An object with mass 3.5 kg is attached to a spring with spring stiffness constant k = 270 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.(a) Calculate the amplitude of the motion._____ m(b) Calculate the maximum velocity attained by the object. [Hint: Use conservation of energy.]______ m/s

48/4= 12

12/2= 6

Answer: C. 6 kg

Answer:

Heating water to produce steam which drives a turbine

Explanation:

Generation of electricity in coal-burning power plants and nuclear power plants both involve heating water to produce steam which drives a turbine.

Answer:

A sloping surface separating air masses that differ in temperature and moisture content is called a front.

A sloping surface separating air masses that differ in temperature and moisture content is called a front.

A sloping surface separating air masses that differ in temperature and moisture content is called a front. Fronts occur when warm air and cold air meet, creating a boundary between them. The warm air is forced to rise over the cold air, resulting in changes in weather conditions.

There are several types of fronts, each associated with distinct weather patterns:

Cold Front: A cold front forms when a cold air mass advances and replaces a warmer air mass. As the cold air displaces the warm air, it forces the warm air to rise rapidly, leading to the formation of cumulonimbus clouds and potentially severe weather conditions such as thunderstorms.

Warm Front: In contrast, a warm front occurs when a warm air mass advances and overtakes a retreating cold air mass. As the warm air rises over the colder air, it produces widespread stratiform clouds and precipitation over an extended area.

Stationary Front: When two air masses meet but neither advances, a stationary front is formed. This results in a prolonged period of cloudy and wet weather along the boundary.

Occluded Front: An occluded front develops when a fast-moving cold front overtakes a slow-moving warm front. This complex type of front often leads to a mix of weather conditions, including precipitation and strong winds.

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Answer:

A. weight of air it displaces.

Explanation:

The force that buoys up a balloon is equal to the weight of the air it displaces, as per Archimedes' Principle.

The force that buoys up a balloon is equal to the weight of the air it displaces. This principle is known as Archimedes' principle and it applies to both liquids and gases, like air. According to this principle, the upward buoyant force exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

In the context of a balloon floating in the air, the balloon and the gas inside it displace a volume of air. The weight of this displaced air pushes upward on the balloon, providing the buoyant force. If the weight of the balloon and the gas inside it are less than the weight of the displaced air, the balloon will rise up into the atmosphere.

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Answer:

0.5 J

Explanation:

For this capacitor we have:

[tex]C=10 mF = 0.01 F[/tex] is the capacitance

V = 20 V is the potential difference

So the charge stored in the capacitor is

[tex]Q=CV=(0.01 F)(20 V)=0.2 C[/tex]

Later, the power supply is removed, so the charge on the capacitor will remain the same. A dielectric of dielectric constant

k = 4.0

is inserted in the gap between the plates. The capacitance of the capacitor change as follows:

C' = k C = (4.0)(0.01 F) = 0.04 F

The energy stored in the capacitor is given by

[tex]U'=\frac{1}{2}\frac{Q^2}{C'}[/tex]

and using Q = 0.2 C, we find

[tex]U'=\frac{1}{2}\frac{(0.2 C)^2}{(0.04 F)}=0.5 J[/tex]

After placing the dielectrics between the plates of the capacitor, the energy stored in the capacitor becomes 0.5 J.

Capacitance is a term used to define the amount of energy stored in the form of an electric charge in an electric device.

Given data:

The capacitance of parallel-plate capacitor is, C = 10 mF = 0.01 F.

The potential of power supply is, V' = 20 V.

The dielectric constant of the material is, ∈ = 4.0.

Let us first calculate the charge stored in the capacitor as,

[tex]q = CV'\\\\q = 0.01 \times 20\\\\q = 0.2 \;\rm C[/tex]

After placing the dielectric, the capacitance of the capacitor is,

[tex]C' = \epsilon \times C[/tex]

Solving as,

[tex]C' = 4.0 \times 0.01\\\\C' = 0.04 \;\rm F[/tex]

Now, the expression for the energy stored in the capacitor is,

[tex]U'=\dfrac{q^{2}}{2C'}[/tex]

Solving as,

[tex]U'= \dfrac{0.2^{2}}{2 \times 0.04}\\\\U'= 0.5 \;\rm J[/tex]

Thus, we can conclude that the energy stored in the capacitor is of 0.5 J.

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Answer:

3.7 atm i.e., pressure doubles

Explanation:

P₁ = Initial pressure = 1.85 atm

P₂ = Final pressure

V₁ = Initial volume = 12.5 L

V₂ = Final volume = 0.5V₁

T = Temperature is constant

From ideal gas law

P₁V₁ = P₂V₂

[tex]\\\Rightarrow P_2=P_1\frac{V_1}{V_2}\\\Rightarrow P_2=1.85\frac{V_1}{0.5V_1}\\\Rightarrow P_2=1.85\frac{1}{0.5}\\\Rightarrow P_2=1.85\times 2\\\Rightarrow P_2=3.7\ atm[/tex]

∴ Final pressure is 3.7 atm i.e., pressure doubles

Final answer:

Boyle's law describes the relationship between pressure and volume of a gas at constant temperature. When the volume is reduced by half, the pressure of the gas would double.

Explanation:

The pressure of a gas in a container is directly proportional to its volume when the temperature is constant, as described by Boyle's law. In this case, when the original volume is reduced by half, the pressure would double, resulting in a pressure of 3.7 atm.

Answer:

2412 psi is the pressure of the gas mixture in the tank.

Explanation:

Pressure of the helium gas = 1,906 psi

Volume of the helium gas = 7.25 L

Pressure of the oxygen gas = 506 psi

Volume of the oxygen gas = 7.25 L

After mixing both gases in a container with volume 7.25 L at with constant temperature.

Since, the temperature and volume remained constant, pressure becomes directly dependent on moles of gases.So, when we mix gases together the moles of gases will also add and along with that pressure of individual gas will also get added to give total pressure of the mixture in a tank.

Total pressure = pressure(Heluim)+pressure(oxygen)

[tex]P_{total}=1,906 psi+506 psi=2,412 psi[/tex]

2412 psi is the pressure of the gas mixture in the tank.

Answer: lambda [tex]\lambda[/tex], nu [tex]\nu[/tex], and 100E

Explanation:

The energy [tex]E[/tex] of a photon is given by:

[tex]E=h\nu[/tex]   (1)

Where:

[tex]h[/tex] is the Planck constant

[tex]nu[/tex] is the frequency

On the other hand, we have an expression that relates the frequency of the photn with its wavelength [tex]\lambda[/tex]:

[tex]nu=\frac{c}{\lambda}[/tex] (2) where [tex]c[/tex] is the speed of light

Substituting (2) in (1):

[tex]E=h\frac{c}{\lambda}[/tex]   (3) This is the energy for a single photon

For 100 photons, the energy is:

[tex]100E=100(h\frac{c}{\lambda})=100h\nu[/tex]   (3)

Where the wavelength and the frequency of the light remains constant.

Therefore, the answer is:

[tex]\lambda[/tex], [tex]\nu[/tex], and 100E

The wavelength, frequency, and energy of a pulse of light containing 100 of these photons is a wavelength, a frequency and 100 energy. Therefore the correct  answer is E.

1. The wavelength [tex](\(\lambda\))[/tex] and frequency (nu) of a photon are related by the speed of light ([tex]\(c\)[/tex]) in a vacuum: [tex]\(c = \lambda \nu\)[/tex].

2. The energy (E) of a photon is related to its frequency by Planck's equation: [tex]\(E = h \nu\)[/tex], where (h) is Planck's constant.

3. For a pulse of light containing 100 photons, the total energy is the sum of the energies of the individual photons.

4. Therefore, the pulse would have the same wavelength ([tex]\(\lambda\)[/tex]), the same frequency [tex](\(\nu\)),[/tex] and 100 times the energy [tex](\(100E\))[/tex] compared to a single photon.

Thus, the correct choice is option E. [tex]\(\lambda, \nu, \text{ and } 100E\)[/tex].

Complete question:

Consider a single photon with a wavelength [tex]\(\lambda\)[/tex], a frequency (nu), and an energy (E). What is the wavelength, frequency, and energy of a pulse of light containing 100 of these photons?

A. [tex]\(0.01 \lambda, \nu, \text{ and } 100E\)[/tex]

B. [tex]\(0.01 \lambda, 0.01 \nu, \text{ and } 0.01 E\)[/tex]

C. [tex]\(100 \lambda, 100 \nu, \text{ and } E\)[/tex]

D. [tex]\(100 \lambda, 100 \nu, \text{ and } 100 E\)[/tex]

E. [tex]\(\lambda, \nu, \text{ and } 100E\)[/tex]

Answer:

Average speed is 60 km/hour

Explanation:

When we need to calculate average speed, we use this equation:

[tex]V = \frac{x_{f} - x_{o}}{t_{f} - t_{o}}[/tex]

Where:   [tex]x_{o} = 0 km[/tex]   position at the beginning

              [tex]x_{f} = 240 km[/tex]   at the end

              [tex]t_{o} = 0 hours[/tex]

              [tex]t_{f} = 4 hours[/tex]

Then:     [tex]V = \frac{240 km - 0 km}{4 hours - 0 hours}[/tex]

              [tex]V = \frac{240 km}{4 hours}[/tex]

Finally    V = 60 km/hour

Answer:

Angular acceleration, α = 26.973 rad/s²

Explanation:

Given data:

Lifted mass, M = 12 kg

Distance of the lifted mass = 27.1 cm = 0.271 m

Effective lever arm, d = 3.3 cm = 0.033 m

Moment of inertia, I = 0.959 kg.m²

Applied force, F = 1504 N

Now,

the torque (T) is given as:

T = F × d

also,

T = I × α

where,

α is the angular acceleration

Now,

Total moment of inertia, I = 0.959 + 12×(0.271)² = 1.840 kg.m²

Now equation both the torque formula and substituting the respective values, we get

1504 × 0.033 = 1.840 × α

⇒ α = 26.973 rad/s²

Answer:

The average acceleration of the driver during the collision is [tex]-348.4\frac{m}{s^{2}}[/tex]

Explanation:

Initial speed of car , [tex]u=85\frac{km}{h}=\frac{85\times 5}{18}\frac{m}{s}[/tex]

=>[tex]u=23.61\frac{m}{s}[/tex]

Finally the car comes to rest .

Therefore final speed of the car , [tex]v=0\frac{m}{s}[/tex]

Distance traveled while coming to rest , s = 0.80 m

Using equation of motion

[tex]v^{2}=u^{2}+2as[/tex]

=>[tex]0^{2}=23.61^{2}+2\times 0.80\times a[/tex]

=>[tex]a=-348.4\frac{m}{s^{2}}[/tex]

Thus the average acceleration of the driver during the collision is [tex]-348.4\frac{m}{s^{2}}[/tex]

Answer:

12.5 ft/s

Explanation:

Height of person = 6 ft

height of lamp post = 10 ft

According to the question,

dx / dt = 5 ft/s

Let the rate of tip of the shadow moves away is dy/dt.

According to the diagram

10 / y = 6 / (y - x)

10 y - 10 x = 6 y

y = 2.5 x

Differentiate both sides with respect to t.

dy / dt = 2.5 dx / dt

dy / dt = 2.5 (5) = 12.5 ft /s

When the person is 15 ft away from the pole, the rate is 7.5 ft/s.

The resultant displacement is calculated as follows;

[tex]R^2 = 6^2 + 10^2\\\\R = 11.6[/tex]

10 ft ------ 5 ft

15 ft ------- ?

= (15 x 5)/10

= 7.5 ft/s

Thus, when the person is 15 ft away from the pole, the rate is 7.5 ft/s.

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Answer:

A) The electric and magnetic fields must be perpendicular to each other in that region

Explanation:

The proton does not experience any acceleration: this means that the net force acting on it is zero.

Therefore, this also means that the electric force and the magnetic force acting on the proton are balanced.

Let's remind that:

- The electric force acting on a positive charged particle has the same direction as the electric field:

F=qE

where F is the force, q is the charge, E is the electric field

- The magnetic force acting on a positive charged particle in motion is perpendicular to the direction of the magnetic field:

F=qv ∧ B

where q is the charge, v is the velocity of the particle, B is the magnetic field

Therefore, for the two forces to be along the same line (but in opposite directions), we must have that the electric field E and the magnetic field B are perpendicular to each other.

The correct statement is that the magnetic field must be zero but not the electric field for a proton moving without acceleration in a region of space, as only then will it not be deflected from its path.

The correct answer to the student's question is E) The magnetic field must be zero but not the electric field in that region. This can be understood by examining the forces experienced by a moving charged particle such as a proton in an electric field and magnetic field. A charged particle moving in a magnetic field experiences a Lorentz force that is always perpendicular to both the particle's velocity and the magnetic field direction.

If the proton is not accelerating in the direction of motion, it implies there's no net force acting on it in that direction. Since a magnetic field's force would always cause an acceleration perpendicular to the velocity, for a proton moving in a straight line with no acceleration, the magnetic field must be zero or parallel to the movement direction.

However, an electric field, if present, could be exerting a force on the proton balanced exactly by other forces (such as another opposite electric field), allowing the proton to have zero net force and continue its motion unaccelerated. Hence, a non-zero electric field could exist, but the magnetic field must be zero or not exerting any influence causing perpendicular acceleration of the proton.

The dielectric constant or relative permittivity of the dielectric slab inserted into the capacitor is approximately 2.28. This was calculated using the change in charge stored on the capacitor before and after the dielectric was inserted.

The question involves understanding the use of a dielectric in a parallel-plate capacitor. The presence of a dielectric alters the capacitance value of the capacitor, allowing it to store more charge for the same applied voltage.

The dielectric constant of a material (also called the 'relative permittivity') is a measure of how much it can increase the capacitance of a capacitor compared to the capacitance when a vacuum is between the plates. The original capacitance C can be calculated as C = Q/V, where Q is the charge stored across the plates, and V is the potential difference across the plates. After the dielectric is inserted, the capacitance C' is calculated as C' = Q'/V, where Q' is the new charge stored.

In this case, you have your original charge (Q) as 172 μC. When the dielectric is inserted, the new charge (Q') is 172 μC + 220 μC = 392 μC. The dielectric constant (k) can be calculated using the equation k = C'/C = Q'/Q = 392/172 ≈ 2.28.

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Answer:

[tex]\frac{d_2}{d_1} = \sqrt2 = 1.41[/tex]

Explanation:

As resistor is connected to the battery of constant EMF then the power across the resistor is given as

[tex]P = \frac{E^2}{R}[/tex]

now if two resistors are made up of same material and of same length then due to different cross sectional area they both have different resistance

Due to different resistance they both will have different power

Since power is inversely depends on the resistance

So if the power is twice that of the other then the resistance must be half

so we have

[tex]R_1 = \rho \frac{L}{A_1}[/tex]

[tex]R_2 = \rho\frac{L}{A_2}[/tex]

since one resistance is half that of other resistance

So the area of one must be twice that of other

so we have

[tex]\frac{A_2}{A_1} = 2[/tex]

[tex]\frac{\pi d_2^2}{\pi d_1^2} = 2[/tex]

[tex]d_2 = 1.41 d_1[/tex]

Answer:

[tex]v_1 = 12 volts[/tex]

[tex]v_2 = 6 volts[/tex]

[tex]v_3 = 36 volts[/tex]

Explanation:

As we know that all the batteries are in series

so the net voltage of all three batteries is given as

[tex]V = v_1 + v_2 + v_3[/tex]

now we know that

[tex]v_1 = 2v_2[/tex]

[tex]v_1 = \frac{1}{3}v_3[/tex]

now plug in all the values in it

[tex]54 = v_1 + \frac{v_1}{2} + 3v_1[/tex]

[tex]54 = 4.5 v_1[/tex]

[tex]v_1 = 12 volts[/tex]

now we have

[tex]v_2 = 6 volts[/tex]

[tex]v_3 = 36 volts[/tex]

Final answer:

To find the actual voltage of each battery connected in series to get a total of 54 volts, we can assign variables to represent the voltage of each battery. By using the given information, we can set up and solve an equation to find the values of the variables.

Explanation:

To find the actual voltage of each battery, we'll assign variables to each battery's voltage. Let's say the voltage of the second battery is x volts.

Using the information given, we know that the voltage of the first battery is twice the voltage of the second battery, so it is 2x volts. The voltage of the third battery is 1/3 the voltage of the first battery, so it is (1/3)(2x) = 2x/3 volts.

Since the total voltage when the batteries are connected in series is 54 volts, we can write the equation: 2x + x + 2x/3 = 54. Solving this equation, we find that x = 15 volts. Therefore, the voltage of the first battery is 2x volts = 2(15) = 30 volts, the voltage of the second battery is x volts = 15 volts, and the voltage of the third battery is 2x/3 volts = (2/3)(15) = 10 volts.

Answer:

reduced speed comes out to be 48.3 km/hr

Explanation:

intial speed = 65 miles per hour

final speed = 35 miles per hour

reduced speed = initial speed - final speed

                          =  65  - 35

                          =  30 mile/hr

1 km = 0.62 mile

1 miles =  1.61 km/hr

so reduce speed in (km/hr) = 30 ×1.61 km/hr

                                             =  48.3 km/hr

hence the reduced speed comes out to be 48.3 km/hr

Answer:

There is no way by which we can tell weather we are on the earth or we left the earth.

Explanation:

Our body responses to acceleration alone when we accelerate upwards at [tex]9.8m/s^{2}[/tex] a fictitious force equal to our [tex]mass\times acceleration[/tex] acts on our body which in this case of acceleration is same as our weight thus we will still feel the effect of gravity thus cannot say weather we left earth or are still there.

1. -23.2 J

The gravitational potential energy of the ball is given by

[tex]U=mgh[/tex]

where

m = 1.1 kg is the mass of the ball

g = 9.8 m/s^2 is the acceleration of gravity

h is the height of the ball, relative to the reference point chosen

In this part of the problem, the reference point is the ceiling. So, the ball is located 2.16 m below the ceiling: therefore, the heigth is

h = -2.16 m

And the gravitational potential energy is

[tex]U=(1.1 kg)(9.8 m/s^2)(-2.16 m)=-23.2 J[/tex]

2. 41.1 J

Again, the gravitational potential energy of the ball is given by

[tex]U=mgh[/tex]

In this part of the problem, the reference point is the floor.

The height of the ball relative to the floor is equal to the height of the floor minus the length of the string:

h = 5.97 m - 2.16 m = 3.81 m

And so the gravitational potential energy of the ball relative to the floor is

[tex]U=(1.1 kg)(9.8 m/s^2)(3.81 m)=41.1 J[/tex]

3. 0 J

As before, the gravitational potential energy of the ball is given by

[tex]U=mgh[/tex]

Here the reference point is a point at the same elevation of the ball.

This means that the heigth of the ball relative to that point is zero:

h = 0 m

And so the gravitational potential energy is

[tex]U=(1.1 kg)(9.8 m/s^2)(0 m)=0 J[/tex]

Answer:

The heat of vaporization 580 cal/g times 602g = cal in human  and do the same for life form.

Explanation:

Electrostatic force between two points in space is defined as,

[tex]F_e=\dfrac{Q_1Q_2}{4\pi r\epsilon_r\epsilon_0}[/tex]

The r is the distance between them.

So if,

[tex]1N=\dfrac{Q_1Q_2}{4\pi 2cm\epsilon_r\epsilon_0}\Rightarrow 2\cdot1N=\dfrac{Q_1Q_2}{4\pi\cdot10^{-2}m\cdot\epsilon_r\epsilon_0}[/tex]

Than,

[tex]\boxed{\dfrac{1}{4}N}=\dfrac{Q_1Q_2}{4\pi\cdot 8cm\cdot\epsilon_r\epsilon_0}\Rightarrow8\dfrac{1}{4}N\Leftrightarrow 2N=\dfrac{Q_1Q_2}{4\pi\cdot10^{-2}m\cdot\epsilon_r\epsilon_0}[/tex]

Hope this helps.

r3t40

Answer:

Separation between the plates, area of the plates and dielectric constant

Explanation:

The capacitance of a parallel plate capacitor is given by:

[tex]C=k \epsilon_0 \frac{A}{d}[/tex]

where

k is the dielectric constant

[tex]\epsilon_0[/tex] is the vacuum permittivity (which has a constant value)

A is the area of the plates

d is the separation between the plates

Therefore from the formula we see that the capacitance of a parallel plate capacitor depends on the following factors:

- Separation between the plates

- Area of the plates

- Dielectric constant

Answer:

option (c)

Explanation:

If a large force is applied on an object for a small duration of time, it is called impulsive force. for example, a bat's man hit the ball. here the contact time of bat and ball is very small while the force applied by the bat is very large.

Impulse = force x small time

To decrease the impulsive effect, the time should be increased.

Catching a fast-moving softball by extending the hand and reducing the force involves increasing the time of the catch, which decreases acceleration and the force needed to stop the ball.

The correct answer to the question is c. time of catch is increased. When catching a fast-moving softball, extending the hand forward just before the catch and allowing the ball to ride backward with the hand effectively increases the time over which the ball is decelerated to a stop. This is due to Newton's second law, which states that the force exerted on an object is equal to the mass of the object times its acceleration (F=ma). By increasing the time of the catch, the acceleration is decreased, and thus the force experienced by the hand is also reduced. This is in contrast to catching the ball abruptly, which would result in a short catch time, higher acceleration, and therefore a larger force needed to stop the ball.

Answer:

Distance the spring is compressed, x = 0.52 m  

Explanation:

Given :

Mass of the bullet, m = 10 g = 0.01 kg

Mass of the block, M = 1.95 kg

spring force constant, k = 16.6 N/m

Distance the spring is compressed =x

Speed of the bullet, v = 300 m/s

Speed of the block = V

Therefore we know that according to the law of conservation of momentum,

m.v = ( m+M )V

or [tex]V = \frac{m\times v}{m+M}[/tex]

   [tex]V = \frac{0.01\times 300}{0.01+1.95}[/tex]

              = 1.53 m/s

Now according to the law of conservation of momentum,

[tex]\frac{1}{2}\times M\times V^{2} =\frac{1}{2}\times k\times x^{2}[/tex]

[tex]x = \sqrt{\frac{\left ( M+m \right ).V^{2}}{k}}[/tex]

[tex]x = \sqrt{\frac{\left ( M+m \right )}{k}}\times V[/tex]

[tex]x = \sqrt{\frac{\left ( 1.95+0.01 \right )}{16.6}}\times 1.53[/tex]

[tex]x = 0.52[/tex] m

Thus, distance the spring is compressed, x = 0.52 m

Answer:E=[tex]\frac{\pi R\left ( \Delta V\right )^2\sqrt{LC}}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}[/tex]

Explanation:

We know resonant frequency is given by

[tex]\omega_0=\frac{1}{\sqrt{LC}}[/tex]

and the operating frequency is given by

[tex]\omega =2\omega_0=\frac{2}{\sqrt{LC}}[/tex]

The capacitance reactance is given by

[tex]X_c=\frac{1}{\omega C}=\frac{\sqrt{LC}}{2C}=\frac{1}{2}\sqrt{\frac{L}{C}}[/tex]

inductive reactance is given by

[tex]X_L=\omega L=\left ( \frac{2}{\sqrt{LC}}\right )L=2\sqrt{\frac{L}{C}}[/tex]

Thus impedance is

[tex]Z=\left ( R^2+\left (X_L-X_C \right )^2 \right )^\frac{1}{2}[/tex]

[tex]Z=\left ( R^2+\left (2\sqrt{\frac{L}{C}}-\frac{1}{2}\sqrt{\frac{L}{C}} \right )^2 \right )^\frac{1}{2}[/tex]

[tex]Z=\left ( R^2+\frac{9}{4}\left ( \frac{L}{C} \right ) \right )^\frac{1}{2}[/tex]

The average power delivered is

[tex]P_{avg.}=\frac{\Delta V^2}{Z}cos\phi =\frac{\left ( \Delta V\right )^2}{Z}\left (\frac{R}{Z} \right )[/tex]

[tex]P_{avg.}=\frac{\left (\Delta V \right )^2R}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}[/tex]

Energy Delivered in one cycle is given by

[tex]E=P_{avg}T[/tex]

[tex]E=\frac{\left (\Delta V \right )^2R}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}\left ( \frac{2\pi }{\frac{2}{\sqrt{LC}}}\right )[/tex]

E=[tex]\frac{\pi R\left ( \Delta V\right )^2\sqrt{LC}}{\left ( R^2+\frac{9}{4}\left (\frac{L}{C} \right )\right )}[/tex]              

Answer:

v = 2 m/s

Explanation:

Here we can use energy conservation to find the speed at the lowest point on its trajectory

As we know that by energy conservation

initial total gravitational potential energy = final total kinetic energy

now the height that is moved by the pendulum while it swing down is given as

[tex]h = L(1 - cos30)[/tex]

[tex]h = 1.5(1 - cos30) = 0.200 m[/tex]

now we can use energy conservation as

[tex]mgh = \frac{1}{2}mv^2[/tex]

[tex]v = \sqrt{2gh}[/tex]

[tex]v = \sqrt{2(9.8)(0.200)}[/tex]

[tex]v = 2 m/s[/tex]

Answer:

v = 1.978 m/s

Explanation:

Given that,

Mass of the object, m = 2 kg

Length of the string, l = 1.5 m

The maximum angle the string makes with the vertical as the pendulum swings is 30°, [tex]\theta=30^{\circ}[/tex]

The pendulum have gravitational potential energy when the angle is maximum. The pendulum has only kinetic energy at its lowest point. Let v is the speed of the object at the lowest point in its trajectory. It can be calculated as :

[tex]mgh=\dfrac{1}{2}mv^2[/tex]

h is the height moved by the pendulum.

[tex]h=l(1-cos(30))[/tex]

[tex]h=1.5(1-cos(30))[/tex]

h = 0.2 m

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{2\times 9.8\times 0.2}[/tex]    

v = 1.978 m/s

So, the speed of the object at the lowest point in its trajectory is 1.978 m/s.

Answer:d

Explanation:

Answer: option is A: An increasingly steeper slope

Explanation: Suppose that you are graphing the position of an object with increasing velocity.

in an x vs t graph.

as the velocity increases, the lapse of time needed to travel a fixed distance dx is shorter and shorter, so you will see a positive slope that as the time passes it will become more vertical (never being actually vertical)

Then the correct option is A: An increasingly steeper slope

(a) 44.7 m/s

We can find the final velocity of the car by using the SUVAT equation:

[tex]v^2-u^2 = 2ad[/tex]

where

v is the final velocity

u = 0 is the initial velocity (the car starts from rest)

[tex]a=0.5 m/s^2[/tex] is the acceleration

[tex]d=2km = 2000 m[/tex] is the displacement

Solving for v,

[tex]v=\sqrt{u^2 +2ad}=\sqrt{0+2(0.5)(2000)}=44.7 m/s[/tex]

(b) 80 s

We can find the time it takes for the car to cover 1.6 km by using the following SUVAT equation:

[tex]d=ut+\frac{1}{2}at^2[/tex]

where in this case we have

d = 1.6 km = 1600 m is the displacement

[tex]a=0.5 m/s^2[/tex] is the acceleration

u = 0

t is the time

Solving for t, we find:

[tex]t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2(1600)}{0.5}}=80 s[/tex]

Answer:

Infra and Red

Explanation:

While many elemental spectral lines are visible, almost all molecular lines lie in the infra portion of the spectrum, since they are at much lower energy. while many elemental spectral lines are visible, almost all molecular lines lie in the red portion of the spectrum, since they are at much lower energy.

Most molecular lines lie in the radio and infrared portions of the spectrum due to their lower energy levels. These lines form unique molecular fingerprints that aid scientists in molecular identification.

In the electromagnetic spectrum, most molecular lines are found in the infrared and radio portions. This is due to the lower energy levels associated with these wavelengths. Spectral lines are characteristic wavelengths of electromagnetic radiation that are emitted or absorbed by different substances. Atomic spectral lines, such as those observed in elements like hydrogen or iron, are often in the visible part of the spectrum. However, interactions within molecules, specifically vibrations and rotations, create spectral fingerprints in the longer infrared and radio wavelengths, hence, most molecular lines are found in these portions.

It's crucial to note that each molecule has its own unique pattern of spectral lines, creating a molecular fingerprint that scientists use to identify different molecules.

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Answer:

option (c)

Explanation:

The time taken by the pendulum to complete one oscillation is called time period.

The number of oscillations completed in one second is called frequency.

The frequency is the reciprocal of time period.

T = 1 / f

If the period is doubled, then the frequency is halved.