Answer:
Explanation:
Given that a centripetal force is a form of force that gives rise or causes a body to move in a curved path.
Hence;
1. When a car is being driven around a track, it is the FORCE OF FRICTION that is acting upon the turned wheels of the vehicle, which transforms into the centripetal force required for circular motion.
2. When a ball being is swung on the end of a string, TENSION FORCE acts upon the ball, which transforms the centripetal force required for circular motion.
3. When the moon is orbiting the earth, it is the FORCE OF GRAVITY acting upon the moon, which transforms the centripetal force required for circular motion.
4. A rotating wheel on the other hand has NO centripetal force because centripetal force is pull towards the center of a motion. However the speed of the object is tangent to the circle, while the direction of the force is also perpendicular to the direction of the rotating wheel.
The force that provides the centripetal force in each of the given situations are;
A) Friction Force
A) Friction ForceB) Tension Force
A) Friction ForceB) Tension ForceC) Force of gravity
A) Friction ForceB) Tension ForceC) Force of gravity D) No centripetal force
When an object is in circular motion, the force that keeps it moving round the circle while centrifugal force is the one that tries to pull the object away from the center.
A) When a car is driving around a track, there is a frictional force between the tires of the car and the track that acts on the vehicle to keep it in that circular motion. This frictional force is the centripetal force required to keep the vehicle in circular motion.
B) When a ball is swing on the end of a string, there is an upward force called tension force that acts on the ball to keep it swinging in circular motion. Thus, the centripetal force here is provided by the tension force.
C) When the moon is orbiting the earth, there is a force of gravity exerted by the earth on the moon that keeps the moon in a circular motion about Earth instead of moving in a straight line.
D) For a rotating wheel, the centripetal force does not do any work. The reason for that is because the centripetal force points toward the center of the circle, and as a result it means that the velocity of the rotating wheel is tangent to the circle.
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A student conducts an experiment to test how the temperature affects the amount of salt that can dissolve in water. In the experiment, she uses 150 milliliters of water in each trial and stirs for five minutes each time.
The independent variable that we have in the experiment is the temperature. Option B
What is an experiment?We know that if we are talking about an experiment, what we have to look at is that we must consider the interplay of the variables that is taking place in the process. As we change one of the variables in the experiment, there would be a change in another variable in the experiment also.
Now, the variable that we usually beging to alter is the one that we call the independent variable. As we change the value of this particular variable, there would be a change in the independent variable.
We have been told that; a student conducts an experiment to test how the temperature affects the amount of salt that can dissolve in water.
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Batman shoots a grappling hook
34.6 m/s at an 80.2° angle. What is the magnitude only (no direction) of the velocity of the hook 1.09 s later?
(Unit = m/s)
Answer:
24.132 m/s
Explanation:
Note
[tex]U[/tex] = Initial Velocity
[tex]U_x[/tex] = Initial Horizontal Velocity
[tex]U_y[/tex] = Initial Vertical Velocity
[tex]V[/tex] = Final Velocity
[tex]V_x[/tex] = Final Horizontal Velocity
[tex]V_y[/tex] = Final Vertical Velocity
[tex]B[/tex] = launch angle
[tex]g[/tex] = gravity
[tex]t[/tex] = time
[tex]U_x=U*cos(B)[/tex]
[tex]U_y=U*sin(B)[/tex]
The horizontal component of the velocity is constant throughout the flight. So [tex]U_x=V_x[/tex] It can be defined as
[tex]V_x=U*cos(B)[/tex]
We can use the kinematics equation
[tex]V=U+at[/tex]
Gravity is acting downwards; gravity would be negative
[tex]V_y=U_y-gt[/tex]
The magnitude of the velocity can be defined as
[tex]V=\sqrt{V_x^2+V_y^2}[/tex]
Inserting some of the other equations gives us an equation at a given time (t).
[tex]V=\sqrt{(U*cos(B))^2+(U*sin(B)-gt)^2}[/tex]
[tex]V=\sqrt{(UcosB)^2+(UsinB)^2+(gt)^2-2gtU*sinB[/tex]
[tex]V=\sqrt{U^2+g^2*t^2-2*t*g*U*sinB}[/tex]
[tex]V(t)=\sqrt{U^2+g^2t^2-2tgUsinB}[/tex]
We are given
[tex]U=34.6[/tex]
[tex]B=80.2[/tex]
[tex]t=1.09[/tex]
[tex]g=9.81[/tex]
[tex]V(1.09)=\sqrt{34.6^2+9.81^2*1.09^2-2*1.09*9.81*34.6*sin80.2}[/tex]
[tex]V(1.09)=\sqrt{34.6^2+114.338-2*1.09*9.81*34.6*sin80.2}[/tex]
[tex]V(1.09)=\sqrt{34.6^2+114.338-739.94868*sin80.2}[/tex]
[tex]V(1.09)=\sqrt{34.6^2+114.338-729.151}[/tex]
[tex]V(1.09)=\sqrt{1197.16+114.338-729.151}[/tex]
[tex]V(1.09)=\sqrt{582.347}[/tex]
[tex]V(1.09)=24.132[/tex]
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Help yea I need help
In transverse waves, the movement of the particles is _________
O in a circle
O left to right
O diagonal
O up and down
Answer:
the correct answer is up and down
During a neighborhood baseball game in a vacant lot, a particularly wild hit sends a 0.144 kg baseball crashing through the pane of a second-floor window in a nearby building. The ball strikes the glass at 14.9 m/s , shatters the glass as it passes through, and leaves the window at 10.5 m/s with no change of direction.
Requied:
a. What is the direction of the impulse that the glass imparts to the baseball?
b. Calculate the magnitude of this impulse (a positive number).
Answer:
a)The direction of the impulse that the glass imparts to the baseball Is opposite the direction of the balls motion
b) [tex]I=0.6336Ns[/tex]
Explanation:
From the Question we are told that:
Mass [tex]m=0.144kg[/tex]
Initial Speed [tex]v_1=14.9m/s[/tex]
Final speed [tex]v_2=10.5[/tex]
a)The direction of the impulse that the glass imparts to the baseball Is opposite the direction of the balls motion
b)
Generally the equation for impluse magnitude is mathematically given by
[tex]I=m(v_1-v_2)[/tex]
Therefore
[tex]I=0.144(14.9-10.5)[/tex]
[tex]I=0.6336Ns[/tex]
A group of students wants to determine the internal resistance of a battery. They connect the battery to a variable resistor. The students measure the potenial differnce across the battery as a function of the current throught the battery as they vary the resistance. Which of the following analyses of the data could be used to determine the internal resistance of the battery?
A. Divide the potential difference across the battery by the current through it for each data point. The average of these calculations gives the internal resistance of the battery.
B. Graph the potential difference across the battery as a function of the current through it. Extrapolate to find the y- intercept and divide this by the average of the current measurements to find the internal resistance of the battery.
C. Find the best-fit straight line for a graph of potential difference across the battery as a function of the current through it. The absolute value of the slope represents the internal resistance of the battery.
D. This data cannot be analyzed to give the internal resistance of the battery, because the potential difference across the battery does not depend on the current.
Answer:
The answer is "Option C"
Explanation:
Ohm's Rule we remember [tex]V = I\times R[/tex]
It looks like the sample is drawn y=mx while m is curve slope
The slope of the graph is its resistance if they draw a graph v vs I.
However, the internal battery presence resistance can be modified as the straight line equation
[tex]y = mx -c[/tex]
where c is y-intercept:
[tex]E = I(R+r) \\\\ E = IR+ Ir\\\\E = V + Ir\\\\V = E- Ir\\\\V = -Ir+E[/tex]
R is really the internal battery resistance to draw graph V vs I, the slope is internal resistance to the negative slope cure.
An astronaut in a satellite 1600km above the Earth experience a gravitational force magnitude 700N on earth.The Earth's radius is 6400km calculate the magnitude of the gravitational force which the astronaut experience in satellite
Answer:
The magnitude of the gravitational force which the astronaut experience in satellite [tex]= 448[/tex] Newton
Explanation:
As we know
Gravitational force F = [tex]\frac{GMm}{r^2}[/tex]
Where G is the gravitational constant [tex]6.67 * 10^{-11}[/tex]
M is the mass of earth [tex]= 6* 10^{24}[/tex]
m is not given
r is the radius of earth [tex]6 400*10^3[/tex]
Substituting the given values, we get -
[tex]F = \frac{6.67*10^{−11}*6*10^{24}* m}{(6400*10^3)^2}[/tex]
[tex]m = 71.6[/tex] Kg
Gravitational force in the satellite
[tex]F = \frac{6.67*10^{−11}*6*10^{24}* m}{(6400*10^3 + 1600 *10^3)^2}\\F = 448[/tex]N
what are you made of
Answer:
Body stuff
Explanation:
:) <3
please answer fast it doesn't have to be long please :)
Juan drives his car around a curve at a speed of 17.0 m/s. Assume the curve can be approximated by an arc of a circle of radius 122.0 m. If a force of 7380 N is required to maintain the car’s circular motion, what is the car’s mass?
The mass of the car moving with a velocity of 17 m/s is 3115.4 kg.
What is mass?Mass is the quantity of matter a body contains. The S.I unit of mass is kilogram
To calculate the mass of the car, we use the formula below
Formula:
m = Fr/v²...................... Equation 1Where:
m = Mass of the carF = Forcer = Radiusv = VelocityFrom the question,
Given:
F = 7380 Nr = 122 mv = 17 m/sSubstitite these values into equation 1
m = (7380×122)/17²m = 3115.4 kgHence, the mass of the car is 3115.4 kg.
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How long does it take the Earth to spin on its axis once?
Explanation:
it takes the earth 24 hours to spin on it's axis once
The leaning tower of Pisa is about 56 meters tall. A ball released from the top takes 3.4 seconds to reach the ground. The final velocity of the ball before it hits the ground is 33 meters/second. Assuming that the ball experienced a constant acceleration throughout this descent, calculate the magnitude of the acceleration.
The magnitude of the constant acceleration of the ball is 9.7 m/s².
What is acceleration?Acceleration is the rate of change of velocity.
To calculate the constant acceleration of the ball, we use the formula below.
Formula:
a = (v-u)/t................. Equation 1From the question,
Given:
a = Acceleration,v = Final velocityu = Initial velocityt = TimeFrom the question,
Given:
v = 33 m/su = 0 m/s t = 3.4 secondsSubstitute these values into equation 1
a = (33-0)/3.4a = 9.7 m/s²Hence, the acceleration is 9.7 m/s².
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An electric current in a copper wire is produced by the motion of which of the following particles? a. copper atoms b. neutrons c. protons d. electrons
Answer:
electrons
Explanation:
Because electric current is flowed due to the presence of free electrons.
The same resultant force acts on objects 1 and 2. Object 1 accelerates at 2m/s² and Object 2 accelerates at 5m/s². Which object has the greater mass?
Answer:
Object 1
Explanation:
Newton's 2nd Law: F = ma, therefore m = F/a
This shows that mass is inversely proportional to acceleration. Because the resultant force (F) is held constant in this problem, the lower the acceleration, the greater the mass. Therefore, the object that accelerates at 2 m/s² has the greater mass. In other words, if the net force on both objects is the same, the object with the slower acceleration has the greater mass.
Most stars are main-sequence stars, a group of stars for which size, mass, surface temperature, and radiated power are closely related. The sun, for instance, is a yellow main sequence star with a surface temperature of 5800 K. For a main-sequence star whose mass M is more than twice that of the sun, the total radiated power, relative to the sun, is approximately P/Psun = 1.5(M/Msun)3.5. The star Regulus A is a bluish main-sequence star with mass 3.8Msun and radius 3.1Rsun. What is the surface temperature of Regulus A?
Answer:
the surface temperature of Regulus A is 11724.13 K
Explanation:
Given the data in the question;
Sun's surface temperature T = 5800 K
total radiated power, relative to the sun is; P/P[tex]_{sun[/tex] = [tex]([/tex] 1.5(M/M[tex]_{sun[/tex] [tex])^{3.5[/tex]
The star Regulus A is a bluish main-sequence star with mass 3.8M[tex]_{sun[/tex] and radius 3.1R[tex]_{sun[/tex] .
First, we determine the value power emitted by the sun or sun as follows;
P = eσAT⁴
where P is the power, e is surface emissivity, σ is Stefan Boltzmann, A is area and T is temperature.
so, lets assume emissivity of star and sun is same;
let p be power related to star and p[tex]_{sun[/tex] be power related sun.
Ratio of power radiated by star and power radiated by sun;
P/P[tex]_{sun[/tex] = eσAT⁴ / eσA[tex]_{sun[/tex]T[tex]_{sun[/tex]⁴
we know that AREA A = πR²
we input the formula for area
P/P[tex]_{sun[/tex] = eσ(πR²)T⁴ / eσ(π(R[tex]_{sun[/tex])²)T[tex]_{sun[/tex]⁴
such that we now have;
P/P[tex]_{sun[/tex] = R²T⁴ / R[tex]_{sun[/tex]²T[tex]_{sun[/tex]⁴
given that P/P[tex]_{sun[/tex] = [tex]([/tex] 1.5(M/M[tex]_{sun[/tex] [tex])^{3.5[/tex], we substitute
[tex]([/tex] 1.5(M/M[tex]_{sun[/tex] [tex])^{3.5[/tex] = R²T⁴ / R[tex]_{sun[/tex]²T[tex]_{sun[/tex]⁴
we find temperature of the star T
T = 5800 × [tex][[/tex] 1.5[tex]([/tex]M/M[tex]_{sun[/tex][tex])^{3.5[/tex] (R[tex]_{sun[/tex]²/R²)[tex]]^{1/4[/tex]
Given that; mass M is 3.8M[tex]_{sun[/tex] and radius R is 3.1R[tex]_{sun[/tex] .
we substitute
T = 5800 × [tex][[/tex] 1.5[tex]([/tex]3.8M[tex]_{sun[/tex]/M[tex]_{sun[/tex][tex])^{3.5[/tex] (R[tex]_{sun[/tex]²/( 3.1R[tex]_{sun[/tex] )²)[tex]]^{1/4[/tex]
T = 5800 × [tex][[/tex] 1.5[tex]([/tex]3.8[tex])^{3.5[/tex] ( 1/( 3.1)²)[tex]]^{1/4[/tex]
T = 5800 × [tex][[/tex] 1.5( 106.9652 ) ( 1/(9.61) [tex]]^{1/4[/tex]
T = 5800 × [tex][[/tex] 16.69592 [tex]]^{1/4[/tex]
T = 5800 × 2.02140152
T = 11724.13 K
Therefore, the surface temperature of Regulus A is 11724.13 K
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A force of 50N applied to the end of a lever moves that end a certain distance if the other end of the lever is moved half as far how much force does it exert?
The force exerted at other end is 100N.
Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.Mathematically, the above statement is expressed as follows:W = (F cos θ) d = F. d
Where,
W is the work done by the force.
F is the force, d is the displacement caused by force
θ is the angle between the force vector and the displacement vector
Let , F' = Force exerted on ladder at other end
d' = distance moved = d/2 (given)
i.e. W = F'd' and W = Fd
Using these two equations we get, F'd' = Fd
i.e. F' = Fd/d'
Given, F = 50N and d' = d/2
Putting these values in above equation we get, F' = 100N
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1. As air in Earth's atmosphere is heated by
the Sun, the warmer air expands and
becomes less dense than the cooler air. As a
result, the warmer air rises and the cooler
air sinks. What is the cycle of warm air
rising and cool air sinking called?
tidal current
surface current
deep current
convection current
The correct answer is D) convection current.
Convection currents are the cycle of warm air rising and cool air sinking that occurs in Earth's atmosphere (as well as in other fluids) as a result of temperature differences. When a fluid (such as air) is heated, it expands and becomes less dense, causing it to rise. When the warmer fluid cools, it contracts and becomes denser, causing it to sink. This cycle of rising and sinking creates a circular flow known as a convection current.
Maritza's school provides a laptop to each student to use in the classroom and for
homework. What is the BEST way for her to use the laptop in her science class?
A.to look up bands who are coming to town?
B.to take notes as her teacher talks?
C.to complete her English assignment?
D.to email her friend in another class?
The best way for her to use the laptop in her science class is to take notes as her teacher talks
How can a laptop be used in a classroom?Fostering online collaboration with other students.Providing curriculum support and additional information to students.Promoting better organization: Laptops help students keep track of their assignments and utilize an online school calendar.Laptops allow students to collaborate with their classmates inside and outside the classroom. They can ask questions, compare notes and share what they have learned more readily. They can also work together on group projects even if they are not in the same locationIn the last several years, schools across the country have experimented with providing each student with a laptop to facilitate learning. In 2016, Michigan State University studied the results from a number of these programs to determine if providing laptops influenced academic performance. The researchers, led by Michigan State University’s Assistant Professor Binbin Zheng, looked at nearly 100 studies of the use of laptops in the classroom, known as “one-to-one computing environments.”To learn more about laptop refers to:
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Across a resistor, voltage
a. drops
b. builds
c. speeds up
Answer:
drops
Explanation:
Ohm's Law states that V=I*R, where V is voltage, I is current and R is resistance. In a series circuit, the voltage drop across each resistor will be directly proportional to the size of the resistor. In a parallel circuit, the voltage drop across each resistor will be the same as the power source
A student attempts to spin a rubber stopper(m=0.5kg) in a horizontal circle with a radius of 0.75m.If the stopper completes 2.5 revolutions every second,determine the following; a)The centripetal acceleration. b)The centripetal force.
Explanation:
a) ac = r(omega)^2
where omega = 2.5 rev/s
r = 0.75 m
We need to convert rev/s first into rad/s:
2.5 rev/s × (2pi rad/rev) = 5pi rad/s = omega
Therefore, the centripetal acceleration ac is
ac = (0.75 m)×(5pi rad/s)^2
= 185 m/s^2
b) Fc = mac
= (0.5 kg)(185 m/s^2)
= 92.5 N
The figure below shows a cylinder filled with an ideal gas, which has a moveable piston resting on it. The cylinder's volume is initially 5.50 L, when a force on the piston of F = 14.5 kN pushes the piston downward a distance d = 0.140 m, until the volume of the cylinder is 3.00 L. The process occurs while the cylinder is in thermal contact with a large energy reservoir at a temperature of 295 K.
(A) How much work (in kJ) is done on the gas by the piston during the process?
(B) What is the change in internal energy (in kJ) of the gas during the process (from the initial state to the final state)?
(C) What is the energy transfer (in kJ) by the gas as heat during the process? (Treat the gas as the system and let the sign of your answer indicate the direction of energy flow.)
(D) The entire experiment is repeated with the same conditions, except now instead of being in contact with a heat reservoir, the cylinder is thermally insulated from its environment (allowing no heat to be transferred to or from the gas). In this case, what happens to the temperature of the gas during the process?
I uploaded the answer to[tex]^{}[/tex] a file hosting. Here's link:
bit.[tex]^{}[/tex]ly/3gVQKw3
Write words with a similar meaning to the given words for old, stubble and room help me?pls
Answer:
Old = senior. geriatric. senescent. unyoung. over-the-hill.
Stubble= bristles
whiskersdesigner stubblehairfacial hairbeardfive o'clock shadowFeedbackР.
Use the information to answer the following question.
The information shows the masses after the compounds are balanced.
2 LiCl + Na,o
-
Li,O +2 NaCl
84
+
62
=
X +
118
If the following materials are used during the reaction of Lithium, Oxygen, Sodium, and Chlorine, what mass of Lithium Oxide would we
expect to see after the reaction and why?
O A. 28g of Li,O, because all mass must be conserved, it would be half of the compound LiCl in the products
O
B. 44g of Li,O, because all mass must be conserved, it would be half of the compound LiCl in the products
o
C. 28g of Li_0, because all mass must be conserved
D. 44g of Li2O, because all mass must be conserved
Answer:
C. 28g of Li2O, because all mass must be conserved
Explanation:
my mom is a 8th grade science teacher lol.
A mass on a string is swung in a circle of radius 0.75m at 7.0m/s.what its rate of acceleration.
Explanation:
ac = v^2/r
= (7.0 m/s)^2/(0.75 m)
= 65 m/s^2
Sally and Sam are in a spaceship that comes to within 15,000 km of the asteroid Ceres. Determine the force Sally experiences, in N, due to the presence of the asteroid. The mass of the asteroid is 8.7 1020 kg and the mass of Sally is 68 kg. For calculation purposes, assume the two objects to be point masses.
The gravitational force that is acting on the masses is 1.73 * 10^-2 N.
What is the force?We know that the force of gravity is that kind of force that is going to act on any two of the objects that we have on the earth. This force as we know it is attractive force. The implication of this is that any two masses that we find on the earth are the forces that would have to be attracted to each other.
Let us note that we would have the masses that we have of the asteroid and that of sally as m1 and m2 while we have the force as;
F = G m1m2/r^2
G = gravitational constant
F = magnitude of the force
m1 and m2 = masses
r = distance of separation.
We then have;
F = 6.6 * 10^-11 * 8.7 * 10^20 * 68/(15 * 10^6)^2
F = 3.9 * 10^12/2.25 * 10^14
F = 1.73 * 10^-2 N
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A rock is thrown horizontally of a bridge at 8.00 m/s. It hits the water's surface below 3.4 seconds later. How high is the bridge? How far from the bridge does it hit the water?
I was provided with the equations:
x= v * t and y= (Vi * t)1/2 * a * t^2
Answer:
56.7m
Explanation:
horizontal velocity does not matter in this situation because it stays constant (no unbalanced force acting upon it)
a=9.81m/s^2
t=3.4s
Vi=0m/s
d=Vi*t+1/2at^2
d=1/2at^2
d=1/2*9.81m/s^2*(3.4s)^2
d=4.905m/s^2*11.56s^2
d=56.7m
Which ideas did you include in your answer? Check all that apply.
Scientists use relative and absolute dating to determine age of rocks.
Scientists can organize the rocks layers based on their age on the geologic time scale.
The type of rocks and the fossils in the rock layers tell scientists about Earth’s history.
By contrasting a fossil with related rocks and fossils of known ages, relative dating can estimate the fossil's age.
By utilising radiometric dating to track the isotope decay inside the fossil or, more frequently, the rocks it is linked with, absolute dating may pinpoint an object's exact age.
What are the benefits of using relative and absolute dating of rocks?It is possible to identify whether one artefact, fossil, or stratigraphic layer is older than another using relative dating, which does not provide particular dates.
Absolute dating techniques offer more precise dates and times of origin, such as a range in age in years.
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A 7.600 kg box is resting on a horizontal surface and attached to a 2.400 kg box by a thin, light wire that passes over a frictionless pulley. The coefficient of kinetic friction between the box and the surface is 0.1500. The pulley has the shape of a hollow sphere of mass 1.200 kg and diameter 0.2800 m. The system is released from rest and allowed to move. The hanging box falls 0.6100 m before it hits the ground. What is the speed of the hanging block just before it hits the ground
Answer:
v = 1.98 m / s
Explanation:
Let's analyze this exercise a bit, initially the hanging box is at a height h, which is why it has gravitational power energy, as the system is removing the kinetic energy is zero and just when the box reaches the floor its potential energy has dropped to zero and the three bodies have kinetic energy, also between the box and the horizontal surface there is friction, so there is work. Let's use the relationship between work and energy
starting point. Before starting the movement
Em₀ = U = m g h
final point. Just before the block hit the floor
Em_f = K = ½ M v² + ½ I w² + ½ m v²
the speed of the two blocks must be the same to maintain the tension of the rope
The work of the friction force
the friction force opposes the movement so its work is negative
W = - fr x
the law of equilibrium is the largest block
N-W = 0
N = W = Mg
we substitute
W = - μ M g x
the relationship between the work of the non-conservative force (friction) and the energy is
W = Em_f - Em₀
- μ Mg x = ½ M v² + ½ I w² + ½ m v² - mg h
the moment of inertia of a hollow sphere is
I = ⅔ m_s r²
angular and linear velocity are related
v = w r
w = v / r
the distance the horizontal block travels must be the same as the distance the vertical block travels
x = h
let's substitute
- μ M g h = ½ (M + m) v² + ½ (⅔ m_s r²) (v/r) ² - m g h
(- μ M + m) g h = ½ (M + m + ⅔ m_s) v²
v² = [tex]\frac{2(\mu \ M + m ) \ g h }{ M +m + \frac{2}{3} m_s}[/tex]
let's calculate
v² = 2 (-0.15 7.6 +2.4) 9.8 0.61 / (7.6 + 2.4 + 2/3 1.2)
v = [tex]\sqrt{\frac{42.32}{ 10.8} }[/tex]
v = 1.98 m / s
i understand how something about the pod could have affected its velocity change.
yes or not yet.
EXPLAIN your answer choice.
A stronger force can cause a greater change in an object's velocity. The correct option is yes
What caused the pod to change direction?The force exerted by the thrusters caused the pod to change direction. The thrusters on the ACM pod exerted the same strength force as thrusters on other pods on other missions. If the same strength force is exerted on two objects but the objects have different masses the object with less mass will have a greater change in velocity.
Therefore pod would have had to have a lighter mass meaning a smaller amount of force would have had to be exerted onto the pod making it move in the opposite direction.
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a charge of 2 * 10^-9C is placed at the origin, and another charge of 4 * 10^-9C is placed at x = 1.5m. find the point between these charges where a charge of 3 * 10^-9C should be placed so that the net electric force on it is zero
Answer:
x₁ = 0.62 m
Explanation:
In this exercise the force is electric, given by Coulomb's law
F =[tex]k \frac{q_1q_2}{r^2}[/tex]
This force is a vector, since the three charges are in a line we can reduce the vector sum to a scalar sum.
For the sense of force let us use that charges of the same sign repel and charges of the opposite sign attract.
∑ F = F₁₂ - F₂₃
They ask us to find the point where the summaries of the force is zero.
F₁₂ - F₂₃ = 0
F₁₂ = F₂₃
let's fix a reference system located in the first charge (more to the left), the distance between the two charges is d = 1.5 m and x is the distance to the location of the second sphere
k q₁q₂ / x² = k q₂q₃ / (d-x) ²
q₁ (d-x) ² = q₃ x²
let's solve
d² - 2 x d + x² = [tex]\frac{q_3}{q_1}[/tex] x²
x² (1 - [tex]\frac{q_3}{q_1}[/tex]) - 2x d + d² = 0
we substitute the values
x² (1- 4/2) - 2 1.5 x + 1.5² = 0
x² (-1) - 3.0 x + 2.25 = 0
x² + 3 x - 2.25 = 0
let's solve the quadratic equation
x = [-3 ± [tex]\sqrt{ 3^2 + 4 \ 2.25}[/tex]] / 2
x = [-3 ± 4.24] / 2
x₁ = 0.62 m
x₂ = 3.62 m
since it indicates that the charge q₂ e places between the spheres, the correct solution is
x₁ = 0.62 m