Answer:
The answer is "0.82 c".
Explanation:
Given:
Spacecraft speed 1 is [tex]u = + 0.66 \ c[/tex]
Space velocity 2 relative to spacecraft 1 is [tex]v = + 0.34\ c[/tex]
The spacecraft velocity 2 measured by the Earth observation
[tex]\to u' = \frac{u +v}{1 + ( \frac{uv}{c^2})}[/tex]
[tex]= \frac{0.66 \ c +0.34\ c}{ 1+ (\frac{0.66\ c \times 0.33\ c }{c^2})}\\\\ = \frac{1 \ c }{ 1+ (\frac{0.2178\ c^2 }{c^2})}\\\\ = \frac{1 \ c }{ 1+ (0.2178 )}\\\\ = \frac{1 \ c }{ 1.2178 }\\\\=0.82\ c[/tex]
As a basketball player starts to jump for a rebound, he begins to move upward faster and faster until he leaves the floor. During this time that he is in contact with the floor, the force of the floor on his shoes is:
Answer:
The force of the floor on his shoes is bigger than his weight.
Explanation:
From Newton's third law of motion which states that to every action there is an equal an opposite reaction, we can say that the ground exerts additional force on the basketball player, thereby overcoming his weight and pushing him off the ground.
So, when the basketball player jumps, his muscles contract or extend appropriately which in turn creates an additional force on the ground. Hence, the force of the floor on his shoes is bigger than his weight.
A spherical conductor of radius = 1.5 cm with a charge of 3.9 pC is within a concentric hollow spherical conductor of inner radius = 3 cm, and outer radius = 4 cm, which has a total charge of 0 pC. What is the magnitude of the electric field 2.3 cm from the center of these conductors?
Answer:
The answer is "66.351 N/C"
Explanation:
Given:
[tex]a=1.5\ cm= 1.5 \times 10^{-2}\ m\\\\q_1=3.9\ pc\\\\b=3\ cm\\\\c= 4\ cm\\\\q_2=0 \ pc\\\\[/tex]
Using Gauss Law:
[tex]\oint \vec{E} \cdot \vex{dA}= \frac{Q_{enc}}{\varepsilon_0 }[/tex]
[tex]E \times 4 \pi\ r^2=\frac{Q_{enc}}{\varepsilon_0}\\\\E= \frac{Q_{enc}}{4 \pi\ r^2 \varepsilon_0}= \frac{1}{4 \pi \varepsilon_0} \frac{Q_{enc}}{r^2}= \frac{k_e\ Q_{enc}}{r^2}\\\\[/tex]
[tex]=\frac{9\times 10^{9} \times 3.9 \times 10^{-12}}{(2.3\times 10^{-2})^2}\\\\=\frac{35.1\times 10^{-3}\ }{(2.3\times 10^{-2})^2}\\\\=\frac{35.1\times 10^{-3}\ }{5.29 \times 10^{-4}}\\\\=\frac{35.1\times 10 }{5.29 }\\\\=\frac{351}{5.29 }\\\\=66.351\ \frac{N}{C}[/tex]
What requirement must a force acting on a object satisfy in order for the object to undergo simple harmonic motion?
Answer:
Simple harmonic motion is the movement of a body or an object to and from an equilibrium position. In a simple harmonic motion, the maximum displacement (also called the amplitude) on one side of the equilibrium position is equal to the maximum displacement.
The force acting on an object must satisfy Hooke's law for the object to undergo simple harmonic motion. The law states that the force must be directed always towards the equilibrium position and also directly proportional to the distance from this position.
In order to achieve the condition of simple harmonic motion, the force must be directed always towards the equilibrium position and also directly proportional to the distance from this position.
The given problem is based on the concept and fundamentals of simple harmonic motion. Simple harmonic motion is the movement of a body or an object to and from an equilibrium position.
In a simple harmonic motion, the maximum displacement (also called the amplitude) on one side of the equilibrium position is equal to the maximum displacement.The force acting on an object must satisfy Hooke's law for the object to undergo simple harmonic motion. The law states that the force must be directed always towards the equilibrium position and also directly proportional to the distance from this position.Thus, we can conclude that in order to achieve the condition of simple harmonic motion, the force must be directed always towards the equilibrium position and also directly proportional to the distance from this position.
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A coil of wire is connected to a galvanometer. When the coil is rotated in a magnetic field, the galvanometer records a current because the free electrons in the moving wire experience a force from the magnetic field that pushes them through the wire.
a. True
b. False
Answer:
True
Explanation:
This is true because the current occurs in the galvanometer not because the t coil that acts as a transformer or because it's ferromagnetic but because of the galvanometer records a current because the free electrons in the moving wire experience a force from the magnetic field that pushes them through the wire.
Define capacitance of a parallel plate capacitor and state one application of it in electric circuit?
Answer:
The capacitance of a parallel plate capacitor is the quantity of charge the capacitor can hold.
This capacitance is proportional to the area of the any of the two plates (if the area of the plates are the same), or the smaller of the two plates (if the plates have different areas) and inversely proportional to the square of the distance of separation (or thickness of the dielectric material) between the plates. It is mathematically expressed as;
C = Aε₀ / d
Where;
C = capacitance
A = Area of one of the plates.
d = distance between the plates
Some of the applications of capacitance (or simply a capacitor) in an electric circuit are;
i. For storage of electrostatic energy.
ii. For filtering and tuning of circuits.
Select the correct answer.
Which statement is true according to Newton's second law of motion?
A.
An object accelerates in the direction opposite to the direction of the force applied.
B.
An object accelerates in the direction perpendicular to the direction of the force applied.
C.
An object accelerates in the same direction as that of the force applied.
D.
An object undergoes no acceleration on the application of force.
E.
An object’s acceleration is independent to the force applied.
Answer:
c
Explanation:
i think the answer is c because the acceleration is directly proportional to the force but inversely proportional to the mass of the body according to the equation
a=f/m
hope this helps
Answer:
See image
Explanation:
Plato
(b) If the object is at 330 feet and its instantaneous velocity is 3 feet per minute at 30 minutes, what is the approximate position of the object at 32 minutes
Answer:
The final position is 36 feet.
Explanation:
initial position, d = 330 feet
speed, v = 3 feet per minute
time, t = 30 minute
now the time is 32 minute
time interval = 2 minute
So, the distance in 2 minutes is
d' = 2 x 3 = 6 feet
So, the final position is
D = 30 + 6 = 36 feet
A horizontail rod (oriented in the east -west direction) is moved northward at a constant velocity through a magnetic field that points straight down. Make a statement concerning the potential induced across the rod.
A) The east end of the rod is at higher potential than the west end.
B) The bottom surface of the rod is at higher potential than the top surface.
C) The top surface of the rod is at higher potential than the bottom surface.
D) The west end of the rod is at higher potential than the east end.
E) The potential is uniform.
Answer:
a
Explanation:
A baseball pitcher brings his arm forward during a pitch, rotating the forearm about the elbow. If the velocity of the ball in the pitcher's hand is 34.0 m/s and the ball is 0.310 m from the elbow joint, what is the angular velocity (in rad/s) of the forearm
Answer:
[tex]\omega=109.67\ rad/s[/tex]
Explanation:
Given that,
The speed of the ball, u = 34 m/s
The ball is 0.310 m from the elbow joint.
We need to find the angular velocity (in rad/s) of the forearm.
We know that,
[tex]v=r\omega\\\\\omega=\dfrac{v}{r}\\\\\omega=\dfrac{34}{0.31}\\\\\omega=109.67\ rad/s[/tex]
So, the required angular velocity of the forearm is 109.67 rad/s.
Question 1 of 10
Which nucleus completes the following equation?
239UHe+?
A. 228 Th
B. 2220
c. 23. Pu
D. 78Th
SUBMIT
Answer:
Option D. ²²²₉₀Th
Explanation:
Let the unknown be ⁿₘZ. Thus, the equation becomes:
²²⁶₉₂U —> ⁴₂He + ⁿₘZ
Next, we shall determine n, m and Z. This can be obtained as follow:
For n:
226 = 4 + n
Collect like terms
226 – 4 = n
222 = n
n = 222
For m:
92 = 2 + m
Collect like terms
92 – 2 = m
90 = m
m = 90
For Z:
ⁿₘZ => ²²²₉₀Z => ²²²₉₀Th
Therefore, the complete equation becomes:
²²⁶₉₂U —> ⁴₂He + ⁿₘZ
²²⁶₉₂U —> ⁴₂He + ²²²₉₀Th
Thus, the unknown is ²²²₉₀Th
A negative point charge q1 = 25 nC is located on the y axis at y = 0 and a positive point charge q2 = 10 nC is located at y =14 cm. Find the y coordinate of the points where the net electric potential due to these two charges is zero.
Answer:
y = 0.1 m
Explanation:
The electrical power for point loads is
V = [tex]k \sum \frac{q_i}{r_i}[/tex]k Sum qi / ri
in this case
V = k ([tex]- \frac{q_1}{r_1 } + \frac{q_2}{r_2}[/tex])
indicate that V = 0
[tex]\frac{q_1}{r_1} = \frac{q_2}{r_2}[/tex]
r₂ = [tex]\frac{q_2}{q_1} r_1[/tex]
the distance r1 is
r₁ = y -0
the distance r2
r₂ = 0.14 -y
we substitute
0.14 - y = [tex]\frac{10}{25}[/tex] y
y ( [tex]\frac{10}{25} + 1[/tex]) = 0.14
y 1.4 = 0.14
y = 0.14 / 1.4
y = 0.1 m
A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide, has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide
Answer:
Following are the response to the given question:
Explanation:
To address this problem, the notions of friction and torque in the kinematic equations of motion have to be applied.
The friction resistance is defined by
[tex]F=\mu mg[/tex]
Here seem to be our values.
[tex]\mu=0.3\\\\m= 120\ kg \\\\g=9.8\ \frac{m}{s^2} \\\\[/tex]
[tex]F=0.3 \times 120 \times 9.8= 36 \times 9.8= 352.8 \ N[/tex]
Take the brain's mid-size weight halfway to the floor, i.e. [tex]d = \frac{0.85}{2} = 0.425 \ m[/tex]. The torque around the bottom of the cooler should be zero to reach the maximum range.
[tex]F \times x= mg \times d\\\\ \text{Re-set for x}\\\\ x=\frac{mg \times d}{F}= \frac{mg \times d}{ \mu m g} =\frac{d}{\mu}=\frac{0.425}{0.3}=1.42 \m[/tex]
Then we may say that distance before turning is 1.42m.
Determinar el flujo de calor a través del piso de losa cuyas medidas 3 X 5 cm y temperaturas superficiales son -20 ºC y 40 ºC, la conductividad térmica del material es de 1,6 X 10 -3 cal/cm s ºC y su espesor es de 10 cm durante 1 hora.
Una aluminio de 12 cm de grosor, pero están perfectamente aislados en las demás paredes. Cada cuarto es un cubo de 4,0 m de arista. Si el aire de uno de los cuartos está a 10 ºC y el otro a 30 ºC. ¿Cuántos calor se conduce durante dos minutos? 1,7X 10 -4 cal/ cm s ºC
Una pared de asbesto de 0,15 cm de espesor 1400°C y 1150 ºC en las superficies interna y externa, respectivamente. ¿Cuál es la perdida de calor a través de una pared que tiene 0,5 m por 3 m de lado, en un tiempo de minuto y medio?
!!!!!!NESECITO AYUDA¡¡¡¡¡
Answer:
0,0560 cal / gºC.
Select the only true statement:
A beam in bending experiences tensile stresses on one side and compressive stresses on the other side.
A beam in bending experiences tensile stresses along the beam center and compressive stresses along the beam’s edges.
A beam in bending experiences only compressive stresses.
A beam in bending experiences only tensile stresses.
Answer:
A beam in bending experiences tensile stresses on one side and compressive stresses on the other side.
Explanation:
A beam of light bending experiences bending stress. There exists tension inside and outside the curve. The transverse plains in the materials remains parallel to the radius during bending.Two resistors with resistance values of 4.5 Ω and 2.3 Ω are connected in series or parallel across a 30 V potential difference to a light bulb. a. Calculate the current delivered through the light bulb in the two cases. b. Draw the circuit connection that will achieve the brightest light bulb
Answer:
plz mark as a pure substance abuse and function of the equation for sulphur dioxide emissions and function of the equation for sulphur dioxide emissions and function of the equation for sulphur dioxide emissions and function of the equation for sulphur dioxide emissions and function of the equation forUse the following information to answer the next question.
Environmental Concerns
1. release of greenhouse gases
2. release of gases that cause acid rain
3. release of excess heat
4. depletion of solar energy
5. depletion of geothermal energy
6. flooding of land
Which of the above environmental concerns are associated with the production of electricity?
Select one:
O A. 2, 3, and 4
O B. 1, 2, 3, and 6
O C. 1, 2, 3, 5 and 6
O D. 1, 3, and 5
Answer:
1.Emitted primarily through the burning of fossil fuels (oil, natural gas, and coal), solid waste, and trees and wood products. Changes in land use also play a role. Deforestation and soil degradation add carbon dioxide to the atmosphere, while forest regrowth takes it out of the atmosphere.
2.Acid rain is caused by a chemical reaction that begins when compounds like sulfur dioxide and nitrogen oxides are released into the air. These substances can rise very high into the atmosphere, where they mix and react with water, oxygen, and other chemicals to form more acidic pollutants, known as acid rain.
3.Untreated, heat exhaustion can lead to heatstroke, a life-threatening condition that occurs when your core body temperature reaches 104 F (40 C) or higher. Heatstroke requires immediate medical attention to prevent permanent damage to your brain and other vital organs that can result in death.
4.The loss of solar energy in passing through the atmospheric layers is called the atmospheric deflection. ... The longer the path traversed, the greater the amount of radiant energy depleted. Various processes whereby heat energy is lost through the atmosphere are known as scattering, diffusion, absorption, and reflection.
5.Geothermal energy is renewable because the Earth has retained a huge amount of the heat energy that was generated during formation of the planet. In addition, heat is continuously produced by decay of radioactive elements within the Earth. The amount of heat within the Earth, and the amount that is lost though natural processes (e.g. volcanic activity, conduction/radiation to the atmosphere), are much, much more than the amount of heat lost through geothermal energy production. At any one geothermal field, however, the temperature of the geothermal reservoir or the fluid levels/fluid pressure in the reservoir may decrease over time as fluids are produced and energy is extracted. Produced fluids can be re-injected to maintain pressures, although this may further cool down the reservoir if care is not taken. Over time, it is commonly necessary to drill additional wells in order to maintain energy production as temperatures and/or reservoir fluid pressures decline.
6.Floods, Floodplains, and Flood-Prone Areas. ... Flooding is a result of heavy or continuous rainfall exceeding the absorptive capacity of soil and the flow capacity of rivers, streams, and coastal areas. This causes a watercourse to overflow its banks onto adjacent lands.
The environmental concerns associated with the production of electricity are the release of greenhouse gases, the release of gases that cause acid rain, the release of excess heat, the flooding of land, and the depletion of geothermal energy so, option C is correct.
What is electricity?The presence or movement of charged particles is electricity. The movement of electrons through a circuit is known as an electric current. The accumulation of electrons on an insulator causes static electricity.
Mostly released when solid trash, trees, and wood products are burned, along with fossil fuels (coal, gas, and oil).
Land use changes also have an impact. Carbon dioxide is released into the atmosphere by deforestation and soil erosion, while it is removed from it by forest regeneration.
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The current loop lies flat on a horizontal surface. Facing the loop from the top, the current moves in a clockwise direction. Which way does the magnetic field point outside the loop?
a) The field points down.
b) The field points down.
c) The field points to the left.
d) The field points up
e) The field points to the right
Answer:
e
Explanation:
the field points to the right
If loop is kept horizontally and direction of current is clockwise , then according to Fleming’s Left Hand Rule the direction of magnetic field will be towards right .
What is Fleming’s Left Hand Rule ?
Fleming’s Left Hand Rule states that if we arrange our thumb, forefinger and middle finger of the left-hand perpendicular to each other, then the thumb points towards the direction of the force experienced by the conductor, the forefinger points towards the direction of the magnetic field and the middle finger points towards the direction of the electric current.
If loop is kept horizontally and direction of current is clockwise , then according to Fleming’s Left Hand Rule the direction of magnetic field will be towards right .
correct answer e) The field points to the right
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4. Which of the following statements best describes the relationship
between mechanical, kinetic and potential energies of an object of mass
m kg that is thrown vertically upwards with in initial velocity of v. m/s.
A. Kinetic energy increases while potential energy decrease and mechanical
energy remains constant.
B. Kinetic energy decreases, while potential energy increases and mechanical
energy remains constant.
C. Both kinetic and potential energies decrease while mechanical energy
increases.
D. Both kinetic and potential energies increase while mechanical energy
remains constant.
(1)
21
Answer:
D
Explanation:
increase while mechanical energy remains constant
22) A driver traveling at 80 km/h brakes her 2000 kg truck to stop for a red light. How much internal energy is produced
Answer:
[tex]E=4.9\times 10^5\ J[/tex]
Explanation:
Given that,
The speed of a driver, v = 80 km/h = 22.22 m/s
The mass of the truck, m = 2000 kg
We need to find how much internal energy is produced. The internal energy produced by a truck is its kinetic energy and it is given by :
[tex]E=\dfrac{1}{2}mv^2\\\\E=\dfrac{1}{2}\cdot22.22^{2}\cdot2000\\\\E=493728.4\ J[/tex]
or
[tex]E=4.9\times 10^5\ J[/tex]
So, [tex]4.9\times 10^5\ J[/tex] of internal energy is produced.
Modern wind turbines are larger than they appear, and despite their apparently lazy motion, the speed of the blades tips can be quite high-many times higher than the wind speed. A turbine has blades 53m long that spin at 14 rpm.
Required:
a. At the tip of a blade, what is the speed?
b. At the tip of a blade, what is the centripetal acceleration?
Explanation:
Given that,
The length of the blades, l = 53 m
The angular velocity = 14 rpm = 1.466 rad/s
(a) The speed at the tip of a blade.
[tex]v=r\omega\\\\=53\times 1.466\\\\=77.69\ m/s[/tex]
(b) The centripetal acceleration at the tip of the blade is :
[tex]a=\dfrac{v^2}{r}\\\\a=\dfrac{77.69^2}{53}\\\\a=113.88\ m/s^2[/tex]
Hence, this is the required solution.
The deflection of a 160-cm-long beam in bending will be _____ times the deflection of an equivalent 120-cm-long beam.
0.75
2.37
1.33
1.78
0.56
0.42
Answer:
Number of time bend length = 1.33 (Approx.)
Explanation:
Given:
Length of beam = 160 centimeter
Length of beam after deflection = 120 centimeter
Find:
Number of time bend length
Computation:
Number of time bend length = Length of beam / Length of beam after deflection
Number of time bend length = 160 / 120
Number of time bend length = 1.33333
Number of time bend length = 1.33 (Approx.)
The deflection of a 160-cm-long beam in bending will be 1.33 times the deflection of an equivalent 120-cm-long beam.
Length of beam = 160 centimeter
Length of beam after deflection = 120 centimeter
The number of time bend length = Length of beam / Length of the beam after deflection.
Number of time bend length = 160 / 120
Number of time bend length = 1.33
What is deflecting?Deflecting is to turn (something) aside, especially from a direct path or fixed direction armor that deflects bullets deflecting attention from the troubled economy deflecting a question.
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A motorcycle daredevil jumps off a 33.0 ramp at 20.3 m/s. The landing ramp is at the same height, 28.0 m away. What is the height of the motorcycle when it reaches the landing ramp? (Unit = m)
The height of the motorcycle daredevil when it reaches the landing ramp is 4.93 m.
Since the ramp is a 33.0° ramp and the motorcycle daredevil jumps off with a speed of 20.3 m/s, the motorcycle dare devil has a horizontal component of speed u = 20.3cos33.0° m/s and a vertical component of speed v = 20.3sin33.0° m/s.
Now, since the other ramp is d = 28.0 m away, it takes the time it takes the motorcycle dare devil to reach it is t.
Considering motion in the horizontal direction, d = ut.
Thus, t = d/u
= 28.0 m/20.3cos33.0° m/s
= 28.0 m/(20.3 × 0.8387) m/s
= 28.0 m/17.025 m/s
= 1.645 s
Let h be the height of the motorcycle daredevil when it reaches the landing ramp in time, t.
Considering the vertical motion and using h = vt - 1/2gt² where v = vertical velocity of motorcycle daredevil = 20.3sin33.0°, t = time taken to reach landing ramp = 1.645 s and g = acceleration due to gravity = 9.8 m/s² (Note that there is a negative in front of g since it is directed downwards)
So, substituting the values of the variables into the equation, we have
h = vt - 1/2gt²
h = 20.3sin33.0° m/s × 1.645 s - 1/2 × 9.8 m/s² × (1.645 s)²
h = 20.3 × 0.5446 m/s × 1.645 s - 1/2 × 9.8 m/s² × 2.706025 s²
h = 18.187 m - 1/2 × 26.519 m
h = 18.187 m - 13.26 m
h = 4.927
h ≅ 4.93 m
So, the height of the motorcycle daredevil when it reaches the landing ramp is 4.93 m.
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The SAME amount of current I passes through three different resistors. R2 has twice the cross-sectional area and the same length as R1, and R3 is three times as long as R1 but has the same cross-sectional area as R1. 1)In which case is the CURRENT DENSITY through the resistor the smallest
Answer:
resistor R₂ has the lowest current density
Explanation:
The current density is
j = I / A
now let's analyze each case
a) R₂ has an area 2A₀ and a length L₀ that R₁
b) R₃ has an area Ao and a length 3L₀ what R₁
we can see that all the area is given in relation to the resistance R₁
the current density in R₁ is
j₁ = I / A₀
the current density in R₂
j₂ = I / 2A₀
j₂ 2 = ½ I/A₀
the current density in R₃
j₃ = I / A₀
j₂ < j₁ = j₃
therefore resistor R₂ has the lowest current density
Calculate area moment of inertia for a circular cross-section with 3 mm diameter:
28 mm4
254 mm4
7 mm4
4 mm4
81 mm4
Answer:
Option D: 4 mm⁴
Explanation:
Formula for area moment of inertia for a circular cross-section is;
I = πd⁴/64
We are given diameter;
d = 3 mm
Thus;
I = π × 3⁴/64
I = 3.98 mm⁴
Approximating to a whole number gives;
I = 4 mm⁴
b) When the ball is near its maximum height it experiences a brief gust of wind that reduces its horizontal velocity by 2.50 m/s. What distance in meters does the ball travel horizontally
Answer:
The horizontal distance is 0.64 m.
Explanation:
Initial velocity, u =2.5m/s
The maximum horizontal distance is
[tex]R = \frac{u^2}{2g}\\\\R = \frac{2.5\times 2.5}{9.8}\\\\R = 0.64 m[/tex]
A wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.15-N force on the 4.00 cm of wire in the field. What is the average field strenth?
Answer:
1.79 T
Explanation:
Applying,
F = BILsin∅................ Equation 1
Where F = Force, B = magnetic field, I = current flowing through the wire, L = length of the wire, ∅ = angle between the magntic field and the force
make B the subject of the equation
B = F/ILsin∅............. Equation 2
From the question,
Given: F = 2.15 N, I = 30 A, L = 4.00 cm = 0.04 m, ∅ = 90° (perpendicular to the field)
Substitute these values into equation 2
B = 2.15/(30×0.04×sin90°)
B = 2.15/1.2
B = 1.79 T
Hence the average field strength is 1.79 T
An upright cylindrical tank with radius 5 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing? (Round the answer to four decimal places.)
Answer:
The height of water increasing is 8.5 x 10^-4 m/s.
Explanation:
radius, r = 5 m
Volume per second, dV/dt = 2 m^3/min = 2/60 m^3/s
Let the height of cylinder is h.
The volume of the cylinder is given by
[tex]V = \pi r^2 h \\\\\frac{dV}{dt} = \pi r^2 \frac{dh}{dt}\\\\\frac{2}{30} = 3.14\times 5\times 5\times \frac{dh}{dt}\\\\\frac{dh}{dt}=8.5 \times 10^{-4} m/s[/tex]
The patellar tendon attaches to the tibia at a 20 deg angle 3 cm from the axis of rotation at the knee. If the force generated in the patellar tendon is 400 N, what is the resulting angular acceleration, in rad/s2), if the lower leg and foot have a combined mass of 4.2kg and a given radius of gyration of 25 cm
Answer:
the resulting angular acceleration is 15.65 rad/s²
Explanation:
Given the data in the question;
force generated in the patellar tendon F = 400 N
patellar tendon attaches to the tibia at a 20° angle 3 cm( 0.03 m ) from the axis of rotation at the knee.
so Torque produced by the knee will be;
T = F × d⊥
T = 400 N × 0.03 m × sin( 20° )
T = 400 N × 0.03 m × 0.342
T = 4.104 N.m
Now, we determine the moment of inertia of the knee
I = mk²
given that; the lower leg and foot have a combined mass of 4.2kg and a given radius of gyration of 25 cm ( 0.25 m )
we substitute
I = 4.2 kg × ( 0.25 m )²
I = 4.2 kg × 0.0626 m²
I = 0.2625 kg.m²
So from the relation of Moment of inertia, Torque and angular acceleration;
T = I∝
we make angular acceleration ∝, subject of the formula
∝ = T / I
we substitute
∝ = 4.104 / 0.2625
∝ = 15.65 rad/s²
Therefore, the resulting angular acceleration is 15.65 rad/s²
Assume that the change in pressure of H2S is small enough to be neglected in the following problem.
H2S(g) ⇌ 2H2(g) + S2(g) Kp =2.2 x 10^-6
a. Calculate the equilibrium pressures of all species in an equilibrium mixture that results from the decomposition of H2S with an initial pressure of 0.824 atm.
b. Show that the change is small enough to be neglected.
Answer:
pH2S = 0.816 atm
pH2 = 0.0153 atm
pS2 = 0.00765 atm
Explanation:
Step 1: Data given
Kp = 2.2 *10 ^-6
Initial pressure H2S = 0.824 atm
Step 2: The equation
H2S(g) ⇌ 2H2(g) + S2(g)
Step 3: The initial pressure
pH2S = 0.824 atm
pH2 = 0 atm
pS2 = 0 atm
Step 4: The pressure at the equilibrium
pH2S = 0.824 - x atm
pH2 = 2x atm
pS2 = x atm
Kp = ((pH2)² * (pS2))/pH2S
2.2 * 10^-6 = ((2x)² * x) / (0.824 - x)
2.2*10^-6 = 4x³ / (0.824 - x)
4x³ = 2.2*10^-6 * (0.824 - x)
x = 0.00765
pH2S = 0.824 - 0.00765 = 0.816 atm
pH2 = 2* 0.00765 = 0.0153 atm
pS2 = 0.00765 atm
The change is small enough to be neglected because 0.00765 << 0.824
If we calculate the result with or without this change the result will not be very different
2.2*10^-6 = 4x³ / (0.824 )
x = 0.00768 atm
pH2S = 0.824 - 0.00768 = 0.816 atm
pH2 = 2* 0.00768 = 0.0154 atm
pS2 = 0.00768 atm
Your car rolls slowly in a parking lot and bangs into the metal base of a light pole. In terms of safety, is it better for your collision with the light pole to be elastic, inelastic, or is the safety risk the same for either case? Explain.
Answer:
AN ELASTIC COLLISION IS SAFER
Explanation:
IT'S BECAUSE THE MOVEMENT IS PRESERVED. YEN AN ELASTIC
COLLISION, THE ELASTIC BODY ABSORBS SOME OF THE MOVEMENT.
THIS CAUSES THE CAR TO SLOW DOWN MORE SLOWLY THAN IN AN
INELASTIC COLLISION WHERE IT DECELERATES FASTER.
ANYWAY I LEAVE YOU THE LINK
(THEY ALREADY DELETED THE ENGLISH SITE, BUT YOU CAN USE
TRANSLATOR):
https://gscourses.thinkific.com
