Suppose that your mass is 59.1 kg, and you are standing on a scale fastened to the floor of an elevator. The scale measures force and is calibrated in newtons. What does the scale read when the elevator is rising and its speed is decreasing at a rate of 6.87 m/s2? Use 9.80 m/s2 for acceleration due to gravity.

Answer:

2.45 N/m

Explanation:

We can find the spring constant by using Hooke's law:

[tex]F=kx[/tex]

where

F is the force applied to the spring

k is the spring constant

x is the stretching of the spring

Here, the force applied is the weight of the mass hanged on the spring. The mass is

m = 10 g = 0.010 kg

So the weight is

[tex]F=mg=(0.010 kg)(9.8 m/s^2)=0.098 N[/tex]

while the stretching is

x = 4 cm = 0.04 m

So the spring constant is

[tex]k=\frac{F}{x}=\frac{0.098 N}{0.04 m}=2.45 N/m[/tex]

When the net torque is zero, there is no overall force causing the object to turn clockwise or counterclockwise.

An object is said to be in a condition of rotational equilibrium if there is no net torque operating on it. In other words, the object is keeping a constant angular velocity while not suffering any rotational acceleration. The object has a constant angular momentum when the net torque is zero.

If the net torque is zero, the item is being pulled in a direction that is equal to the sum of all the clockwise and anticlockwise torques pulling on it. To put it another way, any propensity the object has to spin in one direction is counterbalanced by an equal tendency to rotate in the opposing direction.

Hence, When the net torque is zero, there is no overall force causing the object to turn clockwise or counterclockwise.

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Final answer:

When the net torque is zero, it means that the clockwise and counterclockwise torques are balanced.

Explanation:

When the net torque is zero, it implies that the clockwise and counterclockwise torques balance each other out. In other words, the total torque in the clockwise direction is equal in magnitude but opposite in sign to the total torque in the counterclockwise direction.

Answer:

19 cm

Explanation:

inner radius, a = 16 cm, C = 113 p F = 113 x 10^-12 F

Let b cm be the radius of outer sphere.

The formula of capacitance of spherical capacitor is given by

C = 4π∈0 a b / (b - a)

a b / ( b - a) = C / 4π∈0

a b / ( b - a ) = 113 x 10^-12 x 9 x 10^9

a b / ( b - a ) = 1.017

16 x 10^-2 x b x 10^-2 = 1.017( b - 16) x 10^-2

0.16 b = 1.017 b - 16.272

0.857 b = 16.272

b = 19 cm

Answer:

The velocity after impact 24.96 m/s

Explanation:

Given that,

Mass of falcon = 1.55 kg

Mass of dove = 0.395 kg

Velocity of falcon = 29.5 m/s

Velocity of dove = 7.15 m/s

We need to calculate the velocity after impact

Using conservation of momentum

[tex]m_{1}u_{1}+m_{2}u_{2}=(m_{1}+m_{2})v[/tex]

Where,

u = initial velocity

v = final velocity

[tex]m_{1}[/tex] = mass of falcon

[tex]m_{2}[/tex] = mass of dove

Put the value in the equation (I)

[tex]1.55\times29.5+0.395\times7.15=(1.55+0.395)v[/tex]

[tex]v=\dfrac{1.55\times29.5+0.395\times7.15}{(1.55+0.395)}[/tex]

[tex]v=24.96\ m/s[/tex]

Hence, The velocity after impact 24.96 m/s

Answer:

35.3 N

Explanation:

U = 0, V = 0.61 m/s, s = 0.39 m

Let a be the acceleration.

Use third equation of motion

V^2 = u^2 + 2 as

0.61 × 0.61 = 0 + 2 × a × 0.39

a = 0.477 m/s^2

Force = mass × acceleration

F = 74 × 0.477 = 35.3 N

Final answer:

The magnitude of the net force acting on the kayak, which accelerates from 0 to 0.61 m/s over a distance of 0.39 m with a mass of 74 kg, is approximately 35.25 Newtons (N).

Explanation:

A person in a kayak accelerates from 0 to 0.61 m/s over a distance of 0.39 meters. To find the magnitude of the net force acting on the kayak, we can use the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. We can calculate this as:

To find the net force, we need to first calculate the change in kinetic energy, which is the kinetic energy at 0.61 m/s minus the initial kinetic energy at 0 m/s:

Since work done is equal to force times distance and to the change in kinetic energy, we can express the net force as:

Therefore, the magnitude of the net force acting on the kayak is approximately 35.25 Newtons (N).

Answer:

[tex]a_c = 1.1 m/s^2[/tex]

Explanation:

As we know that net force on the Satellite due to gravity will provide it centripetal force

so we can say here

[tex]F_g = F_c[/tex]

[tex]\frac{GMm}{r^2} = ma_c[/tex]

now we will have

acceleration given by the equation

[tex]a_c = \frac{GM}{r^2}[/tex]

now we have

r = R + 2R = 3R

[tex]a_c = \frac{GM}{9R^2}[/tex]

also we know that acceleration due to gravity on the surface of earth is given as

[tex]g = \frac{GM}{R^2} = 9.8 m/s^2[/tex]

so the acceleration of satellite is given as

[tex]a_c = \frac{9.8}{9} = 1.1 m/s^2[/tex]

Final answer:

The acceleration of a satellite in orbit at an altitude of twice Earth's radius is best approximated using the formula for gravitational acceleration, g = GME / r². Plugging in the values and simplifying, the acceleration is approximately 2.45 m/s², with option B (2.5 m/s²) being the closest approximation.

Explanation:

Calculating the Acceleration of a Satellite in Orbit

In order to best approximate the acceleration a satellite experiences in orbit at an altitude of twice the Earth's radius, we must apply Newton's law of universal gravitation and the formula for gravitational acceleration, g = GME / r². Given that the satellite weighs 104 N at ground control which reflects the gravitational force at Earth's surface, we use this formula to find its gravitational acceleration in orbit. The relevant equation provided, Fpa = GME2thm/r, appears to be a typo, but our main equation for gravitational acceleration does not require mass, as it cancels out during the calculation:

g = GME / r²

Since we're given that the altitude is twice the Earth's radius, the distance r from Earth's center to the satellite in orbit is 3RE (1RE for Earth's radius and 2RE for the altitude above Earth). Considering this, we can calculate:

g = (6.674 x 10-11 m³/kg s²) (5.972 x 1024 kg) / (3 x 6.371 x 106 m)²

After simplifying, we get an acceleration of approximately 2.45 m/s². Therefore, option B, 2.5 m/s², best approximates the acceleration the satellite experiences in orbit at this altitude.

Answer:

EMF = 187.5 volts

Explanation:

As per Faraday's law of electromagnetic induction we know that rate of change in the flux will induce EMF

so we can say

[tex]EMF = -\frac{d\phi}{dt}[/tex]

[tex]EMF = \frac{\phi_i - \phi_f}{\Delta t}[/tex]

now we will have

[tex]EMF = \frac{NBA - 0}{\Delta t}[/tex]

[tex]EMF = \frac{50(1.5)(0.25)}{0.10}[/tex]

[tex]EMF = 187.5 Volts[/tex]

So the induced EMF in the coil will be 187.5 Volts

The specific heat of the gas is 0.381 J/g°C.

The specific heat of a substance is the amount of heat energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius. To find the specific heat of the gas, we can use the equation:

Q = mass * specific heat * change in temperature

In this case, the mass of the gas is 80.0g, the change in temperature is 225°C - 25°C = 200°C, and the energy absorbed by the gas is 6085J. Plugging these values into the equation, we can solve for the specific heat:

6085J = 80.0g * specific heat * 200°C

Specific heat = 6085J / (80.0g * 200°C) = 0.381 J/g°C

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The specific heat of the given gas can be calculated using the formula c = Q / (m * ΔT). By substitifying Q = 6431J (sum of work done by the system and increase in internal energy), m = 80g (mass of gas), and ΔT = 200°C (change in temperature), we find that the specific heat of the gas is roughly 0.40 J/g°C

The specific heat of a substance is the heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius. For the given gas, we first need to calculate the heat absorbed which is the sum of the work done by the system and the increase in its internal energy, which equals 346J + 6085J = 6431J. The following information is given, mass m = 80.0g and the change in temperature ΔT = 200°C (225 °C - 25°C).

The formula for specific heat is:
Q = m*c*ΔT
where:
Q is the heat energy absorbed (or released),
m is the mass of the substance,
c is the specific heat capacity, and
ΔT is the change in temperature.
Solving this equation for the specific heat (c), we find:
c = Q / (m * ΔT).

So, substituting the given values into this formula, we have:
c = 6431J /  (80.0g * 200°C = 0.40 J/g °C which will be the specific heat of the gas.

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Answer: 2.52 Kilometers

Explanation:

We know that the formula to calculate speed is given by :-

[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}\\\\\Rightarrow\text{Distance}=\text{Speed}\times\text{Time}[/tex]

Given: The speed of sound during the storm : [tex]V=3350.0m/s[/tex]

The time taken by sound to travel : [tex]t= 7.20\text{ seconds}[/tex]

Then , the distance traveled by sound :-

[tex]\text{Distance}=350\times7.2=2520\text{ meters}=2.52\text{ kilometers}[/tex]

To find the distance of a lightning strike heard 7.20 seconds after the flash, multiply the sound's speed (350.0 m/s) by the time delay (7.20 s), resulting in a distance of 2520 meters.

We use the speed of sound. Since sound traveled at 350.0 m/s during the storm, we multiply the time it took to hear the thunder by the speed of sound to calculate the distance:

Distance = Speed of Sound × Time

Substituting in the given values:

Distance = 350.0 m/s × 7.20 s = 2520 meters

Therefore, the lightning struck approximately 2520 meters away.

Explanation:

Impulse is change in momentum:

I = Δp

I = (1400 kg) (27 m/s) - (1400 kg) (0 m/s)

I = 37800 kg m/s

Impulse is also average force times time:

I = F ΔT

37800 kg m/s = F (7 s)

F = 5400 N

Answer:

P = 2234400 Watt

Explanation:

Power generation is given as rate of work done

Here the turbine generator is located at 120 m below the free surface

So here rate of work done is given as rate of potential energy

[tex]Power = \frac{dw}{dt}[/tex]

[tex]Power = \frac{mgh}{t}[/tex]

so we have

[tex]Power = (\frac{dm}{dt})gh[/tex]

now we have

[tex]Power = 1900(9.8)(120) = 2234400 Watt[/tex]

so the power generation potential will be 2234400 Watt

4)none of the above.

A transformer is an electrical device  that allows to increase or decrease from one voltage level to another in an AC circuit while conserving the power.  

It is basically composed of two coils magnetically coupled in a core of ferromagnetic material increasing its permeability and effectiveness.

Answer: None of the above

Explanation:

Explanation:

It is given that,

Initially, the jogger is at rest u₁ = 0

He accelerates from rest to 4.86 m, v₁ = 4.86 m

Time, t₁ = 2.43 s

A car accelerates from u₂ = 20.6 to v₂ = 32.7 m/s in t₂ = 2.43 s

(a) Acceleration of the jogger :

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{4.86\ m/s-0}{2.43\ s}[/tex]

a₁ = 2 m/s²

(b) Acceleration of the car,

[tex]a=\dfrac{v-u}{t}[/tex]

[tex]a=\dfrac{32.7\ m/s-20.6\ m/s}{2.43\ s}[/tex]

a₂ = 4.97 m/s²

(c) Distance covered by the car,

[tex]d_1=u_1t_1+\dfrac{1}{2}a_1t_1^2[/tex]

[tex]d_1=0+\dfrac{1}{2}\times 2\times (2.43)^2[/tex]

d₁ = 5.904 m

Distance covered by the jogger,

[tex]d_2=u_2t_2+\dfrac{1}{2}a_2t_2^2[/tex]

[tex]d_2=20.6\times 2.43+\dfrac{1}{2}\times 4.97\times (2.43)^2[/tex]

d₂ = 64.73 m

The car further travel a distance of, d = 64.73 m - 5.904 m = 58.826 m

Hence, this is the required solution.

The reaction quotient (Q) for the given reaction, calculated using initial concentrations of the reactants and the product, is approximately 0.092. This value suggests the reaction will move forward, producing more NH3 to reach equilibrium.

The reaction quotient, commonly referred to as 'Q', is a value used to determine the direction in which a reaction will proceed. It is calculated similarly to the equilibrium constant but uses the initial concentrations instead. For this reaction, the equation for Q would be [NH3]^2 / ([N2] * [H2]^3) based on the balanced chemical equation.

The initial concentrations given in the question are 0.50 M for N2, 3.00 M for H2, and 1.98 M for NH3. To find Qc, substitute these concentrations into our Q equation to get (1.98)^2 / (0.50 * 3.00^3), which simplifies to approximately 0.092.

If Qc < Kc, the reaction will proceed in the forward direction to reach equilibrium, so in this case, since our Qc (0.092) is less than Kc (0.291), the reaction will produce more NH3 to reach equilibrium.

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Answer:

902 ft

Explanation:

First convert mi/h to ft/s.

53.0 mi/h × (5280 ft / mi) × (1 h / 3600 s) = 77.7 ft/s

Sum of the forces on the car in the y direction:

∑F = ma

N - W = 0

N = mg

Sum of the forces on the car in the x direction:

∑F = ma

-F = ma

-Nμ = ma

Substituting;

-mgμ = ma

-gμ = a

Acceleration is constant, so:

v² = v₀² + 2a(x - x₀)

(0 ft/s)² = (77.7 ft/s)² + 2(-32.2 ft/s² × 0.104)(x - 0)

x = 902 ft

The minimum stopping distance is 902 ft.

Answer: I think it is D

Explanation: It is the only one that does not make sense

Final answer:

The correct answer is 'c) Automated robot' because it is a tool used within the assembly process, not a process itself like handling, fitting, or orientation.

Explanation:

The question is asking which of the provided options is not an example of an assembly process. An assembly process involves the steps required to put together parts to make a complete product. The options given are:

Handling - the act of manipulating components in preparation for assembly.

Fitting - the process of putting parts together, which is certainly part of assembly.

Automated robot - often used in assembly to perform repetitive tasks more efficiently.

Orientation - this typically refers to aligning parts in the correct position for assembly.

Based on these definitions, automated robot is not an example of an assembly process but is rather a tool that might be used in the process. Therefore, the correct answer is 'c) Automated robot'

Answer:

2.76 N

Explanation:

m = mass of the object = 1.5 kg

v₀ = initial velocity at t = 0, = 0 i + 5 j

v = final velocity of the object at t = 5, = 6 i + 12 j

t = time interval = 5 sec

a = acceleration of the object = ?

Acceleration of the object is given as

[tex]a = \frac{v - v_{o}}{t}[/tex]

inserting the values

a = ((6 i + 12 j) - (0 i + 5 j))/5

a = (6 i + 7 j)/5

a = 1.2 i + 1.4 j

magnitude of the acceleration is given as

|a| = √((1.2)² + (1.4)²)

|a| = 1.84 m/s²

magnitude of the resultant force is given as

|F| = m |a|

|F| = (1.5) (1.84)

|F| = 2.76 N

To find the magnitude of the resultant force, we use Newton's second law of motion. Evaluating the acceleration at 2.0s gives a magnitude of 24.8 m/s^2. Using the formula F = ma, the magnitude of the resultant force is 37.2 N.

To find the magnitude of the resultant force acting on the object during the time interval, we need to use Newton's second law of motion, which states that the force is equal to the mass of the object multiplied by its acceleration.

First, we need to find the acceleration of the object. We can use the formula:

a(t) = 5.0i + 2.0tj - 6.0t^2 km/s^2

By evaluating a(2.0 s), we get a magnitude of 24.8 m/s^2.

Now, we can use Newton's second law:

F = ma

Substituting the values, we get:

F = 1.5 kg * 24.8 m/s^2

F = 37.2 N

Therefore, the magnitude of the resultant force acting on the object during this time interval is 37.2 N.

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The x component of velocity after 3.5 seconds is 24.75 m/s, calculated using the equation v = v0 + at with the given initial velocity and constant acceleration.

To calculate the x component of velocity after 3.5 seconds for a particle under constant acceleration, we use the equation:

v = v0 + at

Here v is the final velocity, v0 is the initial velocity, a is the acceleration, and t is the time elapsed. Given v0 = 9 m/s in the x direction, and acceleration a = 4.5 m/[tex]s^2[/tex] in the x direction, and time t = 3.5 s, the calculation is:

v = 9 m/s + (4.5 x (3.5))

The x component of velocity after 3.5 seconds is:

v = 9 m/s + 15.75 m/s

v = 24.75 m/s

Answer:

The distance is 0.86 m.

Explanation:

Given that,

Mass = 39 kg

Initial kinetic energy, [tex]K.E_{i} = 160\ J[/tex]

Final kinetic energy, [tex]K.E_{f} = 490\ J[/tex]

We need to calculate the work done

According to work energy theorem

[tex]W = \Delta K.E[/tex]

[tex]W=K.E_{f}-K.E_{i}[/tex]...(I)

Work done is the product of the force and displacement.

[tex]W = mgh[/tex]....(II)

From equation (I) and (II)

[tex]K.E_{f}-K.E_{i}=mgh[/tex]

[tex]490-160=39\times9.8\times h[/tex]

[tex]h = 0.86\ m[/tex]

Hence, The distance is 0.86 m.

Answer:[tex]5.11(10)^{13}miles[/tex]

Explanation:

A light year is a unit of length and is defined as "the distance a photon would travel in vacuum during a Julian year at the speed of light at an infinite distance from any gravitational field or magnetic field. "

In other words: It is the distance that the light travels in a year.  

This unit is equivalent to [tex]5.879(10)^{12}miles[/tex], which mathematically is expressed as:

[tex]1Ly=5.879(10)^{12}miles[/tex]

Doing the conversion:

[tex]8,7Ly.\frac{5.879(10)^{12}miles}{1Ly}=5.11(10)^{13}miles[/tex]  This is the distance from Earth to Sirius in miles.

Final answer:

The distance from Earth to Sirius is approximately 50 trillion miles.

Explanation:

To calculate the distance from Earth to Sirius in miles, we need to convert the light year measurement to miles. We know that 1 light year is the distance light travels in one year, which we can calculate by multiplying the speed of light by the number of seconds in a year. Here's the step-by-step calculation:

Speed of light = 3.00 × 10^8 m/s

Number of seconds in a year = 365 days * 24 hours * 60 minutes * 60 seconds = 31,536,000 seconds

Distance in meters = speed of light * number of seconds in a year = 3.00 × 10^8 m/s * 31,536,000 seconds

Distance in miles = distance in meters / (5280 ft/mi * 12 in/ft)

Plugging in the values into the equation, we get:

Distance in miles = (3.00 × 10^8 m/s * 31,536,000 seconds) / (5280 ft/mi * 12 in/ft)

Simplifying the equation, the distance from Earth to Sirius is approximately 50 trillion miles.

(a) 95.9 m

The initial velocity of the car is

[tex]u=53.0 km/h = 14.7 m/s[/tex]

The car moves by uniformly accelerated motion, so we can use the SUVAT equation:

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

where

v = 0 is the final velocity

d is the stopping distance of the car

a is the acceleration of the car

The force of friction against the car is

[tex]F_f = - \mu mg[/tex]

where

[tex]\mu=0.115[/tex] is the coefficient of friction

m is the mass of the car

[tex]g = 9.8 m/s^2[/tex] is the acceleration due to gravity

According to Newton's second law, the acceleration is

[tex]a=\frac{F}{m}=\frac{-\mu mg}{m}=-\mu g[/tex]

Substituting into the previous equation:

[tex]v^2 - u^2 = -2\mu g d[/tex]

and solving for d:

[tex]d=\frac{v^2 -u^2}{-2\mu g}=\frac{0-(14.7 m/s)^2}{-2(0.115)(9.8 m/s^2)}=95.9 m[/tex]

(b) 19.1 m

This time, the coefficient of friction is

[tex]\mu = 0.575[/tex]

So the acceleration due to friction is:

[tex]a=-\mu g = -(0.575)(9.8 m/s^2)=-5.64 m/s^2[/tex]

And substituting into the SUVAT equation:

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

we can find the new stopping distance:

[tex]d=\frac{v^2 -u^2}{-2a}=\frac{0-(14.7 m/s)^2}{2(-5.64 m/s^2)}=19.1 m[/tex]

Hello There!

"Periodicity" are types of trends that are seen in element properties.

This is the same thing as periodic trends. These are patterns that are present in the periodic table. These trends show different properties of elements and how characteristics increase or decrease.

Answer:

i believe that it is d

Explanation:

In a super heater, the temperature of the steam rises while the pressure remains constant. This process helps to remove the last traces of moisture from the saturated steam.

In a super heater, the conclusion is that option (C) pressure remains constant and temperature rises is the correct choice. A super heater is a device used in a steam power plant to increase the temperature of the steam, above its saturation temperature. The function of the super heater is to remove the last traces of moisture (1 to 2%) from the saturated steam and to increase its temperature above the saturation temperature. The pressure, however, remains constant during this process because the super heater operates at the same pressure as the boiler.

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Answer:

-6.2 m/s (downward)

Explanation:

The velocity of an object thrown vertically upward is given by:

[tex]v= u + at[/tex]

where:

u is the initial velocity

a = g = -9.8 m/s^2 is the acceleration due to gravity

t is the time

In this problem,

u = 27.1 m/s

t = 3.4 s

So, the velocity after 3.4 s is

[tex]v=27.1 m/s + (-9.8 m/s^2)(3.4 s)=-6.2 m/s[/tex]

and the negative sign means the velocity points downward.

Explanation:

It is given that,

Momentum of an object, p = 23.3 kg-m/s

Kinetic energy, E = 262 J

(a) Momentum is given by, p = mv

23.3 = mv...........(1)

Kinetic energy is given by, [tex]E=\dfrac{1}{2}mv^2[/tex]

m = mass of the object

v = speed of the object

[tex]E=\dfrac{1}{2}\times (mv)\times v[/tex]

[tex]262=\dfrac{1}{2}\times 23.3\times v[/tex]

v = 22.48 m/s

(2) Momentum, p = mv

[tex]m=\dfrac{p}{v}[/tex]

[tex]m=\dfrac{23.3\ kg-m/s}{22.48\ m/s}[/tex]

m = 1.03 Kg

Hence, this is the required solution.

An object with momentum 23.3 kg.m/s and kinetic energy of 262J is traveling at a speed of approximately 30.21 m/s and its mass is approximately 0.771 kg based on the physics principles of kinetic energy and momentum.

The question involves the physics concepts of momentum and kinetic energy. We are given the momentum (p) of 23.3 kg.m/s and the kinetic energy (KE) of 262 J of an object.

(a) The formula for kinetic energy is KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity. We can rearrange to find v = sqrt((2*KE) / m). The mass can be obtained from the momentum formula, p = m * v, hence m = p / v. Substituting the second equation into the first gives v = sqrt((2 * KE * v) / p), which simplifies to v = sqrt((2 * 262 J) / 23.3 kg.m/s) = 30.21 m/s.

(b) With the velocity calculated in (a), the mass of the object can now be found by rearranging the momentum formula to m = p / v = 23.3 kg.m/s / 30.21 m/s = 0.771 kg.

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Answer:

3 half life of the unknown radioactive substance have occurred.

Explanation:

Mass of sample = 320.9 ng

Mass after 1 half life = 0.5 x 320.9 = 160.45 ng

Mass after 2 half life = 0.5 x 160.45 = 80.225 ng

Mass after 3 half life = 0.5 x 80.225 =40.11 ng

So 3 half life of the unknown radioactive substance have occurred.

The unknown radioactive substance went through approximately 3 half-lives in the 47 days period.

The subject of your question is related to radioactive decay, particularly the concept of a half-life, which is a term in physics used to describe the time it takes for half the atoms in a sample to decay. In your case, the initial mass of your substance was 320.9 ng and it decreased to 40.11 ng after 47 days. To figure out how many half-lives have occurred, we need to understand that with each half-life, the quantity of the substance halve its original mass.

A useful method to answer your question is to divide the final amount by the starting amount and then take the logarithm base 2 of the result. This will give us the number of times the amount halved, which is the number of half-lives. In your case, the calculation is like this: number of half lives = log2(320.9 ng / 40.11 ng) = approx. 3 half-lives.

This means that in 47 days, approximately 3 half‑lives of the unknown radioactive substance have occurred, based on the given data. It's important to note that because this is an approximate result, the true half-life of the substance might be slightly smaller or larger.

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(a) -0.211 m

At the beginning the mass is displaced such that the length of the pendulum is L = 36.1 cm and the angle with the vertical is

[tex]\theta=65.4^{\circ}[/tex]

The projection of the length of the pendulum along the vertical direction is

[tex]L_y = L cos \theta = (36.1 cm)(cos 65.4^{\circ})=15.0 cm[/tex]

the full length of the pendulum when the mass is at the lowest position is

L = 36.1 cm

So the y-displacement of the mass is

[tex]\Delta y = 15.0 cm - 36.1 cm = -21.1 cm = -0.211 m[/tex]

(b) 0.347 J

The work done by gravity is equal to the decrease in gravitational potential energy of the mass, which is equal to

[tex]\Delta U = mg \Delta y[/tex]

where we have

m = 168 g = 0.168 kg is the mass of the pendulum

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

[tex]\Delta y = 0.211 m[/tex] is the vertical displacement of the pendulum

So, the work done by gravity is

[tex]W=(0.168 kg)(9.8 m/s^2)(0.211 m)=0.347 J[/tex]

And the sign is positive, since the force of gravity (downward) is in the same direction as the vertical displacement of the mass.

(c) Zero

The work done by a force is:

[tex]W=Fd cos \theta[/tex]

where

F is the magnitude of the force

d is the displacement

[tex]\theta[/tex] is the angle between the direction of the force and the displacement

In this situation, the tension in the string always points in a radial direction (towards the pivot of the pendulum), while the displacement of the mass is tangential (it follows a circular trajectory): this means that the tension and the displacement are always perpendicular to each other, so in the formula

[tex]\theta=90^{\circ}, cos \theta = 0[/tex]

and so the work done is zero.

The pendulum falls 0.212 m, the work done by gravity is 0.349 J, and the work done by string tension is 0 J.

The first part of the question asks for the vertical displacement (y-displacement) of the pendulum. The length of the pendulum is the hypotenuse of a right triangle, and the vertical displacement is the adjacent side, so we can use the cosine function to solve: y = L*cos(θ). Plugging in the given values: y = 0.361 m * cos(65.4 degrees) = 0.149 m. So the fall is the length of the pendulum minus this displacement: 0.361 m - 0.149 m = 0.212 m.

The second part of the question asks for the work done by gravity. The work done by gravity is equal to the weight of the pendulum times the vertical distance it falls (Work = m*g*y), or 0.168 kg * 9.8 m/s² * 0.212 m = 0.349 J.

The final part of the question asks for the work done by string tension. The tension force always acts perpendicular to the direction of displacement, meaning it does no work on the pendulum, as work is defined as force times the displacement in the direction of the force. Therefore, the work done by the tension in the string is 0 J.

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The magnetic field direction, when current moves in a circular loop in a counterclockwise sense, points straight up. The right-hand rule is used to determine the orientation of the magnetic field.

When current moves in a circular path, it generates a magnetic field. Using the right-hand rule, where your thumb points to the direction of the current and your fingers curl in the direction of the magnetic field, it can be determined that when looking from above, if the current moves in a counterclockwise sense, the magnetic field direction will be pointing straight up from the loop. Hence, the correct answer is B) points straight up.

This rule, also referred to as RHR-2 (Right Hand Rule-2), is widely applied to illustrate the magnetic fields induced around current carrying conductors. The net force on a current-carrying loop of any plane shape in a uniform magnetic field is zero, but it induces a distinctive orientation of the magnetic field in its surroundings.

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The correct answer is B) points straight up. Using the right-hand rule for a counterclockwise current in a circular loop, the magnetic field inside the loop points straight up.

To determine the direction of the magnetic field inside a current-carrying circular loop, we use the right-hand rule. In this case, the current moves counterclockwise when viewed from above, so follow these steps:

Point your right thumb in the direction of the current.

Notice how your fingers curl in the direction of the magnetic field.

Since the current flows counterclockwise, the right-hand rule shows that the magnetic field lines point straight up inside the loop. Therefore, the correct answer is B) points straight up.

Answer:

The time is 5.21 s.

Explanation:

Given that,

Force F = 646 N

Mass m = 82 kg

Velocity v = 41 m/s

We need to calculate the acceleration

Using formula of force

F= ma

[tex]a = \dfrac{F}{m}[/tex]

[tex]a = \dfrac{646}{82}[/tex]

[tex]a =7.87\ m/s^2[/tex]

We need to calculate the time

Now, using equation of motion

[tex]v = u+at[/tex]

[tex]41=0+7.87 t[/tex]

[tex]t = \dfrac{41}{7.87}[/tex]

[tex]t = 5.21\ s[/tex]

Hence, The time is 5.21 s.