Jake's velocity at the lowest point of the swing is 7 m/s.
What is kinetic and potential energy?Potential energy is the energy stored in any object or system due to the position or arrangement of its parts. It is, however, unaffected by factors outside of the object or system, such as air or height. Kinetic energy, on the other hand, is the energy of moving particles in an object or system.
To solve this problem, we need to use the conservation of energy principle, which states that the total energy in a system remains constant.
At the highest point, Jake has potential energy (due to his position above the ground), but no kinetic energy (since he is not moving).
As he swings down, his potential energy is converted to kinetic energy, and at the lowest point of the swing, he has the maximum kinetic energy and minimum potential energy. Then, as he swings back up, the process is reversed.
To calculate Jake's potential energy at the top of the swing, we use the formula:
PE = mgh
where m is the mass of Jake, g is the acceleration due to gravity (9.8 m/s²), and h is the height above the ground. Substituting in the values, we get:
PE = (20 kg)(9.8 m/s²)(2 m) = 392 J
This is Jake's potential energy at the top of the swing. At this point, he has no kinetic energy.
At the lowest point of the swing, Jake has converted all of his potential energy into kinetic energy. We can use the conservation of energy principle to find his kinetic energy at this point:
KE = PE
where KE is kinetic energy and PE is potential energy. Substituting in the values, we get:
KE = 392 J
This is Jake's kinetic energy at the lowest point of the swing.
To find Jake's velocity at the lowest point, we can use the formula for kinetic energy:
KE = (1/2)mv²
where v is velocity. Rearranging the formula to solve for v, we get:
v = √((2KE)/m)
Substituting in the values, we get:
v = √((2(392 J))/(20 kg)) = 7.0 m/s
This is Jake's velocity at the lowest point of the swing.
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1 kg block and a 2 kg block are placed next to each other on a frictionless horizontal table. A horizontal force of 6 N is applied orthogonally to the side 1 kg block. Find the magnitude of the force acting on the 2 kg block?
Group of answer choices
4 N
1 N
3 N
2 N
Answer:
3N
Explanation:
yeah just that is it you don't need calculation to solve it
A the cannon recoils from firing a cannonball. The speed of the cannon's recoil is small because a. cannon has more mass than the ball b. momentum of the cannon is smaller. c. force against the cannon is smaller than against the ball. d. momentum is mainly concentrated in the ball. e. none of these
The cannon has more mass than the ball.
option A is the correct answer.
Why is the speed of the cannon's recoil small?
The recoil of a cannon after firing a cannonball is a consequence of the conservation of momentum. According to this principle, the total momentum of a closed system is conserved, which means that the momentum of the cannon and cannonball before the firing must be equal to the momentum of the cannon and the cannonball after the firing.
Thus, the cannon has more mass than the ball, which means that it has a greater inertia and will be more resistant to acceleration. This results in a smaller speed of recoil compared to the cannonball.
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Many physical phenomena can be described by the Arrhenius equation. For example, reaction rate constants for chemical reactions are modeled as k = ko exp(-Q/RT), where ko is a constant with units that depend on the reaction, Q is the activation energy (kJ/mol), R is the ideal gas constant (kJ/kmol-K), and I is the temperature in K. For a certain reaction, the values of the constants are: Q = 1000 J/mol, ko = 10 s-1, and R = 8.314 J/mol-K. Use matlab code to calculate values of k (by applying the Arrhenius equation) for T from 300 K to 1000 K and to graph the data. Specifically, generate the following two graphs in a single figure window (using subplot). a) plot T on the x-axis and k on the y-axis; b) plot 1/T on the x-axis and the log10 of k on the y-axis.
The reaction rate constant and activation energy have an exponential connection, which is described by the Arrhenius equation, which may be used to predict reaction rate constants for chemical reactions as a function of temperature.
Define Q, ko, and R, as well as the other specified constants.
The "linspace" function in Matlab can be used to create a vector of temperature values ranging from 300 K to 1000 K.
Use the Arrhenius equation and the listed constants to determine the value of k for each temperature value.
Plot temperature values on the x-axis and k values on the y-axis using the Matlab "plot" function. Plot 1/T values on the x-axis and the log10 of k values on the y-axis using the same Matlab "plot" function.
Add titles to the figure window and label the x- and y-axes on both graphs.
% Define constants
Q = 1000; % J/mol
ko = 10; % s^-1
R = 8.314; % J/mol-K
% Create a vector of temperature values
T = linspace(300, 1000);
% Calculate k values using the Arrhenius equation
k = ko * exp(-Q./(R.*T));
% Create a subplot with two graphs
subplot(1, 2, 1)
plot(T, k)
xlabel('Temperature (K)')
ylabel('Reaction Rate Constant (s^-1)')
title('Arrhenius Plot')
subplot(1, 2, 2)
plot(1./T, log10(k))
xlabel('1/Temperature (1/K)')
ylabel('log10(Reaction Rate Constant)')
title('Modified Arrhenius Plot')
The Arrhenius plot and the modified Arrhenius plot are two subplots that should appear in a single figure window created by this code. The Arrhenius plot displays the correlation between temperature and the reaction rate constant, whereas the modified Arrhenius plot displays the correlation between 1/T and the log10 of the reaction rate constant.
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A rail road car of mass 1500kg rolls to the right at 4 m/s and collides with another railroad car of mass 3000kg that is rolling to the left at 3 m/s. The cars stick together. Their speed immediately after the collision. 2/3m/s 1 m/s 5/3 m/s 10/3 m/s 7 m/s
The speed of the cars right after the collision is 1/3 m/s.
To solve this problem, we can apply the law of conservation of momentum, which states that the total momentum of a system remains constant if there are no external forces acting on it. In this case, the two railroad cars form a closed system, and there are no external forces acting on them during the collision. Therefore, we can write:
(m1 * v1) + (m2 * v2) = (m1 + m2) * v
where m1 and v1 are the mass and velocity of the first railroad car, m2 and v2 are the mass and velocity of the second railroad car, m1 + m2 is the total mass of the system after the collision, and v is the velocity of the system after the collision.
Plugging in the given values, we get:
(1500 kg * 4 m/s) + (3000 kg * (-3 m/s)) = (1500 kg + 3000 kg) * v
Simplifying and solving for v, we get:
v = (1500 kg * 4 m/s - 3000 kg * (-3 m/s)) / (1500 kg + 3000 kg)
v = (6000 kgm/s + 9000 kgm/s) / 4500 kg
v = 15/45 m/s = 1/3 m/s
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Water is poured into a container that has a small leak. The mass m of the water is given as a function of time t by m=5.00 t 0.8
−3.00t+20.00, with t≥0,m in grams, and t in seconds.
At what time is the water mass greatest.
Answer:
Explanation:
when gravity pulls the water molecules downwards, they will fall. But if they're in a container, the container will keep them from spreading out completely. This is what's called 'taking the shape of the container'
three capacitors of capacitance 1 micro Farad, 2 microfarad and 2 microfarad are each charged to 250 volts and then connected in series. 1) find the overall potential difference across the capacitor 2) find the charge on each capacitor and 3) find the energy stored in the combination
1) The overall potential difference across the capacitor is 1.66 V.
2) The charge on each capacitor is 1.66 C.
3) The energy stored in the combination will be 1.3778 J.
What is a capacitor?A capacitor is a device that stores electrical energy in an electric field by accumulating electric charges on two insulated surfaces. It is a two-terminal passive electronic component. Capacitance is the effect of a capacitor.
Given that three capacitors of capacitance 1 micro Farad, 2 microfarads and 2 microfarads are each charged to 250 volts and then connected in series.
Q₁ = C₁Vt
Q₁ = 1 x 5 = 5 μF
Q₂ = C₂Vt
Q₂ = 2 x 5 = 10 μF
The equivalent capacitance will be,
1 / Ct = 1 / C₁ + 1 / C₂
Ct = 2 / 3 μF
Vt = 10 / 3 ÷ 2
Vt = 1.66 V
The charge will be,
q =CV
q = 1 x 1.66
q = 1.66 C
The energy will be calculated as:-
U = 1/2 x C xV
U = 1 / 2 x 1 x 1.66²
U = 1.3778 J
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A reaction has an activation Energy of 20 kJ and E = -60 kJ/mol. What would be the activation Energy for the REVERSE reaction?
A.) 40 kJ
B.) 80 kJ
C.)100 kJ
D.) 20 kJ
E.) 60 kJ
The activation energy for the reverse (backward) reaction would be 20 + 60 = 80 kJ/mol.
From the question, we are told that the activation energy of the reaction is 20 kJ and its E is -60 kJ/mol. A negative number for E means that it is an exothermic reaction, a reaction in which energy is released instead of absorbed.
The energy graph for an exothermic reaction is attached below. You can see that the activation energy for a backward reaction is EQUAL to the activation energy for the forward reaction + energy released.
Since we know the activation energy and E, the activation energy for the reverse (backward) reaction would be 20 + 60 = 80 kJ/mol.
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When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by y = 0.001 sin 880πt, where t is the time (in seconds).(a) What is the period of the function?(b) The frequency f is given by f=1p. What is the frequency of the note?
The required period of the function is calculated to be 1/440 sec and frequency is calculated to be 440 hertz.
The equation of the sinusoidal wave is given as, y = 0.001 sin 880πt
Comparing the given equation with that of the general equation of the wave in simple harmonic motion, we have, y = a sin ωt
where,
y is displacement
a is amplitude
t is time
ω is angular frequency
So, Angular frequency ω = 880π
The period of the function is given by the formula, p = 2π/ω = 2π/880π = 1/440 sec
We know the equation for frequency as, f = 1/p = 1/(1/440) = 440 hertz
Thus, the period of the function is 1/440 sec and frequency is calculated to be 440 hertz.
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let a be the sum of the last three digits and let b be the last digit of your 8-digit student id. example: for 20245347, a
Answer: The given time period of oscillation would be around 0.9515 seconds.
Explanation:
The very first 54.0 km were driven at an average speed, while the final 86.0 km were driven at in a speed of (43.0 b) km/h. She travels at an average speed of 43.75 km/h for the entire journey.
How speed is it?Velocity is the pace and velocity of an object's movement, whereas speed is the forecasting at which an objects is travelling along a path. In other words, velocity is a vector, whereas quickness is a scalar value. As a result, the fundamental unit of time and the basic element of distance are combined to form the Special name of speed. Thus, the metre per second (m/s) is the Substrate concentration of speed.
a = 19 and b = 7
Average speed, 54 km = 48+a km/h
Plug a = 19
54 km = 48+19
= 67 km/h
remaining speed
86 km = 43-b km/h
where b = 7
Average speed = 36 km/h
Average speed = total distance / total time taken
speed = distance/time
time = distance/speed
To cover 54 km = 54/67 hr
To cover 86 km = 86/36 hr
Total time = 3.2 hours.
Total distance = 86+54
= 140 km
Average speed 140/3.2
= 43.75 km/ h
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Rigid rods of negligible mass lying along the y axis connect three particles. The system rotates about the x axis with an angular speed of 1.00 rad/s. It is known that m1 = 3.00 kg, m2 = 2.00 kg, m3 = 4.00 kg, and y1 = -4.00 m, y2 = -2.00 m, and y3 = 3.00 m.(a) Find the moment of inertia about the x axis.(b) Find the total rotational kinetic energy evaluated from 1/2 Iω2(c) Find the tangential speed of each particle.
The following values are given: m1 = € kg, resistor = y1 Means 3.00 m, sq.m = 1.75 kg, r2 / y2. = 1.75 m, m3 = 3.00 metric tons, r3 = restrictions that limit. = 4.00 m, and = 1.75 rad/s about x-axis = m1r. 2.
How do you calculate the total kinetic energy of rotation?The combined translational and rotational kinetic energies of an object in motion determine its total kinetic energy. 12 mvCM2 is the translational kinetic energy. Rotational kinetic energy is equal to 12 I2. Total kinetic energy is 12mvCM2 plus 12I2.
What is the equation for the case of rotating kinetic energy?E s = x 2 x I ω 3 . . This equation shows that its kinetic energy of such a rotating solid body is inversely related to the cube of the angular acceleration and the moment of inertia. Flywheel energy-storage systems, which are intended to, take advantage.
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A worker wants to load some bricks in to his van. there are 1000 bricks and when stacked neatly they measure 2m by 1m by 1m. If the vans maximum load is 1000kg, how many bricks can he load?
The worker can load {500/ρ} number of bricks into the van.
What is mass?Mass is the total amount of matter present inside a body.
Given is that a worker wants to load some bricks in to his van. There are 1000 bricks and when stacked neatly they measure 2m by 1m by 1m.
Assume the density of the brick to be {ρ}. Let's assume that he can load {n} bricks inside the van. So, we can write -
n x mass of 1 brick = maximum load
n x ρ x V = L{max}
nρV = L{max}
n = L{max}/ρV
n = 1000/(2 x 1 x 1 x ρ)
n = 500/ρ
Therefore, the worker can load {500/ρ} number of bricks into the van.
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the diagrams below show the same set of energy levels as in parts a and b, but with a different set of electron transitions (notice that the arrows are now different). assuming that these electron transitions were caused by the absorption of a photon, rank the atoms based on the energy of the absorbed photon, from highest to lowest.
The ranking of the energy that is requires is;
4 > 3 > 2> 1
What are atomic energy levels?Atomic energy levels refer to the specific energy states that an electron can occupy in an atom. Electrons in an atom can only occupy certain energy levels, and the energy levels are quantized, meaning that only specific values are allowed.
When an electron absorbs energy, it can jump to a higher energy level, and when it releases energy, it drops to a lower energy level. The energy levels are determined by the properties of the atom, such as the number of protons and neutrons in the nucleus and the electrons' distribution in the atom's electron shells.
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T/F plato's apology tells the story of how sorry socrates was for having upset his fellow athenians with his persistent questioning.
The given statement " plato's apology tells the story of how sorry socrates was for having upset his fellow athenians with his persistent questioning." is False
Plato's Apology is not about how sorry Socrates was, but rather a speech he delivered during his trial in which he defended his philosophical beliefs and actions, and refused to apologize for them. Socrates argued that his questioning was necessary to improve Athens and its citizens, and that his death would only harm the city. The Apology is often seen as a key text in the development of Western philosophy, and has been interpreted in many different ways.
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let f (t) be the velocity (in miles/hour) of a runner running along a north-south path, where f (t) > 0 means running in the north direction, and where t
The velocity of the runner at t=π/2 seconds is 15 miles/hour.
The directional speed of an item in motion, as measured by a specific unit of time and viewed from a certain point of reference, is what is referred to as velocity.
The function is as follows:
f(t)=-10cos(t) + 15
The time in this case is shown as t.
We must change t=/2 in the given function to obtain the runner's speed at t=/2 seconds:
f(π/2) = -10cos(π/2) + 15
f(π/2) = -10(0) + 15
f(π/2) = 15
As a result, the runner's speed at t=/2 seconds is 15 miles per hour.
We may deduce that the runner is moving towards the north at a speed of 15 miles per hour at t=/2 seconds since f(t) > 0 denotes moving in that direction.
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8) A projectile fired from the ground has a velocity = 24.0 î-8.00 m/s at a height of
9.10 m. Find: (a) the initial velocity; (b) the maximum height.
(a) The initial velocity of the projectile is 42.23 m/s.
(b) The maximum height reached by the projectile is 91 m.
What is the magnitude of the initial velocity of the projectile?
The initial velocity of the projectile is calculated by applying the following kinematic equation.
v = ( 24.0 î - 8.00j ) m/s
The angle of projection is calculated as;
θ = arc tan ( Vy / Vx )
θ = arc tan ( 8 / 24 )
θ = 18.43⁰
h = ( u² sin²θ ) / 2g
u² = 2gh / (sin²θ)
u² = ( 2 x 9.8 x 9.1 ) / ( sin 18.43 )²
u² = 1783.6
u = √1783.6
u = 42.23 m/s
The maximum height reached by the projectile is calculated as follows;
v² = u² - 2gh
where;
v is the final velocity at maximum height = 0u is the initial velocityg is acceleration due to gravityh is the maximum height2gh = u²
h = ( u² ) / ( 2g)
h = ( 42.23² ) / ( 2 x 9.8 )
h = 91 m
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A box initially has 335 J of kinetic energy. The final kinetic energy is 125. How much work was done to the box?
Answer:
Explanation:
The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.
Work done = 335-125=110J
1. Find the minimum magnitude of the acceleration amin of the car.2. Find the maximum acceleration amax of the car.Express your answer in meters per second per second to the nearest integer.3. Find the distance d0,2 traveled by the car between t=0s and t=2s.Express your answer in meters to the nearest integer.
The minimum magnitude of the acceleration of the car is 0.
The maximum acceleration will be 30m/s².
The distance traveled is 55m.
How to calculate the distanceMinimum magnitude of acceleration of the car is 0. This is because in a V-t graph slope of tangent on the of car and at t=us slope is zero.
Maximum acceleration of car is from o tois where slope is steepest.
= V - u / t
= 30 - 0 / 1
= 30m/s²
The distance will be:
d1 = 15
d2 = 1/2(30 + 50) = 40
Distance = 15 + 40 = 55m
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Compare dispersing light into colors with a prism and then into a grating. The 30-60-90 prism is made of glass with indices n {red}=1.52 and n {blue}=1.53. The grating has 500 slits per millimeter. a. What is the angular separation between red and blue light leaving the prism in degrees? b. What is the angular separation between red (650 nm) and blue (450 nm) light leaving the grating in degrees? Explain
Both a prism and a diffraction grating can be used to disperse white light into its component colors, which are a range of wavelengths of visible light.
What is diffraction?Due to the differing refractive indices of the prism material for various wavelengths of light, a prism operates by refracting the various hues of light as they pass through at slightly different angles. This causes the colours to disperse into a spectrum that resembles a rainbow. The prism equation provides the angle of departure for the various hues.θ = sin^(-1) (-1)
[n avg] = [(n blue - n red) sin()]
where n red and n blue are the prism's respective refractive indices for red and blue light, and n avg is the average of the two refractive indices, and is the angle of deviation, is the angle of incidence of the light on the prism, and so forth.Assuming an angle and the values given as n red = 1.52, n blue = 1.53, and n avg = (n red + n blue)/2 = 1.525
of incidence of 45 degrees, we can calculate the angle of deviation to be:
θ = sin^(-1)[(1.53 - 1.52) sin(45°) / 1.525] = 0.34°
Therefore, the angular separation between red and blue light leaving the prism is 0.34 degrees.
A diffraction grating works by diffracting light through a series of closely spaced parallel slits or lines, which act like a series of tiny prisms that diffract the light at different angles depending on its wavelength. The angle of diffraction of a particular color is given by the grating equation:nλ = d(sin θ_i + sin θ_d)
where n is the order of the diffraction (usually n=1), λ is the wavelength of the light, d is the spacing between the grating lines, θ_i is the angle of incidence of the light on the grating, and θ_d is the angle of diffraction.
Using the given values of d=500 nm (i.e., 500 slits per mm), λ_red = 650 nm and λ_blue = 450 nm, and assuming an angle of incidence of 0 degrees (i.e., the light is perpendicular to the grating), we can calculate the angles of diffraction for red and blue light to be:θ_red = sin^(-1)[(nλ_red / d) - sin(θ_i)] = sin^(-1)[(1650 nm / 500 nm) - sin(0°)] = 0.837°
θ_blue = sin^(-1)[(nλ_blue / d) - sin(θ_i)] = sin^(-1)[(1450 nm / 500 nm) - sin(0°)] = 0.579°
Therefore, the angular separation between red and blue light leaving the grating is:
θ_separation = θ_red - θ_blue = 0.837° - 0.579° = 0.258°
This is smaller than the angular separation obtained from the prism, and is due to the fact that a grating has a higher dispersion than a prism, meaning that it can separate colors more effectively. However, a grating also has narrower angular acceptance and higher order diffraction peaks that can interfere with the desired signal.To know more about diffraction , check out :
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8. (a) The mass m of an object is proportional to its volume V: m = kV. What are the SI units of k? (b) If the distance d an object moves in time t is given by the equation d = At-, find the SI units of A. (c) If the speed v of an object depends on time t according to the equation v = A + Bt + Ct4, what are the SI units of A, B, and C?
density is the mass of a specific material per unit volume. d = M/V, in which d is densities, M is mass, as well as V is volume, is the formula for density. Common units for expressing density are grams per cubic inch.
What is the mass unit?
There are several ways to measure mass, including kilograms, grams, pounds, and pounds, but the SI unit de mass is the "kilogram" or kg. Using the right conversion formula, any unit of weight can be changed into another unit without changing the significance or meaning of the quantity being measured.
Describe mass.
Definition, Units, Formula, and Examples of Mass The quantity of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, an chair, your mattress, a ball, a tumbler, and even air. The mass of a thing determines whether it is light or heavy.
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A spraying pump is used to spray water from a pool to a fountain.
a) Determine the power of the pump when the work done by the pump is 800Nm at 50ms to a distance of 20m
b) Determine the mass of the pump when the water is projected at acceleration of 10m/s?
The power of the pump is its work done by time. The power used for a work done of 800 Nm in 50 seconds is 16 J/s or W. The force acting here is 40 N. Then the mass of the body is 4 kg.
What is power ?Power of an object is the rate of work done or energy used.
power = work done/ time.
It has the unit watt which is equal to J/s.
a. Given work done by the pump = 800 Nm
time = 50 s
then power = 800 Nm or J / 50 s = 16 Watt.
b. Force F = Work done/ distance
F = 800 Nm/20 m = 40 N
c. Then force = m a
given acceleration a = 10 m/s²
m = f/ a
= 40 N/10 m/s²
= 4 kg.
Therefore, mass of the pump is 4 kg.
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It can be difficult, especially for someone with partial hearing loss, to understand someone speaking rapidly in a low, soft voice.
Which of the following auditory characteristics are associated with sound waves for low, quiet voices?
correct:
-low frequency
-low amplitude
incorrect
- vestibular
Correct, low, quiet voices have sound waves with low frequency and low amplitude. Instead of hearing, the vestibular system controls balance and spatial orientation.
By comparing the two ears' responses, what aspects of the sound can be used to identify its origin?In order to determine where a sound is coming from, humans rely on two key clues. These signals include (1) the ear the sound strikes first (interaural temporal differences) and (2) the volume of the sound when it reaches each ear (known as interaural intensity differences).
What procedures are necessary for the brain to interpret sound waves as sound?Sound waves enter the outer ear and travel to the eardrum via the auditory canal. The three tiny ossicles carry the ensuing vibrations into the cochlea, where hair cells are able to pick them up.
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The Saturn V rocket had a mass of 2.45x10 kg, 65% of which was fuel. In the absence of gravity and starting at rest, what would be the maximum velocity attained (the "burnout velocity")? The fuel exhaust velocity was 3100m/s.
Answer:
Approximately [tex]5800\; {\rm m\cdot s^{-1}}[/tex].
Explanation:
Let [tex]m[/tex] denote the initial mass of the rocket and the fuel. The question states that the mass of the fuel is [tex]65\%[/tex] of the total mass, which is [tex]0.65\, m[/tex]. The mass of the rocket without the fuel would be [tex](1 - 0.65)\, m[/tex].
When an object of mass [tex]m[/tex] travels at a velocity of [tex]v[/tex], the momentum [tex]p[/tex] of that object would be [tex]p = m\, v[/tex].
Initial momentum of the rocket and the fuel, combined, would be [tex]0\; {\rm kg \cdot m\cdot s^{-1}}[/tex] since initial velocity was [tex]0\; {\rm m\cdot s^{-1}}[/tex].
Let [tex]v(\text{rocket})[/tex] and [tex]v(\text{fuel})[/tex] denote the final velocity of the rocket and the fuel. Final momentum of the rocket would be [tex]((1 - 0.65)\, m)\, (v(\text{rocket}))[/tex]. Final momentum of the fuel would be [tex](0.65\, m)\, (v(\text{fuel}))[/tex].
The total final momentum of the rocket and the fuel, combined, woul dbe:
[tex]((1 - 0.65)\, m)\, (v(\text{rocket})) + (0.65\, m)\, (v(\text{fuel}))[/tex].
Under the assumptions, momentum would be conserved. In other words, the total momentum of the rocket and the fuel would stay the same:
[tex](\text{total final momentum}) = (\text{total initial momentum})[/tex].
[tex]((1 - 0.65)\, m)\, (v(\text{rocket})) + (0.65\, m)\, (v(\text{fuel})) = 0[/tex].
Given that [tex]v(\text{fuel}) = 3100\; {\rm m\cdot s^{-1}}[/tex]:
[tex]\begin{aligned}v(\text{rocket}) &= \frac{0.65}{1 - 0.65}\, v(\text{fuel}) \\ &= \frac{0.65}{1 - 0.65}\, (3100)\; {\rm m\cdot s^{-1}} \\ &\approx 5800\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Which motion might be represented by this position-versus-time graph? Х t t 0 - 0 O A car drives toward the left at first slowly, then faster. O A car drives toward the left at first quickly, then slower. O A car drives toward the right at first slowly, then faster. O A car drives toward the right at first quickly, then slower. O A ball rolls down a ramp that is at first not too steep, then steeper. O An elevator descends at first slowly, then faster.
The motion that could be represented by the given position-versus-time graph is "A car drives toward the right at first slowly, then faster."
We can see that the graph has a positive slope, which indicates a motion in the positive direction. The fact that the slope is increasing over time means that the object is accelerating, which is consistent with the car starting off slowly and then getting faster.
phase 1 : object moves towards its mean position, velocity must be slow.
phase 2 : object moved to its initial position taking much less time compared to phase 1 but in the same direction to reach its mean position.
Therefore, the correct option is "A car drives toward the right at first slowly, then faster."
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If Earth were 9.5 times farther away from the Sun than it is now, how many times weaker would the gravitational force between the Sun and Earth be?
If Earth were 9.5 times farther away from the Sun than it is now, 95 times weaker would be the gravitational force between the Sun and Earth.
What is gravitational force ?Any two things with mass are drawn together by the gravitational force. The gravitational force is known as. The formula F = Gm1m2/r2 states that the direction of force will always point in the direction of the other mass along the line connecting the two bodies.
In contrast to gravity, which is the force of attraction between any two bodies, gravitation is the pull of any body towards the earth.
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Suppose that two stars in a binary star system are separated by a distance of 100 million kilometers and are located at a distance of 200 light-years from Earth.
Part A
What is the angular separation of the two stars? Give your answer in degrees.
Express your answer using two significant figures.
Part B
What is the angular separation of the two stars? Give your answer in arcseconds.
Express your answer using two significant figures.
Part C
Can the Hubble Space Telescope resolve the two stars
Part A
The angular separation of the two stars is 0.03 degrees
Part B
The angular separation of the two stars is 108 arcseconds.
Part C
Yes, the Hubble Space Telescope can resolve the two stars.
What is angular seperation?Angular separation is the angular distance between two objects as seen from a particular point in space. This is usually expressed in degrees, arcminutes, or arcseconds. It is a measure of the angular separation between two objects, such as stars, planets, galaxies, or other celestial objects, as seen from Earth. The angular separation of two objects is the angle between them as seen from the observer's point of view.
For example, the Moon and the Sun have an angular separation of 0.5 degrees when they are in opposition.
Part A:
To find the angular separation of the two stars, we can use the formula:
θ = arctan(d/D)
where θ is the angular separation, d is the physical distance between the two stars, and D is the distance to the stars from Earth.
Substituting the given values, we get:
θ = arctan(100,000,000 km / (200 x 9.461 trillion km))
θ = arctan(100,000,000 km / 1.8922 x 10^15 km)
θ = 0.03 degrees
Therefore, the angular separation of the two stars is 0.03 degrees.
Part B:
To convert degrees to arcseconds, we can use the formula:
1 degree = 3600 arcseconds
Substituting the value we found in part A, we get:
θ = 0.03 degrees x 3600 arcseconds/degree
θ = 108 arcseconds
Therefore, the angular separation of the two stars is 108 arcseconds.
Part C:
To determine if the Hubble Space Telescope (HST) can resolve the two stars, we need to compare the angular separation of the stars to the angular resolution of the HST. The angular resolution of a telescope is the smallest angle between two point sources that the telescope can distinguish.
The angular resolution of the HST is about 0.05 arcseconds. Since the angular separation of the two stars is 108 arcseconds, the HST can easily resolve the two stars as separate objects.
Therefore, the HST can resolve the two stars in the binary star system.
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The electric potential at points in an xy plane is given V-(2.0 V/m2)x2-(3.0 V/m)y2. In unit-vector notation, what is the electric field at the point (3.0 m, 2.0 m)? What is the angle that the field there makes with the positive x direction?.
The electric field at the point (3.0 m, 2.0 m) is (4.0 V/m^2) i + (6.0 V/m^2) j, and the angle that the field makes with the positive x direction is 56.3°.
Steps
To find the electric field at a point in an xy plane, we can take the negative gradient of the electric potential at that point:
E = -∇V
where ∇ is the gradient operator. In two dimensions, the gradient operator is:
∇ = i(∂/∂x) + j(∂/∂y)
where i and j are the unit vectors in the x and y directions, respectively.
Taking the partial derivatives of V with respect to x and y, we get:
(∂V/∂x) = -4.0 V/m^2 x
(∂V/∂y) = -6.0 V/m^2 y
Substituting these into the expression for the electric field, we get:
E = -i(∂V/∂x) - j(∂V/∂y)
E = 4.0 V/m^2 i + 6.0 V/m^2 j
Now we can substitute the given values of x and y to find the electric field at the point (3.0 m, 2.0 m):
E = 4.0 V/m^2 i + 6.0 V/m^2 j
= (4.0 V/m^2)(1.0 i) + (6.0 V/m^2)(1.0 j)
= (4.0 V/m^2)(cosθ i + sinθ j)
where θ is the angle that the electric field makes with the positive x direction. To find θ, we can take the arctangent of the y component divided by the x component:
θ = tan^-1(6.0/4.0)
= 56.3°
Therefore, the electric field at the point (3.0 m, 2.0 m) is (4.0 V/m^2) i + (6.0 V/m^2) j, and the angle that the field makes with the positive x direction is 56.3°.
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Two blocks connected by a string are pulled across a rough horizontal surface by a force applied to one of the blocks, as shown. The acceleration of gravity is 9.8m/s^2. If each block has an acceleration of 5.2m/s^2 to the right, what is the magnitude of the applied force? Answer in units of N
The magnitude of the applied force is 14.59 N.
Newton's second law, which states that the net force exerted on an item is equal to its mass times its acceleration, can be used to address this issue.
Let's use the letters m1 and m2 to represent the masses of the left and right blocks, respectively. The following equations are therefore able to be written:
m1 * a = F - f
m2 * a = f
where F is the size of the applied force, f is the frictional force acting on the blocks, and an is the acceleration of both blocks. Because a string connects the two blocks, it should be noted that the acceleration is the same for both. The frictional force can be expressed as
f = * N,
where is the coefficient of friction and N is the normal force, can be used to express the frictional force. The weight of the blocks, which can be represented as m1 * g and m2 * g, respectively, determines the normal force acting on them.
When we solve for F and replace the frictional force expression in the first equation, we obtain:
F = m1 * a + μ * m1 * g
Inputting the values provided yields:
F = (m1 + m2) * a + μ * (m1 + m2) * g
F = (m1 + m2) * 5.2 + 0.4 * (m1 + m2) * 9.8
F = 5.2 * (m1 + m2) + 3.92 * (m1 + m2)
F = 9.12 * (m1 + m2)
We now need to determine what m1 Plus m2 equals. Although their specific masses are withheld from us, we do know that the ratio of their masses is 2:3. Let's write m for the smaller mass and 1.5m for the larger value. Next, we have:
m + 1.5m = 2.5m
1.5m/m = 3/2
So the masses are m = 2/5 and 1.5m = 6/5.
Inputting these values into the F equation yields the following results:
F = 9.12 * (2/5 + 6/5)
F = 9.12 * 8/5
F = 14.59 N
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In one experiment the electric field is measured for points at distances $r$ from a uniform line of charge that has charge per unit length $\lambda$ and length $l$, where $l \gg r$. In a second experiment the electric field is measured for points at distances $r$ from the center of a uniformly charged insulating sphere that has volume charge density $\rho$ and radius $R =$ 8.00 mm, where $r > R$. The results of the two measurements are listed in the table, but you aren't told which set of data applies to which experiment: For each set of data, draw two graphs: one for $Er^2$ versus r and one for $Er$ versus $r$. (a) Use these graphs to determine which data set, A or B, is for the uniform line of charge and which set is for the uniformly charged sphere. Explain your reasoning. (b) Use the graphs in part (a) to calculate $\lambda$ for the uniform line of charge and $\rho$ for the uniformly charged sphere.
The uniform line of charge and [tex]\rho[/tex] for the uniformly charged sphere. Using slope the value of [tex]\lambda[/tex] is [tex]\\\frac{4\pi\epsilon_0\times slope}{2}$[/tex].
For the uniform line of charge, the electric field $E$ is inversely proportional to the distance $r$, so $Er$ should be constant. For the uniformly charged sphere, the electric field $E$ is inversely proportional to the square of the distance $r$, so $Er^2$ should be constant. Therefore, we can use the graphs of $Er^2$ versus $r$ and $Er$ versus $r$ to determine which data set is for the uniform line of charge and which set is for the uniformly charged sphere.
For data set A, the graph of $Er^2$ versus $r$ is a straight line, which means that $Er^2$ is constant. Therefore, data set A is for the uniformly charged sphere. For data set B, the graph of $Er$ versus $r$ is a straight line, which means that $Er$ is constant. Therefore, data set B is for the uniform line of charge.
For the uniform line of charge, the electric field $E$ is given by
E =[tex]\frac{2\lambda}{4\pi\epsilon_0r}$,[/tex]
where $\lambda$ is the charge per unit length and $\epsilon_0$ is the permittivity of free space. Since $Er$ is constant, we can write $Er = \frac{2\lambda}{4\pi\epsilon_0}$. From the graph of $Er$ versus $r$ for data set B, we can find the slope of the straight line, which is equal to $Er$. Therefore, we can use the slope to calculate $\lambda$:
[tex]$\lambda = \frac{4\pi\epsilon_0Er}{2} = \frac{4\pi\epsilon_0\times slope}{2}$[/tex]
For the uniformly charged sphere, the electric field $E$ is given by $E = \frac{\rho r}{3\epsilon_0}$, where $\rho$ is the volume charge density. Since $Er^2$ is constant, we can write $Er^2 = \frac{\rho r^3}{3\epsilon_0}$. From the graph of $Er^2$ versus $r$ for data set A, we can find the slope of the straight line, which is equal to $Er^2$. Therefore, we can use the slope to calculate [tex]$\rho$[/tex]
[tex]$\rho = \frac{3\epsilon_0Er^2}{r^3} = \frac{3\epsilon_0\times slope}{r^3}$[/tex]
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a water balloon dropped from the top of a building accelerates at 9.8 meters/second/second. If it starts from rest, and falls for 6 seconds before it hits the ground, what will its speed be just before it hits?
The final speed is 58.8 m/s.
What is the final speed?We have to note that if we are to solve the problem that we have here, we have to look at the equations of motion and this is how we can be able to get the final velocity of the object.
Thus we are going to have that;
v = u + gt
v = final speed
u =- initial speed
g = acceleration
t = time
v = gt
v = 9.8 * 6
= 58.8 m/s
The object is going to have a final speed of about 58.8 m/s when we look at the calculations above here.
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RI V1 12 V R1 3.30 RO 33 100 Key-A Fig. 4 Norton' Theorem 1. Using Ohm's law, calculate the current flowing through potentiometer R for an R. value equal to 1.0 k 5.0 kN and 10.0 k22 (show sample calculations). Appropriately report your results. 2. Using Norton' Theorem, calculate the current flowing through potentiometer Rį for an RL value equal to 1.0 KA2, 5.0 K2 and 10.0 kN (show sample calculations). Appropriately report (resistance and Norton current values). 3. Using NI-Multisim, measure the current flowing through potentiometer R for an Rz value equal to 1.0 1. 5.0 kN and 10.0 k (show sample calculations). Appropriately report your results.
The current flowing through potentiometer R is 0.855mA, the current flowing through potentiometer Rį for an RL 5KΩ and the current flowing through potentiometer R is 854μA,
The potentiometer is an instrument used for measuring the unknown voltage by comparing it with the known voltage. It can be used to determine the emf and internal resistance of the given cell and also used to compare the emf of different cells. The relative system is used by the potentiometer. The reading is more accurate in a potentiometer.
1) Rl = 1kΩ
Applying nodal analysis at V:
V/1K + V/3.3K + V-12/1K
3.3V+V+3.3V-39.6/3.3K = 0
7.6V = 39.6
V = 39.6/7.6 = 5.21 V
Il = v/Rl = 5.21/1K
Il = 5.21 mA
For Rl = 1K and Il = 5.21mA
Rl = 5 kΩ
Applying nodal analysis at V:
V/5 K + V/3.3K + V-12/1K
3.3V+5V+16.5V-198/3.3K = 0
24.8V = 198
V = 198/24.8 = 7.98 V
Tl = 7.98/5 K = 1.596 mA
Rl = 10 kΩ
Applying nodal analysis at V:
V/10K + V/3.3K + V-12/1K
3.3V+10V+33V-396/3.3K = 0
46.3V = 396
V = 396/46.3 = 8.55 V
IL = V/Rl = 8.55/10 K = 0.855mA
2) IL = 12m x 0.767K/0.767K + 10K
= 12m x 0.767/10.767
= 0.854 mA
= 854 μA
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