Answers
Given,
A velocity-time graph.
The area under the curve of a velocity-time graph of an object gives us the displacement of the object.
From the graph, we can see that the area under the curve from 7 seconds to 8 seconds is a triangle.
The height of the triangle is h=6 m/s.
And the base of the triangle is b=1 s.
The area of a triangle is given by,
[tex]A=\frac{1}{2}bh[/tex]On substituting the known values,
[tex]\begin{gathered} A=0.5\times6\times1 \\ =3\text{ m} \end{gathered}[/tex]Therefore the displacement of the particle in the time interval 7 s to 8 s is 3 meters.
Thus, the correct answer is option C.
Related Questions
What is the average velocity of a car that travels 48 km north in 2.0 h?
Answers
The average velocity of the car would be 24 kilometers per hour in the north direction if the car travels 48 kilometers in the north for 2 hours.
What is Velocity?The total displacement covered by any object per unit of time is known as velocity. It depends on the magnitude as well as the direction of the moving object.
As given in the problem, we have to find the average velocity of the car if the car travels 48 kilometers in the north for 2 hours.
The average velocity of the car = 48 kilometers / 2 hours
= 24 kilometers per hour
Thus, the average velocity of the car would be 24 kilometers per hour
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The block of a mass 10.2 kg is sliding at an initial velocity of 3.40 m/s in the positive x-direction. The surface has a coefficient of kinetic friction of 0.153.
Answers
m = mass = 10.2 kg
vo = initial velocity = 3.40 m/s
u = coefficient of kinetic friction = 0.153
g= gravity = 9.8m/s^2
a)
Fr = force of kinetic friction = u m g
Fr = 0.153 x 10.2 x 9.8 = -15.30N
b) Block's acceleration
Newton's second law of motion:
F = m*a
a = F/m = -15.30 / 10.2 = -1.5 m/s^2
c) USe the third equation of motion:
2as = vf^2 - vo^2
Where:
Vf= final velocity= 0 m/s
s = displacement
2 * -1.5 * s = 0^2 - 3.40^2
-3s = -11.56
s= -11.56/-3
s= 3.85 m
If a car has a momentum of 2315Ns and its mass is 382kg, how fast is it moving?
Answers
ANSWER:
6.06 m/s
STEP-BY-STEP EXPLANATION:
Given:
Momentum = 2315 N*s
Mass = 382 kg
We can calculate the speed as follows:
[tex]\begin{gathered} p=m\cdot v \\ v=\frac{p}{m} \\ \text{ we replacing} \\ v=\frac{2315}{382} \\ v=6.06\text{ m/s} \end{gathered}[/tex]It moves at a speed of 6.06 m/s
A 2000 kg car is stopped by applying a braking force of 5000 newtons.
Determine the acceleration caused by this braking force.
Answers
A 2000 kg car is stopped by applying a braking force of 5000 newtons. The acceleration caused by this braking force is (a)=2.5 m/s²
What is acceleration?When a object start with a velocity and ends with different velocity, so the change in velocity in a given time is called the acceleration of the object. It is a vector quantity. It can be measured in m/s².
How can we calculate the acceleration?To calculate the acceleration we are using the formula here is ,
F=ma
Here we are given by the question is,
F= The amount of force applied on the car. = 5000N.
m= The mass of the car. = 2000kg
We have to calculate the change in acceleration = a m/s².
Now we put the values in above equation we get,
F=ma
Or, a= F/m
Or, a=5000/2000
Or, a=2.5 m/s².
Now from the above calculation we can say that, The acceleration caused by this braking force is (a)=2.5 m/s².
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What sequence of two displacements moves from (5, 5) m to (- 5, - 5) * m while traveling a distance of exactly 20 meters? How does this distance compare to the single displacement that connects the same starting and ending point?
Answers
The two displacements that move from (5,5) to (-5,-5)
(5,5) → ( 5,-5) [10 units down]
(5,-5) → (-5,5) [ 10 units left ]
The single displacement that connects the 2 points is the hypotenuse of the formed triangle where each side is 10 m long.
Apply Pythagorean theorem:
c2 = 10^2+10^2
c^2 = 100 + 100
c^2 = 200
c =√200
c= 14.14
Compared to the simple displacement (14.14) that connects both points, it is greater.
20m > 14.14 m
Projections of a vector make up the components of that vector. Is this true or false?
Answers
The given statement 'Projections of a vector make up the components of that vector' is true. The direction of a vector
Choose all the answers that apply.Asteroids:only orbit planetsonly orbit the sunare made of frozen gas and icetake millions of years to orbit the sun sometimes come very close to Earth
Answers
ANSWER:
5th option: sometimes come very close to Earth
STEP-BY-STEP EXPLANATION:
Asteroids are small rocky objects that orbit the Sun. Although asteroids orbit the Sun like planets, they are much smaller.
Therefore, of the options the only totally true option is "sometimes come very close to Earth"
So the correct answer is 5th option: sometimes come very close to Earth
A circular loop of wire with a diameter of 13.478 cm is in the horizontal plane and carries a current of 1.607 A counterclockwise, as viewed from above. What is the magnetic field, in microTeslas, at the center of the loop?
Answers
Given:
The number of the loops, n = 1
The diameter of the loop is d = 2r = 13.478 cm
The current in the loop is I = 1.607 A
To find the magnetic field in micro Tesla
Explanation:
The magnetic field can be calculated by the formula
[tex]B\text{ =}\frac{n\mu_0I}{2r}[/tex]Here, the value of the constant is
[tex]\mu_0=\text{ 12.57}\times10^{-7}\text{ H/m}[/tex]On substituting the values, the magnetic field will be
[tex]\begin{gathered} B=\frac{1\times12.57\times10^{-7}\times1.607}{13.478\times10^{-2}} \\ =1.499\text{ }\times10^{-5}\text{ T} \\ =14.99\times10^{-6}\text{ T} \\ =14.99\text{ }\mu T \end{gathered}[/tex]The magnetic field is 14.99 micro Tesla
An aluminum rod and a nickel rodare both 5.00 m long at 20.0°C.The temperature of each is raisedto 70.0°C. What is the differencein length between the two rods?AluminumNickela = 23.10-6C+ B = 69.10-6 0-1a = 13.10-6C1 B = 39.10-6-1(Unit = m)Enter
Answers
The difference in length between the two rods = 0.0025m
Explanations:Linear expansivity of a material is given by the formula:
[tex]\alpha\text{ = }\frac{l_2-l_1}{l_1(\theta_2-\theta_1)}[/tex]For the Aluminium rod:
[tex]\begin{gathered} l_{A1}\text{ = 5.0m} \\ \theta_{A1}=20^0C \\ \theta_{A2}=70^0C \\ \alpha_A\text{ = }23\times10^{-6}C^{-1} \\ \alpha_A\text{ = }\frac{l_{A2}-l_{A1}}{l_{A1}(\theta_{A2}-\theta_{A1})} \\ \text{ }23\times10^{-6}\text{ = }\frac{l_{A2}-5}{5(70-20)} \\ 5\times50\times\text{ }23\times10^{-6}=\text{ }l_{A2}-5 \\ l_{A2}=\text{ (}5750\text{ }\times10^{-6})\text{ + 5} \\ l_{A2}=\text{ 0.00575+5} \\ l_{A2}=\text{ 5.00575m} \end{gathered}[/tex]For the Nickel rod:
[tex]\begin{gathered} l_{N1}\text{ = 5.0m} \\ \theta_{N1}=20^0C \\ \theta_{N2}=70^0C \\ \alpha_N=\text{ 13}\times10^{-6}C^{-1} \\ \alpha_N\text{ = }\frac{l_{N2}-l_{N1}}{l_{N1}(\theta_{N2}-\theta_{N1})} \\ \text{ 1}3\times10^{-6}\text{ = }\frac{l_{N2}-5}{5(70-20)} \\ 5\times50\times\text{ 1}3\times10^{-6}=\text{ }l_{A2}-5 \\ l_{N2}=\text{ (32}50\text{ }\times10^{-6})\text{ + 5} \\ l_{N2}=\text{ }0.00325+5 \\ l_{N2}=\text{ 5.00325m} \end{gathered}[/tex]The difference in length between the two rods will be given as:
[tex]\begin{gathered} l_{A2}-l_{N2}=\text{ 5.00575-5.00325} \\ l_{A2}-l_{N2}=0.0025m \end{gathered}[/tex]The difference in length between the two rods = 0.0025m
The heating element of an iron operates at 110 V with a current of 11 A.(a) What is the resistance of the iron? Ω(b) What is the power dissipated by the iron? W
Answers
(a)
In order to calculate the resistance, we can use Ohm's Law:
[tex]\begin{gathered} R=\frac{V}{I}\\ \\ R=\frac{110}{11}\\ \\ R=10\text{ \Omega} \end{gathered}[/tex](b)
To calculate the power, we can use the formula below:
[tex]\begin{gathered} P=I\cdot V\\ \\ P=11\cdot110\\ \\ P=1210\text{ W} \end{gathered}[/tex]ine? Bir10. Two people are pulling on opposite ends of a rope so that ithas a tension of 150 newtons. If the rope is not moving, withwhat pulling force is each of the two people pulling?
Answers
ANSWER
150 N
EXPLANATION
The rope is not moving, so the net force on it is 0. The force that each person exerts on the rope is equal and opposite to the tension on the rope, so the sum of the forces acting on it is zero.
Hence, the force that each of the two people is exerting on the rope while pulling is 150 Newtons.
Does scarcity effect everyone?
Answers
Answer: Scarcity affects society in every way. First and foremost, scarcity affects the way that individuals make choices. Time and money are two examples of scarce resources that we make choices with every day.
A student pushes a baseball of m = 0.13 kg down onto the top of a vertical spring that has its lower end fixed to a table, compressing the spring a distance of d = 0.18 meters from its original equilibrium point. The spring constant of the spring is k = 970 N/m. Let the gravitational potential energy be zero at the position of the baseball in the compressed spring.
A. What is the maximum height, h, in meters, that the ball reaches above the equilibrium point?
B. What is the ball’s velocity, in meters per second, at half of the maximum height relative to the equilibrium point?
Answers
The maximum height reached by the baseball above the equilibrium point is 12.14 m.
The ball’s velocity, in meters per second, at half of the maximum height relative to the equilibrium point is 458.8 m/s.
What is the maximum height attained by the ball?The maximum height reached by the ball is determined as follows:
Data given:
compression of the spring is d = 0.18 m.mass of the baseball is m = 0.13 kgthe spring constant, K = 970 N/mThe gravitational potential energy at the compressed position is zero.
Based on the law of conservation of energy, the total energy of the system is conserved.
Let the final height from the bottom be h
m * g* h = ¹/₂ * K * d²
h = (k * d²) / (2 * m * g)
h = 970 * 0.18² / (2 * 0.13 * 9.81)
h = 12.32 m
Height above the equilibrium point = 12.32 - 0.18
Height above the equilibrium point = 12.14 m
Velocity is calculated1 as follows:
Half of the maximum height relative to the equilibrium point = 12.14/2 + (0.18) = 6.25 m
¹/₂ * m * v² = ¹/₂ * K * d²
m * v² = K * d²
v = √(K * d² / m)
v = √(970 * 6.25² / 0.13)
v = 458.8 m/s
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Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s. The waves have the same amplitude. The drawing shows the position of the waves at time t = 0 s. Which one of the following drawings depicts the waves on the rope at t = 4.0 s?
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We know the graph when t = 0. Therefore, at t = 4 pulse at "A" will reach to "B" and pulse at "B" will reach to "A".
This means that the graph is contrary, the only one that fulfills this is the graph (e).
Which one of the pulley systems below has the best force advantage?Select one:a. Pulley Ib. Pulley IIc. Pulley IIId. The force advantage is the same.
Answers
a. Pulley I
Explanation
A pulley system is a collection of one or more wheels which are used with a. rope or chain to make it easier to lift things, The main advantage in the use of pulleys is that the effort becomes less as compared to the normal lifting of the weights
the ideal mechanical advantage is equal to the number of rope segments pulling up on the object. The more rope segments that are helping to do the lifting work, the less force that is needed for the job.
so
Step 1
let's check the number of pulleys on each system
so, the firs system has the more rope segements pulling up (4)
therefore, the answer is
a. Pulley I
I hope this helps you
40) Climbing the Empire State Building A new record for running the stairs of the Empire State Building was set on February 4, 2003. The 86 flights, with a total of 1576 steps, was run in 9 minutes and 33 seconds. If the height gain of each step was 0.20 m, and the mass of the runner was 70.0 kg, what was his average power output during the climb? Give your answer in both watts and horsepower.
Answers
The power is given by:
[tex]P=\frac{W}{t}[/tex]where W is the work and t is the time.
We know that the work done is related to the gravitational potential energy by:
[tex]W=mg(y_f-y_0)[/tex]where yf is the final height of the object and y0 is the initial height.
Now, in this case we have a total of 1576 steps, each of them with a height of 0.2 meters that means that the total height gained is:
[tex](1576m)\cdot0.2=315.2\text{ m}[/tex]This in turns means that the work done is:
[tex]W=(70\operatorname{kg})(9.8\frac{m}{s^2})(315.2m)=216227.2\text{ J}[/tex]Now, the time it takes to achieve this is 9 minutes 33 seconds, this is the same as:
[tex]9(60)+33=573\text{ s}[/tex]Finally we use the power formula:
[tex]P=\frac{216227.2\text{ J}}{573\text{ s}}=377.36\text{ W}[/tex]Now we need to remember that 1 Hp is equal to 745.7 W, then we have that this is the same as:
[tex]377.36\text{ W}\cdot\frac{1\text{ Hp}}{745.7\text{ W}}=0.506[/tex]Therefore the power to make that climb is 377.36 W or 0.506 Hp
An unwary football player collides head-on with a padded goalpost while running at 7.5 m/s and comes to a full stop after compressing the padding and his body by 0.27 m. Take the direction of the player’s initial velocity as positive.1.assuming constant acceleration calculate the his acceleration during the collision in meters per second squared.2 how long does the collision last in seconds.
Answers
Answers:
1. a = -104.16 m/s²
2. t = 0.072
Explanation:
To find the acceleration, we will use the following equation:
[tex]v^2_f=v^2_i+2ax[/tex]where vf is the final velocity, vi is the initial velocity, a is the acceleration and x is the distance. So, replacing vf by 0 m/s, vi by 7.5 m/s, and x by 0.27m, we get:
[tex]\begin{gathered} 0^2=7.5^2+2a(0.27) \\ 0=56.25+0.54a \end{gathered}[/tex]Then, solving for a, we get:
[tex]\begin{gathered} 0-56.25=56.25+0.54a-56.25 \\ -56.25=0.54a \\ \frac{-56.25}{0.54}=\frac{0.54a}{0.54} \\ -104.16m/s^2=a \end{gathered}[/tex]Therefore, the acceleration during the collision is -104.16 m/s²
Then, to calculate how long the collision last, we will use the following equation:
[tex]v_f=v_i+at[/tex]So, replacing the values and solving for t, we get:
[tex]\begin{gathered} 0=7.5-104.16t \\ 104.15t=7.5 \\ t=\frac{7.5}{104.15}=0.072s \end{gathered}[/tex]Therefore, the collision last 0.072 seconds
Shown here are astronomical objects located at different distances from earth. rank the objects based on their distances from earth, from farthest to nearest.
- star on far side of Andromeda Galaxy
- star on near side of Andromeda Galaxy
- star on far side of Milky Way Galaxy
- star near center of Milky Way Galaxy
- Orion Nebula
- Alpha Centauri
- Pluto- The Sun
Answers
The distance of astronomical objects is measure very carefully. These are having a different unit. This is the astronomical unit. The distances are very huge.
The distance between objects in space is vast and very difficult to calculate. These are learned under solar system mathematics. The values for these distances are cumbersome for astronomers and scientists to manipulate. Therefore, scientists use a unit of measurement called an astronomical unit.
Let us understand the distances first.
To know the distance of stars in Andromeda Galaxy, we should first know the distance of Andromeda Galaxy. The distance of Andromeda Galaxy from Earth is 2.5 million light years away. The astronomical unit used is the light years.
Thus, from this we can conclude that,
The star near to Andromeda Galaxy must be at a distance of 2.5 million light years away.The star far side from Andromeda Galaxy will be more than 2.5 million light years away.Now to know about the stars in Milky Way Galaxy, the distance of milky way galaxy from Earth is approximately 9 light years away.
So,
The star far from Milky Way Galaxy should be more than 9 light years away from Earth.The star near to the Milky Way Galaxy should be close to 9 light years away from Earth.Orion Nebula is 1,344 light years away.Alpha Centauri is approximately 4.3 light years away from the Earth.The Pluto is approximately 5 billion km away from the Earth.The Sun is approximately 148 million km away from the Earth.Thus, from this we can conclude that,
The farthest is the star on far side of Andromeda Galaxy, then the star on near side of Andromeda Galaxy, then comes the star on far side of Milky Way Galaxy, then the star near center of Milky Way Galaxy, then it is the Alpha Centauri, then the Orion Nebula and then it is the Pluto with the Sun being the nearest one.
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What is the mass of 12 m3 of methylated spirit whose relative density is 0.8 ? ( Hint the density of water = 1000 kgm-3 ) A. 9600 kg B.9400 kg C. 8600 kg
Answers
ANSWER
A. 9600 kg
EXPLANATION
Given:
• The volume of the substance, V = 12m³
,• The relative density of the substance, 0.8
,• The density of water, 1000 kg/m³
Unknown:
• The mass of the substance, m
The relative density of a substance is defined as,
[tex]\rho_{relative}=\frac{\rho_{substance}}{\rho_{water}}[/tex]And the density of a substance is,
[tex]\rho=\frac{m}{V}[/tex]Let's solve the first formula for the density of the substance,
[tex]\rho_{substance}=\rho_{relative}\cdot\rho_{water}=0.8\cdot1000\operatorname{kg}/m^3=800\operatorname{kg}/m^3[/tex]Then, solve the second formula for m,
[tex]m=\rho\cdot V=800\operatorname{kg}/m^3\cdot12m^3=9600\operatorname{kg}[/tex]Hence, the mass of this substance is 9600 kg
Yea thanks thank you for the info thanks
Answers
To help us solve this problem let's plot the points given in the table:
From the graph we notice that this the position can be modeled by a sine function, we also notice that the period of this function is 8. We know that a sine function can be modeled by:
[tex]A\sin(B(x+C))+D[/tex]where A is the amplitude, C is the horizontal shift, D is the vertical shift and
[tex]\frac{2\pi}{B}[/tex]is the period.
From the graph we have we notice that we don't have any horizontal or vertical shift, then C=0 and D=0. We also notice that the amplitude is 15, then A=15. Finally, as we said, the period is 8, then:
[tex]\begin{gathered} 8=\frac{2\pi}{B} \\ B=\frac{2\pi}{8} \\ B=\frac{\pi}{4} \end{gathered}[/tex]Plugging these values in the sine function we have:
[tex]x(t)=15\sin(\frac{\pi}{4}t)[/tex]If we graph this function along the points on the table we get the following graph:
We notice that we don't get an exact fit but we get a close one.
Now, that we have a function that describes the position we can find the velocity by taking the derivative:
[tex]\begin{gathered} x^{\prime}(t)=\frac{d}{dt}\lbrack15\sin(\frac{\pi}{4}t)\rbrack \\ =\frac{15\pi}{4}\cos(\frac{\pi}{4}t) \end{gathered}[/tex]Therefore, the velocity is:
[tex]x^{\prime}(t)=\frac{15\pi}{4}\cos(\frac{\pi}{4}t)[/tex]Once we have the expression for the velocity we can find values for the times we need, they are shown in the table below:
From the table we have that:
[tex]x^{\prime}(0.5)=10.884199\text{ cm/s}[/tex]And that:
• The earliest time when the velocity is zero is 2 s.
,• The second time when the velocity is zero is 6 s.
,• The minimum velocity happens at 4 s.
,• The minimum velocity is -11.780972 cm/s
Which of the following terms represents the number of waves passing a given point each second?Frequency⊝Wavelength⊝Amplitude⊝Velocity⊝CLEAR ALL
Answers
Frequency is defined as number of waves or vibration per unit time.
Therefore, option (a), frequency is the number of waves passing a given point each second, is the correct choice.
what is the mass on grams of 0.56 moles of NaCl
Answers
Answer:
1 mole of Na = 23 g
1 mole of Cl = 35 g
1 mole of NaCl = 58 g
.56 * 58 g = 32.5 g
Hafthor bjornson broke the deadlift record in April 2020, lifting 501kg. A) How much weight (in N) did he lift?B) How hard was the floor pushing up on the weights when they were on the floor?
Answers
Given, the mass that Hafthor Bjornson lifted, m=501 kg
A)
The weight is given by the product of the mass and the acceleration due to gravity.
Thus the weight lifted by him is,
[tex]\begin{gathered} W=mg \\ =501\times9.8 \\ =4909.8\text{ N} \end{gathered}[/tex]Thus the weight he lifted is 4909.8 N
B)
When the weight is on the floor the force applied by the floor on the weights is equal to the weight itself. This force is called the normal force.
Thus the force applied by the floor on the weights is 4909.8 N
Two equal charges q1=q2= -6uC are on the y-axis at y1=3cm and y2= -3cm. What is the magnitude and direction of the electric field on the x-axis at x=4cm. If a test charge q0=2uC is placed at x =4cm find the force the test charge experiences?
Answers
The electric field charges, q₁, and q₂, which are each -6×10⁻⁶ μC, gives:
First part:
The magnitude of the electric field at x = 4 cm is -3.456×10⁷ N/CThe direction of the electric field is towards the origin, along the x-axisSecond part:
The force experienced by the charge is 69.12 NWhat is an electric field?An electric field is the field around a particle that is electrically charged and which exerts a force on charged particles within the field.
The given information are:
The electric charges, q₁ = q₂ = -6 μC
The location of the charge q₁ = y₁ = 3 cm on the y-axis
Location of the charge q₂ = y₂ = -3 cm
First part:
The required location of the point where the electric field magnitude and direction is required is x = 4 cm
The electric field formula is: [tex]\displaystyle{E = \frac{k\cdot q}{r^2}[/tex]
Where:
k = The electrostatic constant ≈ 9 × 10⁹ N·m²/C²
The distances, r, of the charges from the required point are therefore obtained using Pythagorean theorem as follows:
r = √(3² + 4²) = 5
r = 5 cm = 0.05 m
Which gives;
[tex]\displaystyle{E = \frac{9 \times 10^9\times (-6) \times 10^{-6}}{(0.05)^2} = -2.16\times 10^{7}[/tex]
Given that the magnitude of the electric field along the y-axis cancel out, the magnitude of the electric field along the x-axis is found as follows:
[tex]E_x = 2 \times -2.16\times 10^{7}\times \dfrac{4}{5} = -3.456 \times 10^7[/tex]
The magnitude of the electric field at x = 4 is -3.456 × 10⁷ N/C
Second part: The magnitude of the test charge is q₀ = 2 × 10⁻⁶ μC
The force of an electric field, F = E × q
The force experienced by the test charge is therefore:
F = -3.456 × 10⁷ × 2 × 10⁻⁶ = -69.12
The force the test charge experiences is 69.12 N acting towards the origin from the point x = 4 cm.
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What is the volume of a piece of iron ( = 7.9 g/cm3) that has a mass of 0.75 kg? (Enter your answer in cm3.) answer in: cm3
Answers
We will have the following:
[tex]\begin{gathered} \frac{7.9g}{cm^3}\ast\frac{1kg}{1000g}=\frac{0.75kg}{V}\Rightarrow0.0079kg/cm^3=\frac{0.75kg}{V} \\ \\ \Rightarrow V=\frac{0.75kg}{0.0079kg/cm^3}\Rightarrow V=\frac{7500}{79}cm^3 \\ \\ \Rightarrow V\approx94.9cm^3 \end{gathered}[/tex]So, the volume is 7500/79 cm^3, that is approximately 94.9 cm^3.
A 5 cm spring is suspended with a mass of 1 g attached to it which extends the spring by 3.2 cm. The same spring is placed on a frictionless flat surface and charged beads are attached to each end of the spring. With the charged beads attached to the spring, the spring's extension is 0.01 m. What are the charges, in micro-Coulombs, of the beads?
Answers
First, we need to find the spring constant
Force of gravity = force of tension from spring
mg = kx
(1x10^-3)(9.8) = k (3.2x10^-2)
k = .30625
Now we can look at the other situation
Since the spring was moved 0.01 meters, we can find the force
F = kx = (.01)(.30625) = .0030625 N
Now we can set the electric force equal to the force of the beads
kq^2/r^2 = .0030625 N
q = 292 microCoulombs
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Which of the following best represents R= A - B ?
Please help, it’s due soon!
Answers
The option (C) best represents the R = A- B
What is vector in mathematics?A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.
What are the components in vector quantity?A vector primarily consists of two elements, the horizontal component and the vertical component. The horizontal component's value is cosθ, and the vertical component's value is sinθ.
There are two types of vector multiplication, they are dot products and cross products.
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On a fishing trip Justin rides in a boat 12 km south. The fish aren't biting so they go 4 km west. They then follow a school of fish 1 km north. What is his total displacement?
Answers
ANSWER:
The displacement is 11.7 km
STEP-BY-STEP EXPLANATION:
The displacement is the vector sum from the start point to the end point. Vector addition is applying the formula of the distance between two points.. We will use this formula:
[tex]d=\sqrt[]{(x_2-x^{^{}}_1)^2+(y_2-y_1)^2^{}}[/tex]To better understand the exercise, we will draw a picture of the situation, it would look like this:
Replacing the points (-4, -11) and (0, 0)
[tex]\begin{gathered} d=\sqrt[]{(-4-0^{}^{}_{})^2+(-11_{}-0_{})^2} \\ d=\sqrt[]{16+121^{}} \\ d=\sqrt[]{137} \\ d=11.7 \end{gathered}[/tex](20%) Problem 5: Two identical springs, A and B, each with spring constant k = 54.5 N/m, support an object with a weight W = 11.6 N. Each spring makes an angle of 0 = 20.6 degrees to the vertical, as shown in the diagram. Create an expression for the tension in spring A
Answers
The tension in spring A is T = W/(2cosθ)
What is tension?Tension is the stretching force in a spring.
How to find the expression for the tension in the spring?Let
T = the tension in the each spring, W = weight andθ = angle each spring makes with the verticalResolving the tension in each spring vertically, so we can have that
for spring A, the tension is Tcosθ and for spring B, the tension is TcosθNow the vertical component of the tension in each equals the weight. So, we have that
Tcosθ + Tcosθ = W
Adding them together, we have that
2Tcosθ = W
Dividing both sides by 2cosθ, so, we can have that
T = W/2cosθ
Thus, the tension in each spring is T = W/(2cosθ)
So, the tension in spring A is T = W/(2cosθ)
Learn more about tension is spring here:
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What is the resistance in a circuit that has a current of 2.5A and a voltage of 40v
Answers
16 ohms
Explanation
Ohm's law relates the strength of a direct current is directly proportional to the potential difference and inversely proportional to the resistance of the circuit,it is given by the expresssion
[tex]\begin{gathered} V=IR \\ if\text{ we isolate R} \\ R=\frac{V}{I} \end{gathered}[/tex]then
Step 1
a) Let
[tex]\begin{gathered} I=2.5\text{ A} \\ V=40\text{ V} \end{gathered}[/tex]b)replace in the formula
[tex]\begin{gathered} R=\frac{V}{I} \\ R=\frac{40V}{2.5A} \\ R=16\text{ ohms} \end{gathered}[/tex]therefore, the answer is 16 ohm
I hope this helps you
