²)/(2a)
v = 100%u - 10.3%u = 89.7% u = 0.897u
s = [(0.897u)² - u²]/(2a)
s = -0.195u²/2a
percent decrease = 0.195 x 100% = 19.5%
Thus, the percentage decrease in the braking distance of the car is 19.5%.
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What would be the direction of the vector given a horizontal component of 4 and a vertical component of
3?
Answers
Answer:
5
Explanation:
Use the Pythagorean theorem. 3^2 + 4^2 = 25, which is the square of 5.
Brainliest, please :)
The direction of the vector would eventually depend on the horizontal component and vertical component which are 4 and 3 respectively. So, it would be calculated as 5 according to the Pythagoras theorem.
What do you mean by the Direction of the vector?In physics, the direction of the vector may be defined as the orientation of the vector, that is, the angle it makes with the X-axis. A vector is drawn by a line with an arrow on the top and a fixed point at the other end.
The direction in which the arrowhead of the vector is directed gives the direction of the vector. The direction of the vector measures the angle it makes with a horizontal line.
According to the question,
The horizontal component of the vector = 4
The vertical component of the vector = 3
The direction of the vector = square of the horizontal component + square of the vertical component.
= [tex]4^2+3^2[/tex] = 16 + 9 = 25 i.e. = [tex]5^2.[/tex]
Therefore, the direction of the vector would eventually depend on the horizontal component and vertical component which are 4 and 3 respectively. So, it would be calculated as 5 according to the Pythagoras theorem.
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A snowboarder on a slope starts from rest and reaches a speed of 1.6 m/s after 8.4 s.
(a)
What is the magnitude (in m/s2) of the snowboarder's average acceleration?
m/s2
(b)
How far (in m) does the snowboarder travel in this time?
m
Answers
The average acceleration of snowboarder's is 0.19 m/s² and distance travel by snowboarder is 6.70 metres.
We have given that snowboarder start moving from rest means
Initial speed (u) = 0 m/s
Final speed (v) = 1.6 m/s
time taken (t) = 8.4 s
Applying first equation of motion
v = u + at
1.6 = 0 + a×8.4
1.6 = 8.4a
a = 1.6/8.4 m/s²
a = 0.19 m/s²
So average acceleration is 0.19 m/s².
Now Applying second equation of motion
s = ut + 1/2at²
s = (0) × (8.4) + (1/2)(0.19)(8.4)² metre
s = (1/2)(0.19)(8.4)² metre
s = 6.70 metre
So that distance covered by snowboarder is 6.70 metre.
So we find out the average acceleration by using first equation of motion and the average acceleration came out to be 0.19 m/s² and to find out the distance covered by snowboarder we use second equation of motion and the distance came out to be 6.70 metre.
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You are trying to drag an object 5.0 m along a
straight path. You are pulling with a force of 40 N
along a rope that is inclined 30° to the horizontal.
How much work do you do?
Answers
The work done in dragging an object along a straight path is 173.2 J.
What is work done?Work done is equal to product of force applied and distance moved.
Given You are trying to drag an object 5.0 m along a straight path. You are pulling with a force of 40 N along a rope that is inclined 30° to the horizontal.
Work = Force x Distance x cos(angle)
W= 40 x 5 x cos 30°
W = 173.2 Joules
Thus, the work done is 173.2 Joules
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Set the Coleman window to 29.92 in Hg and record the pressure altitude:
What is the altimeter reading in ft above sea level?
Answers
Answer:
The long pointer measures altitude in intervals of 10,000 feet (2 = 20,000 feet). The short, wide pointer measures altitude in intervals of 1,000 feet (2 = 2,000 feet). The medium, thin pointer measures altitude in intervals of 100 feet (2 = 200 feet).
how the current have both magintude and direction
Answers
Electric current is the vector quantity it has both magintude and direction.
What is electric current?The pace at which electrons travel through a conductor is known as electric current. The ampere is the SI unit for electric current. Electrons are tiny particles that reside within a substance's molecular structure.
Because it has both a magnitude and a direction, the current is a vector. However, a vector always abides by the law of vector addition.
Current is a scalar since it follows algebraic addition and doesn't obey it. Additionally, the current is represented as the dot product of the area vector and the current density vector.
Hence, electric current is the vector quantity it has both magnitude and direction.
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A force of 42 N changes the length of Elastic X by 1.2 m while a force of 24 N changes the length of Elastic Y by 2.1
m. Calculate the work done on both Elastic X and Elastic Y. Solve this problem by showing your work in an
organized step-by-step fashion and include proper significant digits. (3 marks)
Answers
The work done on both Elastic X and Elastic Y is 25.2 J.
Work done on elastic XThe work done on the Elastic X is calculated as follows;
W = ¹/₂fx
where;
f is the applied force to material Xx is the extension of material XW = ¹/₂(42)(1.2)
W = 25.2 J
Work done on elastic YThe work done on the Elastic Y is calculated as follows;
W = ¹/₂fx
where;
f is the applied force to material Yx is the extension of material YW = ¹/₂(24)(2.1)
W = 25.2 J
Thus, the work done on both Elastic X and Elastic Y is 25.2 J.
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Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s2 until it reaches a speed of 80 ft/s. Afterwards it maintains this speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 60 ft/s. Determine the distance traveled by car A when they pass each other.
Answers
The distance traveled by car A when they pass each other is 3,428.56 ft.
Time when the two cars pass each other(Va)t - (Vb)t = d
where;
Va is speed of car AVb is speed of car Bt is time when they pass each otherd is the distance between them80t - (-60)t = 6000
80t + 60t = 6000
140t = 6000
t = 6000/140
t = 42.857 s
Distance traveled by car at the calculated times = vt
s = 80 x 42.857
s = 3,428.56 ft
Thus, the distance traveled by car A when they pass each other is 3,428.56 ft.
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Compare the electric and gravitational force between the electron and the proton in a hydrogen atom. The electric charge of the electron is -1.60x10-19C and the same but positive for the proton. The electron’s mass is 9.11x10-31 kg, while the proton’s mass is 1.67x10-27kg. Assume the distance between them is 5.3x10-11 m.
Answers
The gravitational attraction between electron and proton is 10−40 whereas electrostatic force of attraction between a proton and an electron is 10-8.
What is the gravitational force between electron and proton in a hydrogen atom?The gravitational attraction between electron and proton in a hydrogen atom is weaker than the coulomb attraction by a factor of about 10−40 while on the other hand, the electrostatic force of attraction between a proton and an electron in a hydrogen atom is 10- 8 which is 9 times.
The electric charge of the electron and proton are the same i.e. -1.60x10-19C whereas their gravitational force is different due to difference in mass.
So we can conclude that gravitational attraction between electron and proton is 10−40 whereas electrostatic force of attraction between a proton and an electron is 10-8.
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An owl is carrying a mouse to the chicks in its nest. It is 4.00 m west and 12.0 m above the center of the 30 cm diameter nest and is flying east at 3.50 m/s at an angle 32° below the horizontal when it accidentally drops the mouse. Will it fall into the nest? Find out by solving for the horizontal position of the mouse (measured from the point of release) when it has fallen the 12.0 m.
m (from the point of release)
Answers
The mouse will be 4.61 meters distant horizontally. and the owl won't fall into the nest.
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
Diameter of nest,d = 30 cm
The velocity of flying, V = 3.50 m/s toward the east
The angle of flying below the horizontal, Θ = 32°
Position of owl,12.0 m above the middle of the 30 cm-diameter nests, at 4.00 m west.
Height of owl above the ground,h = 12 m
Distance from the west direction, a = 4.00 m
The vertical component of velocity,vₐ
The horizontal component of velocity,vₓ
After covering a vertical distance of 12 m, the vertical component of the mouse's velocity, v, is given by
vₐ-u²=2gh
u = asinΘ
Substitute the above value;
vₐ²- (a sin Θ )² = 2gh
Substitute the given value;
vₐ² - (4 sin 32)² = 2 ×9.81 ×12
vₐ² - (4 × 0.53)² = 235.44
vₐ² - 4.494 = 235.44
vₐ² = 235.44 + 4.494
vₐ² = 239.934
vₐ = 15.49 m/s
The time required to descend the aforementioned 12 meters;
[tex]\rm t = \frac{v_{rel}}{g}[/tex]
t = (vₐ - u )/g
t =( vₐ - a sin Θ )/g
Substitute the given value;
t =(15.49 - 4 ×sin 32°) / 9.81
t= (15.49 - 4 * 0.53) / 9.81
t =(15.49 - 2.12) / 9.81
t = 13.37 / 9.81
t= 1.36 s
Horizontal distance traveled for the given period;
x=uₓ × t
x =a cosΘ × t
Substitute the given value;
x = 4×(cos 32°)×1.36
x= 4×0.848×1.36
x= 4.61 m
Hence, the mouse will be 4.61 meters distant in the horizontal direction. and the owl won't fall into the nest,
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A student holding a 324Hz tuning fork approaches a wall at a speed of 6ms^(-1). The speed of sound in air is 336ms^(-1). What frequency will the student detect from waves omitted from the fork and waves coming from the wall?
Answers
The frequency the student detect from waves omitted from the fork and waves coming from the wall is 348.1 Hz.
Frequency detected by the student
The observed frequency is determined by applying Doppler effect;
f' = f₀(v + v₀)/(v)
where;
f' is the observed frequencyv is speed of soundv₀ is the source speedf₀ is the original frequencyf' = 342(6 + 336)/(336)
f' = 348.1 Hz
Thus, the frequency the student detect from waves omitted from the fork and waves coming from the wall is 348.1 Hz.
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A bullet is fired horizontally into an initially stationary block of wood suspended by a string and remains embedded in the block. The bullet’s mass is m = 0.0075 kg, while that of the block is M = 0.95 kg. After the collision the block/bullet system swings and reaches a maximum height of h = 1.1 m above its initial height. Neglect air resistance.
Calculate the ratio, expressed as a percent, of the kinetic energy of the block/bullet system immediately after the collision to the initial kinetic energy of the bullet.
KEf/KEi(%) =
Answers
The ratio of the kinetic energy of the block/bullet system immediately after the collision to the initial kinetic energy of the bullet is 0.78 %.
Final velocity of the block/bullet systemApply the principle of conservation of energy to determine the final velocity of the block/bullet system.
K.E = P.E
¹/₂mv² = mgh
¹/₂v² = gh
v² = 2gh
v = √2gh
where;
h is the maximum height reached by the systemv is the initial velocity of the systemv = √(2 x 9.8 x 1.1)
v = 4.64 m/s
Initial velocity of the bulletApply the principle of conservation of linear momentum.
m₁u₁ + m₂u₂ = v(m₁ + m₂)
where;
u₁ is the initial velocity of the bulletu₂ is the initial velocity of the blockv is the final velocity after collisionm₁ is mass bulletm₂ is mass of block(0.0075)u₁ + (0.95)(0) = 4.64(0.0075 + 0.95)
0.0075u₁ = 4.4428
u₁ = 4.4428/0.0075
u₁ = 592.37 m/s
Initial kinetic energy of the bulletK.Ei = ¹/₂m₁u₁²
K.Ei = ¹/₂(0.0075)(592.37)²
K.Ei = 1,315.88 J
Final kinetic energy of the block/bullet systemK.Ef = ¹/₂(m₁ + m₂)v²
K.Ef = ¹/₂(0.0075 + 0.95)(4.64)²
K.Ef = 10.31 J
Ratio of final kinetic energy to initial kinetic energy= K.Ef/K.Ei x 100%
= (10.31 / 1,315.88) x 100%
= 0.78 %
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A solid, homogeneous sphere with of mass of M = 2.35 kg and a radius of R = 12.9 cm is resting at the top of an incline as shown in the figure.
The height of the incline is h = 1.29 m, and the angle of the incline is θ = 20.1°. The sphere is rolled over the edge very slowly. Then it rolls down to the bottom of the incline without slipping.
What is the total kinetic energy (translational plus rotational kinetic energy) of the sphere when it reaches the bottom of the incline?
Answers
The total kinetic energy of the sphere when it reaches the bottom of the incline is 44.57 J.
Total kinetic energy of the sphereThe total kinetic energy of the sphere = translational + rotational kinetic energy.
Translational kinetic energyK.E = ¹/₂mv²
K.E(bottom) = P.E(top) = mgh
K.E = (2.35)(9.8)(1.29)
K.E = 29.71 J
Rotational kinetic energyK.E(rot) = ¹/₂Iω²
K.E(rot) = ¹/₂I(v²/R²)
where;
I is rotational kinetic energyI = ¹/₂MR²
K.E(rot) = ¹/₂( ¹/₂MR²)(v²/R²)
K.E(rot) = ¹/₄Mv²
K.E(rot) = ¹/₄M(2gh)
K.E(rot) = ¹/₂Mgh
K.E(rot) = ¹/₂(29.71) = 14.855 J
Total kinetic energy = 29.71 + 14.855 = 44.57 J
Thus, the total kinetic energy of the sphere when it reaches the bottom of the incline is 44.57 J.
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C1=4F, C2=4F, C3=2F, C4=4F, C5= 9.2 F. Calculate the equivalent capacitance
between A and B points.
Answers
The equivalent capacitance between A and B points is 2.5F.
What is parallel plate capacitor?The two parallel plates placed at a distance apart used to store charge when electric supply is on.
The capacitance of a capacitor is given by
C = ε₀ A/d
From the given circuit C1, C2 and C3, C4 are in parallel C1=4F, C2=4F, C3=2F, C4=4F, C5= 9.2 F
C1, C2 = 4 +4 =8F
C3, C4 = 2 +4 =6F
Now , all capacitors are in series.
Total equivalent capacitance is
1 / Ceq = 1/ 8 +1/6 +1/ 9.2
Ceq = 2.5 F
Thus, the equivalent capacitance between A and B points is 2.5F.
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An object with a mass of m = 3.85 kg is suspended at rest between the ceiling and the floor by two thin vertical ropes.
The magnitude of the tension in the lower rope is 12.8 N. Calculate the magnitude of the tension in the upper rope.
Answers
The magnitude of the tension in the upper rope is 24.93 N.
Tension in the lower rope
The tension in the lower rope is calculated as follows;
T1 + T2 = W
where;
T2 is tension in upper ropeT1 is tension in lower ropeW is weight of the rope12.8 + T2 = (3.85)(9.8)
12.8 + T2 = 37.73
T2 = 37.73 - 12.8
T2 = 24.93 N
Thus, the magnitude of the tension in the upper rope is 24.93 N.
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which charateristic of the observant function?
Answers
Answer:
All people with the observant trait are often a steadying force that always wants to get things done. Their energy is very elegant in the sense of working on real things in real time.
Explanation:
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