whats the right answer ? please help
An object weighs 50 Newtons when measured in air. When submerged completely underwater the same object weighs only 35 Newtons. Is this object less dense or more dense than the surrounding water? The o

The resulting equation of motion for the system is given by m × x''(t) + k × x(t) = f(t), which is 2 × x''(t) + 18 * x(t) = 2 * sin(2t).

What is  equation of motion?

The equations of motion are a set of mathematical relationships that describe the motion of objects under the influence of forces. There are different sets of equations of motion, depending on the specific scenario and the type of motion being considered (linear motion, projectile motion, circular motion, etc.). The equations of motion for linear motion, also known as the equations of uniformly accelerated motion.

To find the equation of motion for the system, we start with Newton's second law of motion, which states that the sum of forces acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the 2-kg mass attached to the spring.

The force exerted by the spring is proportional to the displacement of the mass from its equilibrium position, and it can be expressed as F_spring = -k× x(t), where k is the spring constant and x(t) is the displacement of the mass at time t.

In addition to the force exerted by the spring, there is an external force f(t) = 2 ×sin(2t) acting on the mass.

Applying Newton's second law, we have the equation of motion: m ×x''(t) + k ×x(t) = f(t).

Substituting the given values, m = 2 kg and k = 18 N/m, we obtain 2 ×x''(t) + 18 × x(t) = 2 ×sin(2t).

Therefore, the resulting equation of motion for the system is 2 × x''(t) + 18 × x(t) = 2 × sin(2t).

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To find the position function of the particle, we can integrate the given acceleration function, a(t), twice with respect to time. Given that a(t) = t^2 + 2t - 7, we'll integrate it twice to obtain the position function, s(t).

Let's proceed with the integration step by step:

Step 1: Integrate a(t) with respect to time to find the velocity function, v(t):

∫(a(t) dt) = ∫((t^2 + 2t - 7) dt)

Integrating each term separately:

∫(t^2 dt) + ∫(2t dt) - ∫(7 dt)

= (1/3)t^3 + t^2 - 7t + C1

Since we know that v(0) = 0, we can substitute t = 0 and solve for the constant C1:

v(0) = (1/3)(0)^3 + (0)^2 - 7(0) + C1

0 = 0 + 0 + 0 + C1

C1 = 0

Therefore, the velocity function becomes:

v(t) = (1/3)t^3 + t^2 - 7t

Step 2: Integrate v(t) with respect to time to find the position function, s(t):

∫(v(t) dt) = ∫(((1/3)t^3 + t^2 - 7t) dt)

Integrating each term separately:

∫((1/3)t^3 dt) + ∫(t^2 dt) - ∫(7t dt)

= (1/12)t^4 + (1/3)t^3 - (7/2)t^2 + C2

Since we know that s(0) = 0, we can substitute t = 0 and solve for the constant C2:

s(0) = (1/12)(0)^4 + (1/3)(0)^3 - (7/2)(0)^2 + C2

0 = 0 + 0 + 0 + C2

C2 = 0

Therefore, the position function becomes:

s(t) = (1/12)t^4 + (1/3)t^3 - (7/2)t^2

Hence, the position function of the particle moving along the s-axis is given by s(t) = (1/12)t^4 + (1/3)t^3 - (7/2)t^2.

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Answer:

charge, distance

Explanation:

te distance between the particles and the am amount of electric charge the they carried

The position that visible light occupies lies between infrared and ultraviolet region. Option B is correct.

Visible light is a type of electromagnetic radiation that occupies the wavelength range between infrared and ultraviolet radiation. It has a wavelength range of approximately 400-700 nanometers (nm).

Electromagnetic radiation consists of waves of electric and magnetic fields that oscillate perpendicular to each other and travel through space. The electromagnetic spectrum encompasses all types of electromagnetic radiation, including radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

The different types of electromagnetic radiation are distinguished by their wavelength and frequency. Visible light is the only part of the electromagnetic spectrum that is visible to the human eye and is responsible for the colors we see in the world around us.

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On the surface of Mars, the period of the simple pendulum is approximately 2.27 seconds.

The period of a simple pendulum is given by the formula T = 2π√(L/g), where T represents the period, L is the length of the pendulum, and g is the acceleration due to gravity.

To find the period on the surface of Mars, we need to calculate the length of the pendulum using the given values of T and g for Mars. Rearranging the formula, we have L = (\(T^2\) * g) / (4\(\pi ^2\)).

Substituting the values into the equation, L = (1.\(60^2\)* 3.71) / (4\(\pi ^2\)). Evaluating this expression, we find L ≈ 0.532 m (rounded to three decimal places).

Using this length and the acceleration due to gravity on Mars (g = 3.71 \(m/s^2\)), we can calculate the period on Mars using the original formula. T = 2π√(0.532/3.71). After performing the calculation, we find that the period on the surface of Mars is approximately 2.27 s (rounded to two decimal places).

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Answer:

My teacher said 36m when I asked her

Explanation:

HOPE THIS HELPS!!

The average speed of April, given the data from the question is 13.33 m/s

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

Average speed is simply defined as the total distance travelled divided by the total time taken to cover the distance .

Average speed = Total distance travelled / total time

From the question given above, the following data were obtained:

Average speed = Total distance travelled / total time

Average speed = 1600 / 120

Average speed = 13.33 m/s

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Complete question

As shown in the figure below, April enters a race. She runs leftward 100 m to her horse, then she rides 500m to her truck, then she drives 1000m in a total time of 120s.What is her average velocity over the 120s period? What is her average speed over the 120s period?

Answer:

-13 | Velocity

13 | Speed

The elements found at Group 1, Period 2 are lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr). These elements are known as alkali metals and have one valence electron in their outermost shell.

The elements found at Period 4, Group 9 are cobalt (Co), rhodium (Rh), and iridium (Ir). These elements are known as transition metals and have high melting and boiling points, are good conductors of electricity and have multiple oxidation states. They are also known for their use in catalytic converters, jewelry, and other industrial applications.

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Answer:

Deceleration is reverse of acceleration

The maximum speed of the oscillation is 0.105 m/s. We can use the following equations to solve this problem:

The amplitude of the oscillation can be found using the maximum acceleration and the frequency:

a_max = 4π²f²A

where a_max is the maximum acceleration, f is the frequency, and A is the amplitude.

Plugging in the given values, we get:

0.15 m/s² = 4π²(1.4 Hz)²A

Solving for A, we get:

A = 0.012 m

So the amplitude of the oscillation is 0.012 m.

The maximum speed of the oscillation can be found using the amplitude and the frequency:

v_max = 2πfA

where v_max is the maximum speed.

Plugging in the values we calculated earlier, we get:

v_max = 2π(1.4 Hz)(0.012 m)

Solving for v_max, we get:

v_max = 0.105 m/s

So the maximum speed of the oscillation is 0.105 m/s.

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The question is not complete. The complete question is :

During a certain period of time, the angular position of a rotating object is given by \($\theta =2t^2 +10t+5$\), where θ is in radians and t is in seconds.  Determine the angular position, angular speed, and angular acceleration of the door (a) at t = 0.00 seconds, (b) at t = 3.00 seconds.

Solution :

Given :

Displacement or angular position of the object, \($\theta =2t^2 +10t+5$\)

∴ Angular speed is   \($\omega = \frac{d \theta}{dt}$\)

                                 ω = 10 + 4t

And angular acceleration is \($\alpha = \frac{d \omega}{dt}$\)

                                              α = 4

a). At time, t = 0.00 seconds :

   Angular displacement is \($\theta =2t^2 +10t+5$\)

                                            \($\theta =2(0)^2 +10(0)+5$\)

                                               = 5 rad

  Angular speed is  ω = 10 + 4t

                                 ω = 10 + 4(0)

                                     = 10 rad/s

Angular acceleration is α = 4 \($rad/s^2$\)

b). At time, t = 3.00 seconds :

   Angular displacement is \($\theta =2t^2 +10t+5$\)

                                            \($\theta =2(3)^2 +10(3)+5$\)

                                               = 53 rad

  Angular speed is  ω = 10 + 4t

                                 ω = 10 + 4(3)

                                     = 22 rad/s

Angular acceleration is α = 4 \($rad/s^2$\)

Explanation:

A weather front is a boundary separating air masses of several characteristics eg. Air density, wind and humidity. Disturbed weather often arises from these differences

Answer:

B

Explanation:

cause

Answer: A

Explanation:

The moon has less mass than Earth.

Just took the test.

Answer:

0.05m

Explanation:

Given parameters:

Force constant of the spring  = 40000N/m

Potential energy  = 42J

Unknown:

Extension  = ?

Solution:

To solve this problem, use the expression below:

           E.PE  = \(\frac{1}{2}\) k e²  

k is spring constant

e is the extension

              42  =  \(\frac{1}{2}\)  x 40000 x e²  

               e  = 0.05m

Answer:

False

Explanation:

This depends on how much air is in the ball, I think

To react completely with 0.500 L of volume of 0.500 M Na2CO3, you would need 0.250 L of 2.00 M HCl.

Write down the balanced chemical equation for the reaction between HCl and Na2CO3:

2 HCl + Na2CO3 → 2 NaCl + H2O + CO2

Determine the stoichiometry of the reaction:

From the balanced equation, we can see that 2 moles of HCl react with 1 mole of Na2CO3.

Calculate the number of moles of Na2CO3:

Given that the volume of Na2CO3 solution is 0.500 L and the concentration is 0.500 M, we can use the formula:

Moles = Concentration × Volume

Moles of Na2CO3 = 0.500 M × 0.500 L = 0.250 moles

Use the stoichiometry to determine the number of moles of HCl needed:

According to the stoichiometry of the balanced equation, 1 mole of Na2CO3 reacts with 2 moles of HCl.

Therefore, to react with 0.250 moles of Na2CO3, we would need 2 × 0.250 = 0.500 moles of HCl.

Convert moles of HCl to volume:

Given that the concentration of HCl is 2.00 M, we can use the formula:

Volume = Moles / Concentration

Volume of HCl = 0.500 moles / 2.00 M = 0.250 L

Convert the volume to liters:

The final answer is 0.250 liters of 2.00 M HCl are needed to react completely with 0.500 L of 0.500 M Na2CO3.

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The can be obtained by using the balanced chemical equation: Na2CO3 + 2 HCl → 2 NaCl + H2O + CO2  Write the balanced chemical equation for the reaction.

Na2CO3 + 2 HCl → 2 NaCl + H2O + CO2

Calculate the number of moles of Na2CO3. Using the formula n = c × V, where n is the number of moles, c is the concentration, and V is the volume, we get:

n = c × V

= 0.500 M × 0.500 L

= 0.250 mol

Calculate the number of moles of HCl required.The balanced chemical equation shows that 2 moles of HCl react with 1 mole of Na2CO3. Hence, the number of moles of HCl required can be calculated as follows

:n(HCl) = 2 × n(Na2CO3)

= 2 × 0.250 mol

= 0.500 mol

Calculate the volume of 2.00 M HCl required.The number of moles of HCl required is 0.500 mol. Using the formula V = n/c, where V is the volume, n is the number of moles, and c is the concentration, we get:

V = n/c

= 0.500 mol ÷ 2.00 M

= 0.250 L

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3. The acceleration of the bicycle is 0.36 m/s²

4. The distance traveled by the person is 2.25 m

5. The initial speed of the car is 7 m/s

The acceleration of the bicycle can be obtained as follow:

v² = u² + 2as

Inputting the given parameters, we have:

6² = 0² + (2 × a × 50)

36 = 0 + 100a

36 = 100a

Divide both side by 100

a = 36 / 100

a = 0.36 m/s²

Thus, the acceleration is 0.36 m/s²

The distance traveled by the person can be obtain as follow:

v² = u² + 2as

1.5² = 0² + (2 × 0.5 × s)

2.25 = 0 + s

s = 2.25 m

Thus, we can conclude that the distance is 2.25 m

The initial speed of the car can be obtain as follow:

v² = u² + 2as

15² = u² + (2 × 2 × 44)

0 = u² + 176

Collect like terms

u² = 225 - 176

u² = 49

Take the square root of both sides

u = √49

u = 7 m/s

Thus, the initial speed of the car is 7 m/s

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Answer:

True

Explanation:

Answer:

(a) -6.67 \(m/s^2\)

(b) 0.68

Explanation:

Given that the mass of the truck, \(m_1=8000\) kg.

Mass of the package, \(m_2=3000\) kg.

As the package does not slide, so the acceleration of both, truck as well as the package, is the same.

Let \(a\;\; m/s^2\) is the acceleration of the combined mass, m.

\(m=m_1+m_2= 8000+3000=11000\) kg.

The initial velocity of the combined mass, u= 20 m/s.

Time required to stop, t=3 seconds.

Final velocity, v=0.

Displacement traveled, s=50 m.

(a) As  \(a=\frac {v-u}{t}\)

\(\Rightarrow a=\frac{0-20}{3}=-\frac{20}{3} =6.67 m/s^2\)

Hence the acceleration of the truck is \(-6.67 m/s^2.\)

(b) Now, \(a=-6.67 m/s^2\) is the acceleration of the package, this acceleration is due the frictional force, f.

Due to inertia, on application of break, the package have tendency to slide to left (in  the direction of velocity). But the package does not slides, this is only due to the frictional force, f, which acts in the right direction ( opposite to the direction of velocity).

So, the magnitude of frictional force required on \(m_2\)  to avoid slide is

\(f=|m_2a|=\frac{20}{3}m_2\times(i)\)

Now, let \mu be the minimum coefficient of the friction, so

The force due to friction, \(f_r= \mu N\),

where \(\mu N\) is the normal reaction.

\(N=m_2g\), where g is the acceleration due to gravity.

So, \(f_r=\mu m_2g\cdots(ii)\)

To avoid slide, \(f_r\geq f\)

\(\Rightarrow \mu m_2g\geq\frac{20}{3}m_2\) [from (i)and (ii)]

\(\Rightarrow \mu\geq \frac{20}{3\times 9.81}\)    \([ as \;g=9.81 m/s^2]\)

\(\Rightarrow \mu \geq 0.68\)

Hence, the minimum value of coefficient of friction between packages and the truck os 0.68.

Answer:

Acceleration (b) not sure tho

Explanation:

For someone with a negative Weber slope for weight detection, it would be easier to tell the difference between 20 pounds and 21 pounds.

The Weber's Law states that the just noticeable difference (JND) between two stimuli is proportional to the magnitude of the stimuli. A negative Weber slope indicates that the JND decreases as the magnitude of the stimuli increases. In this case, as the weight increases, the person's ability to discriminate between the weights becomes easier.

Therefore, option C, telling the difference between 20 pounds and 21 pounds, would be easier for someone with a negative Weber slope for weight detection.

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The two resistances are calculated to be R = 6.63 ohm and r = 1.01 ohm when two situations are given.

Let the two resistances are r and R.

When they are connected in series,

V = 12 V

i = 1.57 A

When they are joined in series, the equivalent resistance is

Rs = r + R

So, By using Ohm's law

V = i × Rs

Rs = V / i = 12 / 1.57 = 7.64 ohm

R + r = 7.64 ohm  ----(1)

When they are connected in parallel:

V = 12 V

i = 10.5 A

When connected in parallel, the equivalent resistance,

Rp = (R + r)/(R r)

So, By using Ohm's law

V = i Rp

Rp = V / i = 12 / 10.5 = 1.14 ohm ----(2)

(R + r)/(R r) = 1.14

By substituting the value of R + r from equation (1) in equation (2), we get

r R = 7.64/1.14

r R = 6.70 ohm² ----(3)

R - r = √[(R+r)² -4 R r] = √[ 7.64² - 4× 6.7] = √[ 58.37 - 26.8] = √ 31.57 = 5.62 ohm

R - r = 5.62 ----(4)

(1) + (4) = 2R = 13.26

So, R = 6.63 ohm

r = 1.01 ohm

Thus, the two resistances are R = 6.63 ohm and r = 1.01 ohm.

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Answer:OOF

Explanation:

The magnetic field exactly midway between the wires, as viewed from your position, is zero.

Explanation:-

When two horizontal wires with identical currents carry current directly towards an observer, the magnetic field exactly midway between the wires, as viewed from the observer's position, is zero or no magnetic field is produced due to the wires. This is because the magnetic fields produced by both wires cancel each other out.

Let’s first talk about the direction of the magnetic field produced by the wires.

According to the right-hand rule, the magnetic field for a current-carrying wire points towards the direction of the curl of fingers of the right hand when the thumb points in the direction of the current.

A current flowing in the plane of the page towards an observer means that the current is pointing out of the page. Therefore, the magnetic field due to each wire will be pointing in the direction perpendicular to the current-carrying wire in a counterclockwise direction (as viewed from above).

So, if we look at the point directly midway between the two wires, we will see that the magnetic fields from each wire are equal in magnitude and opposite in direction. As a result, they will cancel each other out at the midpoint and there will be no net magnetic field there.

Therefore, the answer is that the magnetic field exactly midway between the wires, as viewed from your position, is zero.

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When an object is moved closer to the concave mirror, then

a)magnitude of image distance increases.

b)the image height become larger.

In concave mirror, we know that when an object is placed at the focus, its image will formed in enlarged size at infinity, it means height of image is large as compared to height of object. Here the scenario is same when object is placed at the center of curvature, object formed at the center of curvature of mirror in opposite direction of object. When object is moved closer to mirror from the center of curvature, image starts moving away from the mirror.

Image will formed below the positive y-axis and nature of image will be inverted and size of image starts increasing when it moves closer to mirror.

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The kinetic energy of the spring is obtained as 12 J. Option C

We know that the kinetic energy is the energy that is required to stretch the spring. We can use the graph that has been shown to show the force constant of the spring.

We can find the force constant as the slope of the graph as follows;

K = \(y_{2} - y_{1} /x_{2} - x_{1}\)

K = 60 - 0/0.3 - 0.2

K = 60/0.1

K = 600 N/m

We then have;

W = KE = 1/2 Kx^2

Thus;

KE = 0.5 * 600 * (20 * 10^-2)^2

KE = 12 J

It would have a kinetic energy of 12 J.

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The magnetic material is distributed this way because magnets possess a unique property known as magnetism, which enables them to attract or repel other magnets.

This property arises due to the alignment of magnetic domains, which are small regions within the magnetized material that possess a net magnetic moment. When these domains are aligned in the same direction, the magnet exerts a strong magnetic force, whereas when they are aligned in opposite directions, the magnet exerts a weaker force.
The distribution of magnetic material is critical in determining the strength and direction of the magnetic field produced by a magnet. The magnetic field lines are concentrated at the poles of the magnet, where the magnetic force is the strongest. Therefore, the magnetic material is often distributed in a manner that maximizes the alignment of magnetic domains at the poles while minimizing the alignment in other regions. This is achieved through a variety of methods, including shaping the magnet into a specific geometry or introducing magnetic materials that reinforce the magnetic field.
In summary, the distribution of magnetic material is essential in determining the strength and direction of the magnetic field produced by a magnet. The alignment of magnetic domains plays a crucial role in this process, and magnets are designed in a way that maximizes the alignment at the poles while minimizing it in other regions.

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Distance is the physical length travelled. While the displacement is the shorter distance between any two given points.

Distance is a numerical representation of the distance between two objects or locations.

Distance can refer to a physical length or an estimate based on other factors in physics or common use. |AB| is a symbol for the distance between two points A and B.

Displacement is defined as the shortest distance between the two points.

Sam determines the distance by doing the calculation as;

distance = speed × time

Hence, the Sam determines the distance and displacement by the respective formulas.

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Answer:

11760 kg / (m-s^2)

Explanation:

Just do the units FIRST

kg    m   m

m^3  s^2  1      

     now you can see that the two m's in the top cancel two m's in the denominator and you are left with

kg/ (m-s^2)   as units        

Now do the numbers

1000 * 9.8 * 1.2 = 11760

so answer is   11 760  kg / (m-s^2)