Mastering Problems
57. Ranking Task Rank the following objects according
to the magnitude of the acceleration, from least to
greatest. Specifically indicate any ties,
A. A falling acorn accelerates from 0.50 m/s to
10.3 m/s in 1.0 s.
B. A car accelerates from 20 m/s to rest in 1.0 s.
C. A centipede accelerates from 0.40 cm/s to 2.0 cm/s
in 0.50 s.
D. While
being hit, a golf ball accelerates from rest to
4.3 m/s in 0.40 s.
E. A jogger accelerates from 2.0 m/s to 1.0 m/s in 8.3 s.
Answers
Answer:
C , E , A , D , B
Explanation:
We evaluate the accelerations for each case, using the formula: a = (vf - vi) / t
A) a = (10.3 - 0.5 ) / 1 = 9.8 m/s^2 --> magnitude: 9.8 m/s^2
B) a = (0 - 20) / 1 = - 20 m/s^2 --> magnitude : 20 m/s^2
C) a = (0.02 - 0.004) / 1 = 0.016 m/s^2 --> magnitude : 0.016 m/s^2
D) a = (4.3 - 0) / 0.4 = 10.75 m/s^2 --> magnitude : 10.75 m/s^2
E) a = (1 - 2) / 8.3 = - 0.12 m/s^2 --> magnitude: 0.12 m/s^2
Then, comparing magnitudes from least to greatest:
C , E , A , D , B
The order of the magnitude of the acceleration, from least to greatest is:
C < E < A < D < B
In physics, acceleration (a) is the rate at which velocity changes (Δv) with time (t).
We will calculate the acceleration for each scenario using the following expression.
\(a = \frac{v-u}{t}\)
where,
u: initial velocityv: final velocityA. A falling acorn accelerates from 0.50 m/s to 10.3 m/s in 1.0 s.Data
u: 0.50 m/sv: 10.3 m/st: 1.0 s\(a = \frac{10.3m/s-0.50m/s}{1.0s} = 9.8 m/s^{2}\)
B. A car accelerates from 20 m/s to rest in 1.0 s.
Data
u: 20 m/sv: 0 m/s (rest)t: 1.0 s\(a = \frac{0m/s-20m/s}{1.0s} = -20 m/s^{2}\\\\|a| = 20 m/s^{2}\)
C. A centipede accelerates from 0.40 cm/s to 2.0 cm/s in 0.50 s.
Data
u: 0.40 cm/sv: 2.0 cm/st: 0.50 s\(a = \frac{2.0cm/s-0.40cm/s}{0.50s} = 3.2cm/s^{2} \times \frac{1m}{100cm} = 0.032 m/s^{2}\)
D. While being hit, a golf ball accelerates from rest to 4.3 m/s in 0.40 s.
Data
u: 0 m/s (rest)v: 4.3 m/st: 0.40 s\(a = \frac{4.3m/s-0m/s}{0.40s} = 11 m/s^{2}\)
E. A jogger accelerates from 2.0 m/s to 1.0 m/s in 8.3 s.
Data
u: 2.0 m/sv: 1.0 m/st: 8.3 s\(a = \frac{1.0m/s-2.0m/s}{8.3s} = -0.12 m/s^{2}\\\\|a| = 0.12 m/s^{2}\)
The order of the magnitude of the acceleration, from least to greatest is:
C < E < A < D < B
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Related Questions
Two cars, C and D, travel in the same direction on a long, straight section of highway. During a particular time interval Δt0, car D is ahead of car C and is speeding up while car C is slowing down 07 During the interval Δt0, it is observed that car C gains on car D (i.e., the distance between the cars decreases). Explain how this is possible, and give a specific example of such a case.
Answers
Answer:
Car C increases it velocity
Explanation:
From the problem statement, we can see that the two cars all along maintained the same velocities, even though car D was ahead, but at the said time, car C gained on car D, hence the velocity of car C increased more than that of car D, that was why the gap decreased.
A good way to exemplify this is to picture a friend stylishly waiting for you at a distance to meet with them, but they did not stop moving, they reduced their pace, you might have to increase your pace to meet with them, now you can observe the distance between you and them closes
A system experiences a change in internal energy of 36 kJ in a process that involves a transfer of 14 kJ of heat into the surroundings. Simultaneously, which of the following is true?
a. Q= 14 u=36
b. U=Q-W
c. 14-36=22
d. 22 kJ of work is done on the system.
Answers
Answer:
b. U = Q - W
Explanation:
Given;
change in internal energy, ΔU = 36 kJ
heat transferred to the surroundings Q = 14 kJ
Apply first law of thermodynamic; the change in internal energy is equal to heat added to the system minus work done by the system.
ΔU = Q - W
Since heat was lost to surroundings, Q = - Q
ΔU = (-Q) - W
36 kJ = -14 kJ - W
36 kJ + 14 kJ = - W
50 kJ = - W
W = - 50 kJ (the negative sign shows that work has been done on the system)
Thus, 50 kJ of work is done on the system.
The only correct answer in the given options is "b" U = Q-W
In the diagram, R₁ = 40.0 , R2= 25.4 , and R3 = 70.8 . What is the equivalent resistance of the group?
Answers
According to the diagram the equivalent resistance of the group is
40.05 ohms
How to find the equivalent resistanceThe equivalent resistance is calculated by investigating the diagram to note that R2 and R3 are in parallel and both are in series to R1
Resistors in parallel is solved by
Resistors in parallel = 1/25.4 + 1/70.8
Resistors in parallel = 0.0535 ohms
Equivalent resistance
Equivalent resistance = Resistors in parallel + Resistor in series
Equivalent resistance = 0.0535 + 40
Equivalent resistance = 40.0535
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In the Skycoaster amusement park ride, riders are suspended from a tower by a long cable. A second cable then lifts them until they reach the starting position indicated in (Figure 1). The lifting cable is then released, and the riders swing down the circular arc shown. If the four riders have a total mass of 330 kg
, what is the tension in the left cable just before release?
Answers
Tension in the left cable is 4395.9 N.
What is meant by tension ?Tension is defined as a pulling force that acts along the length of a flexible medium like rope or cables.
Here,
The total mass of the riders is given, m = 330 kg
Let the tension in the left cable be T₁ and that in the right cable be T₂.
From the figure,
T₁ cos 15 = T₂ cos 26
T₁ = T₂ cos 26/cos 15
Also,
T₁ sin15 + T₂ sin 26 = mg
Substituting values,
(T₂ cos 26/cos 15) sin 15 + T₂ sin 26 = 330x 9.8
0.241 T₂ + 0.438 T₂ = 3234
0.679 T₂ = 3234
T₂ = 4762.8 N
Therefore, Tension in the left cable, T₁ = 0.930x 4762.8
T₁ = 4395.9 N
Hence, The tension in the left cable is 4395.9 N
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Your question was incomplete. Attaching the image here.
3. A circular section of copper cable has a resistance of 0.50. What will be the resistance of a
copper cable of the same length but of twice its diameter?
Answers
What is Concave lenses ?
Answers
Explanation:
A concave lens is also known as a diverging lens because it is shaped round inwards at the centre and bulges outwards through the edges, making the light diverge. They are used to treat myopia as they make faraway objects look smaller than they are.
A marble is attached to a compressed horizontal spring and is then released. Which equation correctly shows the conservation of mechanical energy for this system?
Answers
The equation that shows the conservation of energy is 1/2mv^2=1/2kx^2
What is the equation of the mechanical energy of a compressed spring?The mechanical energy of a compressed spring can be calculated using the equation:
E = (1/2) k x^2
where E is the mechanical energy stored in the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
This equation is based on the principle of conservation of mechanical energy, which states that the total mechanical energy of a system (i.e. the sum of kinetic and potential energies) remains constant in the absence of non-conservative forces such as friction or air resistance. When a spring is compressed, work is done on the spring, which stores potential energy in the form of elastic potential energy.
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1. A string generates 120 vibrations every second.
a. What is its frequency?
b. What is its period?
Answers
Answer:
a:120hz
Explanation:
frequency=1 vibration per second so 120 seconds=120 vibrations
A body of mass 12kg travelling at 4.2m/s² collides with a second body of mass 18kg at rest. Calculate their common velocity of the two bodies coalesce after collision
Answers
When a body of mass 12kg travelling at 4.2m/s² collides with a second body of mass 18kg at rest, their common velocity after the collision is 1.68 m/s.
When two objects of different masses collide, they can exchange momentum. An object's mass and velocity together make up its momentum. When two objects collide, their momentum is conserved, meaning that the total momentum of the two objects before the collision equals the total momentum of the two objects after the collision. This principle can be used to calculate the velocity of the two objects after a collision.A body of mass 12 kg is travelling at a velocity of 4.2 m/s and collides with a second body of mass 18 kg at rest. The total mass of the system is 12 kg + 18 kg = 30 kg. To determine the velocity of the two objects after the collision, we need to use the conservation of momentum principle. Before the impact, the system's entire momentum is:momentum before = \((mass_1 x velocity_1) + (mass_2 x velocity_2)\)where mass1 is the mass of the first object, velocity1 is the velocity of the first object, \(mass_2\) is the mass of the second object, and \(velocity_2\) is the velocity of the second object. In this case,\(mass_1 = 12 kg, velocity_1 = 4.2 m/s, mass_2 = 18 kg\), and \(velocity_2 = 0\) (because the second object is at rest). Substituting these values into the equation above, we get: momentum before = (12 kg x 4.2 m/s) + (18 kg x 0)momentum before = 50.4 kg m/sFollowing the collision, the system's overall momentum is:momentum after =\((mass_1 + mass_2) * velocity\)where mass1 + mass2 is the total mass of the system, and velocity is the velocity of the two objects after the collision. Let's call this velocity "v". Substituting the values we know into the equation above, we get: momentum after = (12 kg + 18 kg) x vmomentum after = 30 kg x vUsing the conservation of momentum principle, we know that momentum before = momentum after. Therefore, we can set these two equations equal to each other and solve for v.50.4 kg m/s = 30 kg x vv = 50.4 kg m/s ÷ 30 kgv = 1.68 m/sFollowing the impact, the two bodies' common velocity is 1.68 m/s. Hence, the answer to this problem is that when a body of mass 12kg travelling at 4.2m/s² collides with a second body of mass 18kg at rest, their common velocity after the collision is 1.68 m/s.For more questions on collision
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Both plant and animal cells have a nucleus.
True or False
Answers
Answer:
the answer is true ;)
Explanation:
Answer:
true
Explanation:
because they just are
What happened to the Western Africa empires?
Answers
Answer:
they died lol XD Gang op.....
Which two options describe physical properties of matter?
Answers
Answer:
A and B
Explanation:
A.P.E.X
Why is the temperature constant during the melting of water?
Answers
\( \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}}\)
Why is the temperature constant during the melting of water?
\( \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}\)
\( \orange{\underline{\huge{\bold{\textit{\green{\bf{ REASON}}}}}}}\)
THE HEAT WE R SUPPLYING TO THE WATER TO RAISE THE TEMP OF THE WATER IS USED BY THE MOLECULES TO BREAK INTERMOLECULAR BONDS WHICH HELP IN THE CHANGING OF THE LATTICE (STRUCTURE) OF THE WATER .
ICE HAS A HEXAGONAL RING LIKE STRUCTURE WHICH IS CONVERTED INTO REGULAR CRYSTALLINE STRUCTURE WHICH CAN ONLY BE FORMED WITH THE HELP OF FORMATION OF NEW BONDS AND BREAKDOWN OF OLDER ONES
THE AMOUNT OF ENERGY WHICH IS USED IN CONVERSATION OF THE STATE OF FROM SOLID TO LIQUID IS KNOWN AS LATENT HEAT OF FUSION.
SO TEMP REMAIN CONSTANT DURING CHANGE IN STATE .
\( \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star\)
A plane starting at rest from one end of the runway undergoes a uniform acceleration of 4.8 m/s² for 15 seconds before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to takeoff?
Answers
Starting from rest and accelerating at 4.8 m/s², the plane's velocity at time t is
v(t) = (4.8 m/s²) t
so that after 15 s, its speed at takeoff be
v(15 s) = (4.8 m/s²) * (15 s) = 72 m/s
In this time it takes for the plane to take off, it will travel a distance at time t of
x(t) = 1/2 (4.8 m/s²) t²
and it takes 15 s to take off, so the runway would have to have a length of
x(15 s) = 1/2 (4.8 m/s²) * (15 s)² = 540 m
The components of vector Upper A Overscript right-arrow EndScripts are Ax and Ay (both positive), and the angle that it makes with respect to the positive xaxis is θ. Find the angle θ if the components of the displacement vector Upper A Overscript right-arrow EndScripts are:
(a) Ax = 12 m and Ay = 12 m,
(b) Ax= 19 m and Ay = 12 m, and
(c) Ax = 12 m and Ay = 19 m.
(a) θ = Number____________ Units____
(b) θ = Number____________ Units____
(c) θ = Number ____________Units____
Answers
Answer:
(a) θ = 45° = 0.78 rad
(b) θ = 32.27° = 0.56 rad
(c) θ = 57.27° = 1 rad
Explanation:
When a vector is resolved into its rectangular components, the formula for the direction angle of the vector with positive x-axis is given as:
tan θ = Ay/Ax
θ = tan⁻¹(Ay/Ax)
(a)
Ax = 12 m
Ay = 12 m
θ = tan⁻¹(12 m/ 12 m)
θ = tan⁻¹(1)
θ = 45° = 0.78 rad
(b)
Ax = 19 m
Ay = 12 m
θ = tan⁻¹(12 m/19 m)
θ = tan⁻¹(0.6315)
θ = 32.27° = 0.56 rad
(c)
Ax = 12 m
Ay = 19 m
θ = tan⁻¹(19 m/12 m)
θ = tan⁻¹(1.58333)
θ = 57.27° = 1 rad
An electromagnet in the galvanometer tunes the pointer to indicate the amount of current present.Why does an electromagnet act like a loop of wire in a magnetic field?
Answers
Answer and Explanation:
An electromagnet is made up of a coil of wire through which an electric current flows. When an electric current flows through the wire, it creates a magnetic field around the wire. The magnetic field is created because the moving electrons in the wire produce a magnetic field, as described by the right-hand rule.
When an electromagnet is placed in a magnetic field, the magnetic field produced by the current in the wire interacts with the external magnetic field. This interaction causes a force to be exerted on the wire, which causes the wire to move. The force is proportional to the strength of the magnetic field and the current flowing through the wire. This is the principle behind how an electromagnet can act like a loop of wire in a magnetic field.
In a galvanometer, an electromagnet is used to create a magnetic field that interacts with the magnetic field produced by the current flowing through the circuit. This interaction causes a force to be exerted on the wire in the electromagnet, which in turn moves the pointer of the galvanometer. The greater the current flowing through the circuit, the greater the force exerted on the wire in the electromagnet, and the greater the deflection of the pointer.
The refractive index of water with respect to air is 5/3 and that of glass is 3/2.What is the refractive index glass with respect to water?
Answers
Answer:
9/8
Explanation:
Given the functions f(x)=(1/x-3)+1 and g(x) = (1/1+4)+3
Which statement describes the transformation of the graph of function f onto the graph of function g?
O The graph shifts 2 units right and 7 units down.
O The graph shifts 7 units left and 2 units up.
O
e graph shifts 7 units right and 2 units down.
O The graph shifts 2 units left and 7 units up.
Answers
The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.
To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.
The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.
The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.
By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:
The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.
The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.
The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.
Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.
Hence, the correct statement is: The graph shifts 2 units right and 7 units down.
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4. A 40.0 kg child swings in a swing supported by two chains, each 3.00 m long. If the tension in each at the lowest point is 350N, find (i) The child’s speed at the lowest point ,
Answers
The child's speed at the lowest point is 5.42 m/s.
At the highest point of the swing, the child is momentarily at rest and has only potential energy. At the lowest point, the child has only kinetic energy.
Using the conservation of mechanical energy, we can write:
Potential energy at highest point = Kinetic energy at lowest point
mgh = (1/2)mv²
where m is the mass of the child, g is the acceleration due to gravity, h is the height of the swing at the highest point, and v is the speed of the child at the lowest point.
First, we need to find the height of the swing at the highest point. Since the swing is supported by two chains, the height of the swing at the highest point is half the length of the chains:
h = (1/2)3.00 m = 1.50 m
Next, we can solve for the child's speed at the lowest point:
mgh = (1/2)mv²
40.0 kg * 9.81 m/s² * 1.50 m = (1/2) * 40.0 kg * v²
588 J = 20.0 kg * v²
v² = 29.4 m²/s²
v = 5.42 m/s
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Two people, one of mass 85 kg and the other of mass 50 kg, sit in a rowboat of mass 90 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.5 m apart from each other, now exchange seats. How far does the boat move?
Answers
Answer:
0.11m
Explanation:
let's assume the boat is of uniform construction
Ignoring friction losses
Also assume the origin is at the end of the boat originally with the heavier person
the center of mass of the whole system will not change relative to the water when the two swap ends
Originally, the center of mass is
85[0] + 90[3.5/2] + 50[3.5] / (85 + 90 + 50) = 1.14m from the origin
after the swap, the center of mass is
50[0] + 90[3.5/2] + 85[3.5] / (85 + 90+ 50) = 1.030m from the origin
The center of mass has shifted
1.14-1.030 = 0.11m
as no external force acted on the system, the center of mass relative to the water will not change. The boat will therefore shift towards the end where the heavier person originally sat
a car accelerates from 4 meters/second to 16 meter/second in 4 seconds. The cars acceleration is how many meter/seconds.
Answers
Answer:
=3 metre per second ^2
Explanation:
Formula for acceleration is
V-U÷T
In the given information
V=16
U=4
T=4
Acceleration =16-4/4
=3 metre per second ^2
When a calcium atom forms an ion, it loses two electrons. What is the electrical charge of the calcium ion? a) −2 b) −1 c)+ 1 d) + 2
Answers
Answer:
Option D
+2
Explanation:
We know that Calcium has 20 electrons and 20 protons. It lost two electrons, it has 20 protons, but only 18 electrons. This makes calcium a positive ion with a charge of +2.
The force F shown in Figure 4.30 has a moment of 40 Nm about the pivot. Calculate the magnitude
of the force F.
Answers
\(\boxed{\sf \tau=rFsin\theta}\)
Put values
\(\\ \rm\hookrightarrow 40=2Fsin40\)
\(\\ \rm\hookrightarrow Fsin40=20\)
\(\\ \rm\hookrightarrow 0.64F=20\)
\(\\ \rm\hookrightarrow F=31.25N\)
The moment of force is 40 Nm here. The displacement is 2.5 m and the angle of inclination is 45°. The force about the pivot is then 28.2 N.
What is moment of force?Moment of force is the product of the force and distance from a fixed axis. Moment of force can be calculated for both balanced and unbalanced forces.
The expression for moment of force relating the distance d and force f with an angle of inclination θ is written as below:
moment of force = f d sin θ
Given that moment of force = 40 Nm
distance from the fixed axis from the figure = 2 m
angle of inclination = 45 °
40 Nm = 2 f sin 45.
20 = f sin 45
f = 20 N / sin 45
= 28.2 N
Therefore, the force about the pivot is 28.2 N.
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what is dispersion of light?
Answers
Answer:
\( \huge \bold \blue{ \underline{ answer}}\)
The splitting up of light into its constituent colours while passing from one medium to the other is called dispersion.
At its highest temperature, a space heater has a resistance of 17.5 Ω when it is plugged into a wall outlet that supplies a peak voltage of 176.8 V sinusoidally at 60 Hz . What is the average power output ⎯⎯⎯⎯ of the space heater?
Answers
At its highest temperature, a space heater has a resistance of 17.5 Ω when it is plugged into a wall outlet that supplies a peak voltage of 176.8 V sinusoidally at 60 Hz . the average power output of the space heater is 888 watts.
The average power output of the space heater can be calculated using the root mean square (RMS) values of the voltage and current. The RMS voltage and current are related to the peak voltage and the resistance of the space heater as follows:
V_RMS = V_peak / sqrt(2)
I_RMS = V_RMS / R
where V_RMS is the RMS voltage, I_RMS is the RMS current, V_peak is the peak voltage, and R is the resistance of the space heater.
Substituting the given values, we get:
V_RMS = 176.8 V / sqrt(2) = 124.8 V
I_RMS = 124.8 V / 17.5 Ω = 7.12 A
The average power output of the space heater is given by:
P_avg = V_RMS * I_RMS * cos(θ)
where cos(θ) is the power factor, which we will assume to be 1 for a resistive load like the space heater.
Substituting the values for V_RMS and I_RMS, we get:
P_avg = 124.8 V * 7.12 A * 1 = 888 W.
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An artillery shell is fired at a target 200 m above the ground. When the shell is 100 m in the air, it has a speed of 100 m/s. What is its speed when it hits its target?
Answers
The speed of the artillery shell when it hits its target is 100 m/s.
Given:
Initial vertical displacement (y) = 200 m
Vertical displacement at 100 m in the air (y') = 100 m
Final velocity in the vertical direction (vy') = 0 m/s (at the highest point of the trajectory)
Using the equation for vertical displacement in projectile motion:
y' = vy^2 / (2g),
where g is the acceleration due to gravity (approximately 9.8 m/s^2), we can solve for the initial vertical velocity (vy).
100 m = vy^2 / (2 * 9.8 m/s^2),
vy^2 = 100 m * 2 * 9.8 m/s^2,
vy^2 = 1960 m^2/s^2,
vy = sqrt(1960) m/s,
vy ≈ 44.27 m/s.
Now, since the horizontal motion is independent of the vertical motion, the horizontal speed of the shell remains constant throughout its trajectory. Therefore, the speed of the shell when it hits its target is 100 m/s.
Hence, the speed of the artillery shell when it hits its target is 100 m/s.
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A helium balloon (in the shape of a sphere) has radius 7.25 m .
For the density of air, please use 1.29 kg/m^3, and for Helium, use .179 kg/m^3
How much additional mass (payload) could this balloon lift? You should assume the balloon's skin, plus other parts of the balloon's structure have a total mass of 920 kg . Note however that this number does NOT yet include the mass of the helium filling the balloon, which you will need to account for!
Answers
Additional mass (payload) of a helium baloon lift is , \(M_{payload}=853.47kg\)
What is mass?
The amount of matter in a particle or object is represented by the dimensionless quantity mass (symbolised m). The kilogram is the International System's (SI) preferred unit of mass (kg).
The weight of the helium gas, the skin, other components of the balloon's construction, as well as the payload, must be balanced by the buoyant force. Using this, we determine the necessary payload mass.
Given pair= \(1.29kg/m^{3}\)
buoyant force b = V*pair g
\(=(\frac{4}{3} *\pi R^{3} ) pair*g\\=20179.87N\)
mass of helium is,
\(m=(\frac{4}{3} * \pi R^{3} )(0.179)\\m=285.7kg\)
so total mass, \(M=m+920kg\)
\(M=1205.7kg\)
so, b = \((M+M_{payload}) g\)
\(M_{payload}=853.47kg\)
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A block of mass m is hung from the ceiling by the system of massless springs consisting of two layers. The upper layer consists of 3 strings in paralle, and the lower layer consists of 2 strings in parallel. The horizontal bar between the two layers has negligible mass. The force constants of all springs are k. Calculate the period of the vertical oscillations of the block.
Answers
Answer:
T₀ = 2π \(\sqrt{\frac{m}{k} }\) T = \(\sqrt{\frac{5}{6} }\) T₀
Explanation:
When the block is oscillating it forms a simple harmonic motion, which in the case of a spring and a mass has an angular velocity
w = \(\sqrt{k/m}\)
To apply this formula to our case, let's look for the equivalent constant of the springs.
Let's start with the springs in parallels.
* the three springs in the upper part, when stretched, lengthen the same distance, therefore the total force is
F_total = F₁ + F₂ + F₃
the springs fulfill Hooke's law and indicate that the spring constant is the same for all three,
F_total = - k x - k x - kx = -3k x
therefore the equivalent constant for the combination of the springs at the top is
k₁ = 3 k
* the two springs at the bottom
following the same reasoning the force at the bottom is
F_total2 = - 2 k x
the equivalent constant at the bottom is
k₂ = 2 k
now let's work the two springs are equivalent that are in series
the top spring is stretched by an amount x₁ and the bottom spring is stretched x₂
x₂ = x -x₁
x₂ + x₁ = x
if we consider that the springs have no masses we can use Hooke's law
\(-\frac{F_{1} }{k_{1} } - \frac{F_{2}}{k_{2} } = \frac{F}{k_{eq} }\)
therefore the equivalent constant is the series combination is
\(\frac{1}{k_{eq} } = \frac{1}{k_{1} } + \frac{1}{k_{2} }\)
we substitute the values
\frac{1}{k_{eq} } = \frac{1}{3k } + \frac{1}{2k }
\frac{1}{k_{eq} } = \frac{5}{6k} }
k_eq = \(\frac{6k}{5}\)
therefore the angular velocity is
w = \(\sqrt{\frac{6k}{5m} }\)
angular velocity, frequency, and period are related
w = 2π f = 2π / T
T = 2π / w
T = 2π \(\sqrt{\frac{5m}{6k} }\)
T₀ = 2π \(\sqrt{\frac{m}{k} }\)
T = \(\sqrt{\frac{5}{6} }\) T₀
What causes deep moonquakes
Answers
Answer:
There are at least four different kinds of moonquakes: (1) deep moonquakes about 700 km below the surface, probably caused by tides; (2) vibrations from the impact of meteorites; (3) thermal quakes caused by the expansion of the frigid crust when first illuminated by the morning sun after two weeks of deep-freeze lunar ...
Explanation:
Answer:
The moonquakes are probably a result of the moon going contraction or tides
Answer ASAP and only if you know its correct
this is science btw
Answers
Answer:
jupiter
Explanation:
from the list, Jupiter is closest to the sun.