If love is the answer, then what is the question?

Answer:

yeah

Explanation:

electric fields help the charged particles interact

and isn't magnetic field the same as electric field.

Answer:

T = 74.3N

Explanation:

We are given;

v(t) = (2.00m/s²)t+(0.600m/s³)t²

So, when v = 9 m/s;

9 = 2t + 0.6t²

0.6t² + 2t - 9 = 0

Solving this quadratic equation,

t = -5.88 or 2.55

We'll pick t = 2.55 s

Now, kinematic acceleration will be the derivative of the acceleration.

Thus, a = dv/dt = 2 + 1.2t

So, acceleration at that time t = 2.55s is; a = 2 + 1.2(2.55) = 5.06 m/s²

Since the rope is subject to both acceleration and gravity, Tension is;

T = mg + ma

T = m(g + a)

T = 5(9.8 + 5.06)

T = 74.3N

Answer:

The human eye and brain together translate light into color. Light receptors within the eye transmit messages to the brain, which produces the familiar sensations of color. ... Rather, the surface of an object reflects some colors and absorbs all the others. We perceive only the reflected colors.

Explanation:

Final answer:

The eye and brain work together to perceive color. Light enters the eye and is detected by cones in the retina, which send signals to the brain. The brain processes these signals and combines information from different cones to create the perception of color.

Explanation:

The eye and brain work together to give you perception of color through a complex process. When light enters the eye, it is detected by special cells called cones in the retina. These cones are sensitive to different wavelengths of light and send signals to the brain. The brain then processes these signals and combines the information from different cones to create the perception of color.

For example, if you see a red object, the red cones in your eye will be activated and send signals to the brain. The brain then interprets these signals as the color red. Similarly, the green cones are activated by green light and the blue cones by blue light. By combining the information from all three types of cones, the brain is able to perceive a wide range of colors.

Answer:

x₁ = 15 m, x₂ = 12 m , x_total = 27m, v₁ = 5 m / s ,  v₂ = - 3 m / s

Explanation:

In this exercise we will use the kinematics of uniform motion

        v = d / t

let's apply this equation for the first move

        v₁ = Δx / t = (x₂-x₀) / t

        v₁ = (12- (-3)) / 3

        v₁ = 5 m / s

the distance traveled is x₁ = 15 m

Now let's analyze the return movement

        v₂ = Δx / dt

        v₂ = (0 - 12) / 4

        v₂ = - 3 m / s

The negative sign indicates that the vehicle is moving to the left

the distance traveled is x₂ = 12 m

The total dystonia is

     x_total = x₁ + x₂

     x_total = 15 +12

     x_total = 27m

In the attached we have the graphics of the movement

Answer:

75 m

Explanation:

wavelength = frequency/ speed = 75 m

Answer:

C after the hurricane of 1900s

Explanation:

They didn’t remove 8 feet of soil they put 8 feet of soil

Answer:

1. 60 W

2. 24 W

3. 0.83 A

4. 25200 J

Explanation:

1. What we are simply asked to look for is Electrical Power. It is the rate electrical energy is being transferred.

It is given as:

[tex]P = IV[/tex]

where I = current and V = voltage.

Therefore, Power is:

P = 0.50 * 120 = 60 W

2. Power, as given in the formula above is:

P = 2.0 * 12

P = 24.0 W

3. According to the formula of Power, current is given as:

[tex]I[/tex] = [tex]\frac{P}{V}[/tex]

Power is 100 W and voltage is 120 V, therefore, current is:

[tex]I = \frac{100}{120} \\\\\\I = 0.83 A[/tex]

4. Recall that power is the time rate of transfer of electrical energy. Mathematically:

[tex]P = \frac{E}{t}[/tex]

where t = time

This means that Electrical energy is:

[tex]E = Pt[/tex]

Recall that Power is:

[tex]P = IV[/tex]

Therefore, Electrical energy is:

[tex]E = IVt[/tex]

[tex]E = 210 * 12 * 10\\\\\\E = 25200 J[/tex]

1. At "60 W" the bulb convert electric energy to light

2. Power used by lamp will be "24.0 W".

3. The current flow will be "0.83 A".

4. The electric energy delivered to the motor will be "25200 J".

According to the question,

1. Current, I = 0.50 A

  Voltage, V = 120 V

We know,

→ Power (P) = Current (I) × Voltage (V)

                     = 0.50 × 120

                     = 60 W

2. Current, I = 2.0 A

  Voltage, V = 12.0 V

then,

→ P = 2.0 × 12

       = 24.0 W

3. Power, P = 100 W

  Voltage, V = 120 V

We know,

→ Current, I = [tex]\frac{P}{V}[/tex]

                    = [tex]\frac{100}{120}[/tex]

                    = 0.83 A

4. Current, I = 210 A

Potential difference, V = 12.0  

We know,

→ E = Pt

    P = IV

or,

The electrical energy be:

→ E = IVt

       = 210 × 12 × 10

       = 25200 J

Thus the above answer is correct.

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Answer:

The correct option is;

The voltages become negative instead of positive and keep the same magnitudes

Explanation:

Here we have that there is a change in direction from positive to negative with the direction pointing to opposite of the initial direction whereby the field strength does not change due to the reversal of the. Therefore the voltage becomes negative instead of negative while keeping the the magnitude.

That is there is a electric field reversal or a change electric field direction.

Answer: 11.5 Hz, 29.83 m

Explanation:

Given

Linear density of the cable, μ = 0.2 kg/m

Tensión in the cables, T = 500 N

Wavelength of the wave, = 4.5 Waves

Distance between the poles, L = 20 m

Temperature of, t = 20° C

Speed of sound, v = 343 m/s

λ = length / number of waves =

λ = 20 / 4.5

λ = 4.44 m

Frequency of a standing wave is the same as frequency of a hum. Calculated using the formula

F = n/2L * √(T/μ)

F = 1/λ * √(T/μ)

F = 1/4.44 * √(500/0.2)

F = 0.23 * √2500

F = 0.23 * 50

F = 11.5 Hz

Wavelength of the hum,

λ = v/f

λ = 343 / 11.5

λ = 29.83 m

The wavelength of the hum produced by the cable is approximately 4.44 meters, and the frequency is approximately 11.26 Hz, calculated using the known linear density, tension, and distance between poles.

The student is asking about the properties of a standing wave created when the wind blows across a cable hung between two poles. Given the linear density (µ) of 0.2 kg/m, the tension in the cable (500 N), and the distance between poles (20 meters), we are to find the frequency and wavelength of the hum produced by the cable.

Firstly, we can calculate the wavelength (λ) of the wave using the information that 4.5 wavelengths fit between the two poles that are 20 meters apart:

λ = 20 meters / 4.5 wavelengths = 4.44 meters (approx)

Next, we can find the speed (v) of the wave on the cable using the formula:

v = sqrt(T / µ)

Plugging in the given values, we get:

v = sqrt(500 N / 0.2 kg/m) = sqrt(2500 m2/s2)

v = 50 m/s

Now, using the wave speed (v) and the wavelength (λ), we can calculate the frequency (f) of the wave using the formula:

f = v / λ

f = 50 m/s / 4.44 m = 11.26 Hz (approx)

Therefore, the wavelength is approximately 4.44 meters, and the frequency of the hum is approximately 11.26 Hz.

Answer:

300 K

Explanation:

First, we have find the specific heat capacity of the unknown substance.

The heat gained by the substance is given by the formula:

H = m*c*(T2 - T1)

Where m = mass of the substance

c = specific heat capacity

T2 = final temperature

T1 = initial temperature

From the question:

H = 200J

m = 4 kg

T1 = 200K

T2 = 240 K

Therefore:

200 = 4 * c * (240 - 200)

200 = 4 * c * 40

200 = 160 * c

c = 200/160

c = 1.25 J/kgK

The heat capacity of the substance is 1.25 J/kgK.

If 300 J of heat is added, the new heat becomes 500 J.

Hence, we need to find the final temperature, T2, when heat is 500 J.

Using the same formula:

500 = 4 * 1.25 * (T2 - 200)

500 = 5 * (T2 - 200)

100 = T2 - 200

=> T2 = 100 + 200 = 300 K

The new final temperature of the unknown substance is 300K.

Answer:

Multiplying the mass of any student by a factor of 4.5 gives the kinetic energy of the student.

Explanation:

because

Answer: the question was asked to think about how to multiply a mass speech student by a factor to include the student. Kinetic energy, are there any common factors that appeal to them? The table shows mass energy and constant velocity. Let's calculate a constant factor, multiply it by mass, get the energy and see if we can do it. It's very easy. You can do it just in case. Only kinetic energy divided by mass can be produced. That is, the first is 100 and 21.5 divided by 27. Now you have the next 4.5. This is one. Then it is 162 divided by 36. This is 4.5. January 3, 202

Divide 5 by 45 to get 4.5. And hopefully you can see the patterns that are appearing here. In the fourth one, 243 divided by 54 gives 4.5. The fifth 288 divided by 64. Since it is 4.5, you can guess what it will be like. And finally, in the sixth case, it's 3 to 8.5 divided by 73. This is also equivalent to 4. Well, this common factor 4.5 was found.

Kinetic energy is a form of energy that an object or particle has due to its movement. When work is done on an object by applying a net force that transfers energy, the object accelerates, thereby gaining kinetic energy. In physics, the kinetic energy of an object is the energy that the object has due to its motion.

This is defined as the work required to accelerate an object of a given mass from a stationary state to a specified velocity. After the body gains this energy during acceleration, the body retains this kinetic energy unless the velocity changes.

All moving objects use kinetic energy. Examples of kinetic energy are walkers, thrown baseball, bread crumbs falling from a table, and charged particles in an electric field.

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Answer:

C.

Explanation:

Answer:

All particles made of quarks are called hadrons.

All particles madeup of two or more quarks held together by a force  are called ; ( C ) Hadrons

Hadrons are subatomic particles which are made of two or more quarks which are held firmly by a force similar to electric force. An example of Hadron is Baryon which contains three quarks which are held closely together.

Hence we can conclude that All particles made of quarks are called Hadrons

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Answer:

The cytoplasm holds all the organelles, except the nucleus.

Explanation:

The cytoplasm holds all organelles, with the primary exception being the nucleus, which is separated by a nuclear envelope. Other organelles like chloroplasts, mitochondria, and vacuoles, are held within the cytoplasm.

The cytoplasm, the watery fluid inside cells, houses almost all the organelles. The primary organelle that it does not encompass is the nucleus. The nucleus stays separated from the cytoplasm by a nuclear envelope.

Other organelles such as chloroplasts, mitochondria, and vacuoles are embedded within the cytoplasm. These organelles perform various roles within cells, while the nucleus controls the cell's activities and contains the cell's genetic information.

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The final velocity of the truck driver does not change after making a U-turn and driving in the opposite direction.

The final velocity of the truck driver does not change after making a U-turn and driving in the opposite direction. While the truck's speed changes, the velocity remains the same because velocity takes into account both the speed and direction of motion. Since the speed remains constant at 30 mph and the direction changes, the velocity is still 30 mph, just in the opposite direction.

Question:

(a) She catches the Frisbee and holds it.  

Answer:

The correct option is;

A perfectly inelastic collision

Explanation:

A perfectly inelastic collision is one in which there is maximum amount of loss of kinetic energy in the system. In a perfectly inelastic collision, the colliding members lose their initial speed and they stick together resulting in a loss of kinetic energy.

Since she catches and holds on to the Frisbee, the kinetic energy of the Frisbee is lost as she holds on to it so as to combine her mass to that of the Frisbee.

Complete Question in order

See the first image attached

Answer and Explanation:

The three images attached discussed the solution to this question

second Image                                                                                      

Third Image                                                                                          

and Fourth Image

If the images are not clear enough right-click on it and open in a new tab

Answer:

     v₀ = 240  m / s

Explanation:

This problem must be solved in two parts, first we must use the conservation of the moment, then the conservation of energy.

Let's start by applying moment conservation, to the system formed by the block and bullet, in this case the forces during the crash are internal and the moment is conserved

Instant starts. Before the crash

          p₀ = m v₀

Final moment. Right after the crash

         [tex]p_{f}[/tex] = (m + M) v

The moment is preserved

         Po =p_{f}

        M v₀ = (m + M) v

        v = m / (m + M) v₀        (1)

This is the speed with which the bullet block system comes out, now we can use energy conservation

Starting point. Right after the crash

         Em₀ = K = ½ (m + M) v²

Final point. Highest point of the path

         [tex]Em_{f}[/tex] = U = (m + M) g y

         Em₀ = Em_{f}

         ½ (m + M) v² = (m + M) g y

          v = √2 g y                 (2)

We substitute 1 in 2

              m / (m + M) v₀ = √ 2gy

            v₀ = (m + M) / m √ 2gy

Let's calculate

           v₀ = (0.0134 +0.800) /0.0134    √ (2 9.8 0.8)

           v₀ = 240  m / s

Answer:

298.04 m/s

Explanation:

Let m = mass of bullet = 0.0134 kg and M = mass of block = 0.800 kg.

Since the bullet becomes embedded in the block and rises a vertical height,h = 0.800 m

The kinetic energy change of mass + block =  potential energy of mass + block at height, h

ΔK = -ΔU

So, 1/2(m + M)(v² - V²) = -[(m + M)gh - 0] where v is the velocity of the bullet + block at height, h. Since the tension, T is the centripetal force at height, h, it follows that

T = (m + M)v²/r  r = length of cord = 1.44 m

v = √(Tr/(m + M)) = √4.76 N × 1.44 m/(0.800 + 0.0134)kg = √(6.8544/0.8134) = √8.427 = 2.9 m/s

So. 1/2(v² - V²) = -gh

v² - V² = -2gh

V = √(v² + 2gh) = √((2.9 m/s)² + 2 × 9.8 m/s² × 0.8 m) = √(8.41 + 15.68) = √24.09 = 4.91 m/s

This is the velocity of the bullet plus block at collision.

From the law of conservation of momentum,

momentum of bullet = momentum of bullet plus block

mv₀ = (m + M)V where v₀ = initial speed of bullet

v₀ = (m +M)V/m = (0.0134 kg + 0.800 kg)4.91 m/s ÷ 0.0134 kg = 3.994 ÷ 0.0134 kg = 298.04 m/s

Answer:

Explanation:

Given

Original volume V1=30cm^3 converting to L

=30/1000=0.03L

Constant pressure P= 648 tors

Converting to atm; 648 tors*1atm/760 torr=0.853 atm

Work=984J= 984**1L/101.33=9.7L.atm

Note before

W= -P(Vfinal-Vinitial)

-9.7/0.853+0.03L=11.68L

Answer:

Final expanded volume 11.43 L

Explanation:

The picture attached shows the solution

Answer:

Energy is conserved.

Explanation:

According to law of conservation of energy ,energy can neither be created nor be destroyed .

When the player kicks the soccer ball, the kinetic energy is transferred to the ball and it will roll for a while and then stops. The combination of force and distance is called as work.Greater the force faster the ball will go.

The force with which the soccer player player kicked the ball will be having it effects on the ball. As the ball rolls in the ground  kinetic energy which the ball got from the player will be lost in the form of heat due to friction.

According to the Newton first law of motion,the object continues to remain  in rest or move with constant speed unless acted upon by the external force.

Answer:

in physics, a photon is a bundle of electromagnetic energy. It is the basic unit that makes up all light

Explanation:

Answer:

The quantum of light and other electromagnetic energy, regarded as a discrete particle having zero rest mass, no electric charge, and an indefinitely long lifetime. It is a gauge boson.

Answer:

I'm sorry, I don't think there is any answer to give seeing as no question has been asked

Answer:

No question

Explanation: Sorry

Answer:

(a) 38.5m/s

(b) 64.4m/s

Explanation:

First, we can obtain the launch speed from the definition of kinetic energy:

[tex]K=\frac{1}{2}mv^2\\\\v=\sqrt{\frac{2K}{m}}\\\\[/tex]

Plugging in the given values, we obtain:

[tex]v=\sqrt{\frac{2(1550J)}{0.55kg}}\\\\v=75.0m/s[/tex]

Now, from the conservation of mechanical energy, considering the instant of launch and the instant of maximum height, we get:

[tex]E_0=E_f\\\\K_0=U_g_f+K_f\\\\\frac{1}{2}mv_0^2=mgh_f+\frac{1}{2}mv_0_x^2\\\\\frac{1}{2}mv_0^2=mgh_f+\frac{1}{2}mv_0^2\cos^2\theta\\\\\implies \cos\theta=\sqrt{1-\frac{2gh_f}{v_0^2}}[/tex]

And with the known values, we compute:

[tex]\cos\theta=\sqrt{1-\frac{2(9.8m/s^2)(140m)}{(75.0m/s)^2}}\\\\\cos\theta=0.513\\\\\theta=59.12\°[/tex]

Finally, to know the components of the launch velocity, we use trigonometry:

[tex]v_0_x=v_0\cos\theta=(75.0m/s)\cos(59.12\°)=38.5m/s\\\\v_0_y=v_0\sin\theta=(75.0m/s)\sin(59.12\°)=64.4m/s[/tex]

It means that the horizontal component of the launch velocity is 38.5m/s (a) and the vertical component is 64.4m/s (b).

Answer:

Fraction of the specimen's is 0.4.

Explanation:

We know,

Mass = volume × density

Weigh= mass × g

          = volume × density× g

          = density× g × volume

          [tex]=\rho.g.V[/tex]

An object weighs less submerged due to buoyant force acting on it.

[tex]\therefore W_{wet}= W_{dry}-B[/tex]

[tex]B= W_{dry}-W_{wet}[/tex]

   [tex]=W_{\textrm{fluid displaced}}[/tex]

   [tex]=\rho_{fluid}. g.V_{submerged}[/tex]

Given that, the weighs of the specimen in dry is twice of the weighs in air.

[tex]W_{wet}=\frac 12W_{dry}[/tex]

Then ,

[tex]B= W_{dry}-W_{wet}[/tex]

   [tex]= W_{dry}-\frac12W_{dry}[/tex]

   [tex]=\frac12W_{dry}[/tex]

   [tex]=\rho_{Rock}. g.V_{Rock}[/tex]

Therefore,

[tex]\rho_{fluid}. g.V_{submerged}=\frac12\rho_{Rock}. g.V_{Rock}[/tex]

[tex]\Rightarrow \rho_{Rock}. g.V_{Rock}=2\rho_{fluid}. g.V_{submerged}[/tex]

[tex]\Rightarrow \frac{.V_{Rock}}{V_{submerged}}=\frac{2\rho_{fluid}. g}{\rho_{Rock}.g}[/tex]

[tex]\Rightarrow \frac{.V_{Rock}}{V_{submerged}}=\frac{2\rho_{fluid}}{\rho_{Rock}}[/tex]

[tex]\Rightarrow \frac{.V_{Rock}}{V_{submerged}}=\frac{2\times 1.0 \times 10^3\ kg /m^3}{5.0\times 10^3 \ kg/m^3}[/tex]

                     =0.4

Fraction of the specimen's is 0.4.

Answer:

Explanation:

velocity of salmon with respect to water, v(s,w) = 5 mi/h at N 45° E

velocity of water with respect to ground, v(w,g) = 2 mi/h due east

Let the true velocity of salmon is velocity of salmon with respect to water is v(s,g)

First write the velocities in vector from

[tex]\overrightarrow{v}_{s,w}=5(Cos 45\widehat{i}+Sin 45\widehat{j})=3.54\widehat{i}+3.54\widehat{j}[/tex]

[tex]\overrightarrow{v}_{w,g}=2\widehat{i}[/tex]

Using the formula of relative speed,

[tex]\overrightarrow{v}_{s,w}=\overrightarrow{v}_{s,g}-\overrightarrow{v}_{w,g}[/tex]

[tex]3.54\widehat{i}+3.54\widehat{j}=\overrightarrow{v}_{s,g}-2\widehat{i}[/tex]

[tex]\overrightarrow{v}_{s,g}=5.54\widehat{i}+3.54\widehat{j}[/tex]

This i the true velocity of salmon.

The true velocity of the fish as a vector is [tex]5.54i \ + \ 3.54j[/tex].

The given parameters;

The true velocity of the fish as a vector is calculated as follows;

[tex]v_f = v\ cos(\theta)i \ + \ v\ sin(\theta)j \ + \ 2i\\\\v_f = 5cos(45) i \ + 5sin(45)j \ + \ 2i\\\\v_f = 3.54i \ + \ 3.54j \ + 2i\\\\v_f = 5.54i \ + \ 3.54 j[/tex]

Thus, the true velocity of the fish as a vector is [tex]5.54i \ + \ 3.54j[/tex].

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Answer:

a) 1.1mm

b) 2.513kg/ms^2

Explanation:

You can use the formula for the calculation of the wavelength of a wave

f=1.40MHz=1.40*10^{6}Hz

1 )

[tex]\lambda=\frac{v}{f}=\frac{1540m/s}{1.40*10^{6}Hz}=1.1*10^{-3}m=1.1mm[/tex]

2)

The Young modulus can be computed by using the expression:

[tex]v=\sqrt{\frac{Y}{\rho}}\\\\Y=v^2\rho[/tex]

where Y is the Young modulus and p is the density of the material. Here, you have considered that the prostate gland can be taken as a vibrating membrane or string.

By replacing you obtain:

[tex]Y=(1540m/s)^2(1060kg/m^3)=2.513*10^9kg/ms^2[/tex]

hence, the Young modulus of the prostate glande is 2.513kg/ms^2

Answer:

1) 1.1 x [tex]10^{-3}[/tex] m

2)2.51 x[tex]10^{9}[/tex]Pa

Explanation:

Given:

Speed of sound in prostate 'V'= 1540m/s

frequency 'f'  = 1.40 MHz = 1.40 x [tex]10^{6}[/tex]Hz

density of prostate'ρ' = 1060 kg/m3

1) As we know that the relationship of the speed of sound, its frequency, and wavelength is the same as for all waves

V= fλ

λ= V/f => 1540/1.40 x [tex]10^{6}[/tex]

λ= 1.1 x [tex]10^{-3}[/tex] m

Thus, the wavelength of the sonogram ultrasound is 1.1 x [tex]10^{-3}[/tex] m

2)The speed of sound in a solid the depends on the Young's modulus of the medium and the density

V=√Y/ρ.

V² = Y/ρ

Y= V² x ρ=> 1540² x 1060

Y= 2.51 x[tex]10^{9}[/tex]Pa

Thus, Young's modulus for the prostate gland is 2.51 x[tex]10^{9}[/tex]Pa

Answer:

Final speed = 148.21m.s

Time of flight = 7.82seconds

Explanation:

The motion of the body is a projectile motion.

Projectile is a motion created by an object launched in air and allowed to fall to freely under the influence of gravity.

Taking the maximums height reached H = 75m

Angle of launch = 15°

Using the maximum height formula to get the velocity U of the object

H = U²sin²theta/2g

Where g is the acceleration due to gravity = 9.81m/s²

75 = U²(sin15°)²/2(9.81)

1471.5 = U²(sin15°)²

1471.5 = 0.06699U²

U² = 1471.5/0.06699

U² = 21,965.9

U = √21,965.9

U = 148.21m/s

The time taken for the skier to reach the bottom of this hill starting from rest is the time of flight T.

T = 2Usintheta/g

T = 2(148.21)sin15°/9.81

T = 296.42sin15°/9.81

T = 76.72/9.81

T = 7.82seconds

Answer:

a. 3π/2 b. 0.36 m c. 0.234 m/s d. 42.55 m/s²

Explanation:

Here is the complete question

A mass  m  =  1.1  kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant  k  =  130  N/m and negligible mass. The mass undergoes simple harmonic motion when placed in vertical motion, with its position given as a function of time by  y ( t ) =  A c o s ( ω t  −  ϕ ) , with the positive y-axis pointing upward. At time  t  =  0  the mass is observed to be passing through its equilibrium height with an upward speed of  v 0 =  3.9  m/s.

A. Find the smallest positive value of  ϕ ,  in radians.

B. Calculate the value of  A  in meters.  

C. What is the mass's velocity along the y-axis in meters per second, at the time  t  = 0.15  s?  

D. What is the magnitude of the mass's maximum acceleration, in meters per second squared?

Solution

a. Since y ( t ) =  A c o s ( ω t  −  ϕ ), the smallest possible value for ϕ is gotten when c o s ( ω t  −  ϕ ) = 0 ⇒ ω t  −  ϕ = cos⁻¹ 0 = π/2

ω t  −  ϕ = π/2.

At t = 0, ω t  −  ϕ = ω  0 −  ϕ = 0 −  ϕ = π/2

−  ϕ = π/2

ϕ = -'π/2

Since this is a negative angle, we add 2π to the right side.

So, ϕ = -'π/2 + 2π = 3π/2

ϕ = 3π/2

b. Since v = Aω = A√(k/m) where v = maximum velocity at time t = 0 = 3.9 m/s. A = amplitude, k = spring constant = 130 N/m and m = mass = 1.1 kg

A = v/√(k/m) = 3.9 m/s/√(130 N/m/1.1 kg) = 3.9/√118.18 = 3.9/10.87 = 0.36 m

c. To find its velocity, we differentiate y(t)

So, v = dy(t)/dt = dA c o s ( ω t  −  ϕ )/dt = -'ωAsin( ω t  −  ϕ ) = v₀sin( ω t  −  ϕ )

v = v₀sin( ω t  −  ϕ ) = v₀sin( ω t  −  ϕ)

Substituting the value of the variables,

v = 3.9sin( 10.87 t  −  3π/2)

At t = 0.15 s,

v = 3.9sin( 10.87 × 0.15  −  3π/2)

v = 3.9sin( 1.6305  −  4.7124)

v = -'3.9sin( -3.0819)

v = -'3.9 × - 0.06

v = 0.234 m/s

d. The maximum acceleration, a

a = Aω² = Ak/m = 0.36 × 130/1.1 = 42.55 m/s²

Answer:

a) F = 10.4 rad/s

b) A = 0.375 m

c) ϕ = 3π/2

d) V(t) = -ωAsin( ω t - 3π/2 )

e) V = 0.144 m/s

f) a = 40.625 m/s²

Explanation: Given that

mass m = 1.2 kg

The spring constant k = 130 N/m Time t = 0

Distance d = 0.35 m 

y( t ) =  A c o s ( ω t  −  ϕ )

At time  t  =  0

Speed of  Vo = 3.9  m/s.

a) Find the angular frequency of oscillations in radians per second

W = √(k/m)

2πF = √(k/m)

F = 1/2π√(k/m)

F = 1/2π √(130/1.2)

F = 1.66Hz

1 Henz = 6.28 rad/s therefore,

F = 1.66 × 6.28

F = 10.4 rad/s

b) Calculate the value of  A  in meters.  

V = Aω = A√(k/m)

where V = 3.9 m/s the maximum velocity at time t = 0

A = amplitude

A = v/√(k/m)

A = 3.9/√(130/1.2)

A = 3.9/10.4

A = 0.375 m

c. Determine the value of  ϕ in radians

If y( t ) =  A c o s ( ω t  −  ϕ ) We can obtain the smallest possible value of ϕ when c o s ( ω t  −  ϕ ) = 0

ω t  −  ϕ = cos⁻¹ 0 = π/2

ω t  −  ϕ = π/2.

At t = 0,

ω(0) −  ϕ = π/2

−  ϕ = π/2

ϕ = -'π/2

This is a negative angle, let us add 2π to the right side. So,

ϕ = -'π/2 + 2π = 3π/2

ϕ = 3π/2

d. Enter an expression for velocity along y axis as function of time in terms of A, ϕ and t using the value of ϕ from part c.

To find expression for velocity, we differentiate y(t) with respect to time t So,

V = dy/dt = dA c o s ( ω t  −  ϕ )/dt

V = -ωAsin( ω t  −  ϕ )

Therefore

V(t) = -ωAsin( ω t + π/2 )

Or

V(t) = -ωAsin( ω t - 3π/2 ) ...... (1)

e. What is the velocity of mass at time t = 0.25 s?

From equation (1)

V(t) = V₀sin( ω t  −  ϕ )

Substituting the value of the variables,

V = 3.9sin( 10.4t  −  3π/2)

At t = 0.25 s,

V = 3.9sin( 10.4 × 0.25 − 3π/2)

V = 3.9sin( 2.6 −  4.7124)

V= -3.9sin( -2.1124)

V= -3.9 × - 0.037

V = 0.144 m/s

f. What is the magnitude of mass's maximum acceleration?

The maximum acceleration a = Aω²

a = Aω² =

a = Ak/m

a = 0.375 × 130/1.2

a = 40.625 m/s²

Answer:

magnitude of the frictional torque is 0.11 Nm

Explanation:

Moment of inertia I = 0.33 kg⋅m2

Initial angular velocity w° = 0.69 rev/s = 2 x 3.142 x 0.69 = 4.34 rad/s

Final angular velocity w = 0 (since it stops)

Time t = 13 secs

Using w = w° + §t

Where § is angular acceleration

O = 4.34 + 13§

§ = -4.34/13 = -0.33 rad/s2

The negative sign implies it's a negative acceleration.

Frictional torque that brought it to rest must be equal to the original torque.

Torqu = I x §

T = 0.33 x 0.33 = 0.11 Nm