Three ropes A, B and C are tied together in one single knot K. (See figure.)
If the tension in rope A is 65.3 N, then what is the tension in rope B?

Answer:

(a) The rms voltage across the resistor is given by V = (2.20 102 V) sin 2ft.

V = (2.20 102 V) sin 2ft

V = (2.20 102 V) (0.707)

V = 1.56 102 V

(b) The rms current flowing through the resistor is given by I = V/R.

I = V/R

I = (1.56 102 V)/(1.90 102 Ω)

I = 8.21 A

Review procedures and confirm results to avoid possible errors.

Explanation:

The gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.

Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.

Given data

Mass of object 1,m = 80 kg

Mass of object 2,M = 50 kg

Gravitational constant,G = 6.6 × 10⁻¹¹ kg⁻² m²

Distance of seperation,R = 0.2 m

The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.

[tex]\rm F = G\frac{mM}{R^ 2} \\\\ F = 6.6 \times 10^{-11 }\times \frac{80 \times 50 }{(0.2)^2} \\\\F = 6.6 \times 10^{-6 } \ N[/tex]

Hence the gravitational attraction between them will be 6.6 × 10 ⁻⁶ N.

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The cost of gas is $1.27 per liter and the gallon of gas costs $4.80. where 1 gallon is equal to 3.78541 liters.

To convert the cost of gas from dollars per liter to dollars per gallon, The conversion factor between liters and gallons.

1 gallon is equal to 3.78541 liters (the exact conversion factor is 3.785411784).

Given the cost of gas is $1.27 per liter, let's calculate the cost per gallon:

Cost per gallon = Cost per liter × Liters per gallon

Cost per gallon = $1.27 × 3.78541

Cost per gallon = $4.80

So, a gallon of gas costs $4.80.

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Hi there!

1.

Let's use the rotational equivalent of Newton's Second Law.

[tex]\Sigma \tau = I\alpha[/tex]

τ = Torque (Nm)

I = Moment of Inertia (1/2mR² for solid cylinder)

α = Angular acceleration (rad/sec²)

The torque is equivalent to:
[tex]\tau = r \times F[/tex]

r = distance from lever arm to pivot point, aka the radius for this cylinder (0.111 m)
F = applied force (7.161 N)

We are already given various values, so let's create a working equation and solve.

[tex]rF = I\alpha \\\\\alpha = \frac{rF}{I}[/tex]
[tex]\alpha = \frac{(0.111)(7.161)}{\frac{1}{2}(2.15)(0.111^2)} = \boxed{60.013 \frac{rad}{sec^2}}[/tex]

2.

So, let's begin by doing a summation of forces acting on the block.

We have its force of gravity downward(+), and the tension from the string upward. (-), assigning signs based on the path of the falling block.

[tex]\Sigma F = F_g - T\\\\\Sigma F = m_b g - T\\\\m_b a = m_b g - T[/tex]

Solving for 'T':

[tex]T = m_b g - m_b a[/tex]

Let's now do a summation of torques on the cylinder. We only have the torque caused by the tension in the string connected to the block.

[tex]\Sigma \tau = rT\\\\I\alpha = r(T = m_b g - m_b a)[/tex]

Using the relationship between angular and translational acceleration:

[tex]a = \alpha r\\\\alpha = \frac{a}{r}[/tex]

And the equation for the moment of inertia:
[tex]I = \frac{1}{2}Mr^2[/tex]

Simplify the expression.

[tex]\frac{1}{2}Mr^2(\frac{a}{r}) = r( m_b g - m_b a)\\\\\frac{1}{2}Ma = ( m_b g - m_b a)[/tex]

Solve for 'a':
[tex]\frac{1}{2}ma + m_b a= m_b g \\\\a = \frac{m_b g}{\frac{1}{2}M + m_b} = \frac{0.730(9.81)}{\frac{1}{2}(2.15) + 0.730} = \boxed{3.97 \frac{m}{s^2}}[/tex]

3.

This is just a case of kinematics since we have a constant acceleration. To solve for this instance, however, let's use calculus.

We know that:
[tex]a(t) = 3.97[/tex]

v(t) is the integral. There is no initial velocity (block starts from rest), so:
[tex]v(t) = 3.97t + C\\C = 0 m/s \\\\v(t) = 3.97t[/tex]

Now, we can take the integral of the velocity/time equation to find the displacement between the interval.

[tex]\int\limits^{0.590}_{0.390} {3.97t} \, dt = \boxed{0.389 m}[/tex]

4.

So, let's now find the translational acceleration produced by the new cylinder. Use the kinematic equation:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]

Since the block starts from rest, we can do some simplifying and rearranging:
[tex]2\Delta x = at^2\\\\a = \frac{2\Delta x}{t^2} = \frac{2(0.450)}{0.490^2} = 3.748 \frac{m}{s}^2[/tex]

So, let's go back to our summation of torques equation. This time, however, we cannot simplify 'I'.

[tex]I(\frac{a}{r}) = r( m_b g - m_b a)[/tex]

Solving for 'I':
[tex]I = \frac{r^2( m_b g - m_b a)}{a} = \frac{(0.111^2)(7.161 - .730(3.748))}{3.748}\\\\ = \boxed{0.0145 kgm^2}[/tex]

Answer:

Fruit Punch

Explanation:

A pure substance is whereby there is only one type of element or a compound in the periodic table in the substance.

Carbon: Well its just C in the periodic table, so this is definitely pure.

Water Molecule: What makes water? H2O right? Contains Hydrogen and Oxygen, and as we all know H2O is a compound, therefore this is a pure substance.

Fruit Punch: What makes fruit punch, water and fruits. Fruits may contain citric acid(a compound itself), and is mixed with water with already has a compound, so having 2 different compounds will result in a mixture and therefore it will not be pure.

The density of the mixture is determined as 1,013.75 kg/m³.

The density of the mixture is calculated as follows;

density = total mass of the mixture / total volume of the mixture

mass of the fresh water = density x volume

                                        = 1000 kg/m³ x 0.0018 m³

                                        = 1.8 kg

mass of the sea water = 1025 kg/m³ x 0.0022 m³

                                     = 2.255 kg

Total mass = 1.8 kg + 2.255 kg = 4.055 kg

Total volume = 0.0018 m³  + 0.0022 m³ = 0.004 m³

Density = 4.055 kg/0.004 m³ = 1,013.75 kg/m³

Thus, the density of the mixture is determined as 1,013.75 kg/m³.

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Answer:

Approximately [tex](-4.9\times 10^{2}\; {\rm N})[/tex] (rounded to two significant figures.)

Explanation:

The impulse [tex]\mathbf{J}[/tex] on an object is equal to the change in the momentum [tex]\mathbf{p}[/tex] of this object. Dividing impulse by duration [tex]\Delta t[/tex] of the contact would give the average external force that was exerted on this object.

If an object of mass [tex]m[/tex] is moving at a velocity of [tex]\mathbf{v}[/tex], the momentum of that object would be [tex]\mathbf{p} = m\, \mathbf{v}[/tex].

Let [tex]m[/tex] denote the speed of this ball. Let [tex]\mathbf{v}_{0}[/tex] denote the velocity of this ball before the contact, and let [tex]\mathbf{v}_{1}[/tex] denote the velocity of the ball after the contact.

Momentum [tex]\mathbf{p}_{0}[/tex] of this ball before the contact: [tex]\mathbf{p}_{0} = m\, \mathbf{v}_{0}[/tex].

Momentum [tex]\mathbf{p}_{1}[/tex] of this ball after the contact: [tex]\mathbf{p}_{1} = m\, \mathbf{v}_{1}[/tex].

Impulse, which is equal to the change in momentum:

[tex]\mathbf{J} = \mathbf{p}_{1} - \mathbf{p}_{0} = m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}[/tex].

Since the velocity of the ball after the contact is in the [tex](-x)[/tex] direction, [tex]\mathbf{v}_{1} = -20.0\; {\rm m\cdot s^{-1}}[/tex]. The average external force on this ball would be:

[tex]\begin{aligned} \mathbf{F} &= \frac{\mathbf{J}}{\Delta t} \\ &= \frac{m\, \mathbf{v}_{1} - m\, \mathbf{v}_{0}}{\Delta t} \\ &= \frac{m\, (\mathbf{v}_{1} - \mathbf{v}_{0})}{\Delta t} \\ &= \frac{0.145\; {\rm kg} \times ((-20.0\; {\rm m\cdot s^{-1}}) - 14\; {\rm m\cdot s^{-1}})}{0.010\; {\rm s}} \\ &\approx -4.9 \times 10^{2}\; {\rm N}\end{aligned}[/tex].

(Rounded to two significant figures.)

Due to density, the two bats have the same size, shape, and mass.

The two bats could be the same size, shape, and mass if they have the same density because density is directly proportional to mass so if the density same, the mass will also be the same.

So we can conclude that due to density, the two bats have the same size, shape, and mass.

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Answer:

See below

Explanation:

speed = freq * wavelength

          =  5 Hz    * .6 m = 3 m/s

speed = freq * wavelength

   3      =   freq  *  .4 m         freq = 7.5 hz

1. The speed of the waves is 3 m/s. 2. for a wavelength of 0.4 m, the frequency would be 7.5 Hz.

To find the speed of the waves, we can use the equation:

[tex]\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \][/tex]

Given that the frequency is 5 Hz and the distance between successive crests (wavelength) is 60 cm, we need to convert the wavelength to meters:

[tex]\[ \text{Wavelength} = 60 \, \text{cm} = 0.6 \, \text{m} \][/tex]

Plugging in the values, we have:

[tex]\[ \text{Speed} = 5 \, \text{Hz} \times 0.6 \, \text{m} = 3 \, \text{m/s} \][/tex]

Therefore, the speed of the waves is 3 m/s.

Now, to find the frequency at which the wavelength is 0.4 m, we rearrange the equation:

[tex]\[ \text{Frequency} = \frac{\text{Speed}}{\text{Wavelength}} \][/tex]

Substituting the given values:

[tex]\[ \text{Frequency} = \frac{3 \, \text{m/s}}{0.4 \, \text{m}} = 7.5 \, \text{Hz} \][/tex]

Thus, for a wavelength of 0.4 m, the frequency would be 7.5 Hz.

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The design that would be used to make an efficient commercial vehicle chassis that has many realistic truck components is:

This refers to the main vehicle structure of a car that bears all the main stress that other components are attached to.

Hence, we can see that to make a good design for an efficient commercial vehicle chassis that has many realistic truck components, we would have to consider various factors such as handling maximum stress, maximum equilateral stress, and deflection.

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The magnitude is 13.12 mV.

The steps are attached below.

The standard SI unit of the magnetic field is the tesla (T). As an end result, we can use these equations and the equation for an induced emf due to changes in magnetic flux, ϵ=−NΔϕΔt ϵ = − N Δ ϕ Δ t, to calculate the importance of a precipitated emf in a solenoid.

The magnitude of the precipitated contemporary depends on the rate of trade of magnetic flux or the fee of reducing the magnetic area strains.

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Answer:

5 m /s^2

Explanation:

Change in velocity = 35 - 10 = 25 m/s

change in time = 5 s

decelleration = 25/5 = 5 m/s^2

Answer:

A. the center of mass

Explanation:

[tex]C_m[/tex] is usually used to designate the center of mass of an object or system of objects.

B. is incorrect because the combined mass of a system is usually denoted by ∑m.

C. is incorrect because the momentum of a system is denoted by the letter p.

The net force on the canoe is obtained as 65.0 N [forward]

The frictional force is the force that opposes motion. We know that the net force is the actual force that moves the canoe in a given direction.

Hence, the total force acting in the forward direction = 60.0N + 90.0N = 150 N and the total backwards force =  85.0N

Net force =  150 N - 85.0N = 65.0 N [forward]

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B. The meaning of 'atomos' according to Democritus in 450 BCE is indivisible.

A Greek philosopher  known as Democritus first thought of the existence of tiny particles that compose everything around us.

Democritus of Abdera, named the building blocks of matter atomos, meaning literally “indivisible.

Thus, the meaning of 'atomos' according to Democritus in 450 BCE is indivisible.

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The depth of the well at the given air temperature is 456.3 m.

The depth of the well is calculated from the principle of echo.

v = 2d/t

2d =  vt

d = vt/2

where;

d = (338 x 2.7)/2

d = 456.3 m

Thus, the depth of the well at the given air temperature is 456.3 m.

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The distance car moves with an average speed of 75 km/hr from town P to town Q in 2 hours is 149,760 m.

Given:
Speed = 75 km/hr

Time = 2 hr

The distance can be calculated from the product of velocity and time.

The standard unit of distance is a meter.

Convert speed and time into meters per second and seconds:

v = 75×5/18

v = 20.8 m/s

t = 3600×2

t = 7200 s

The distance is computed as:

v = d/t

d = vt

d = 20.8×7200

d = 149,760 m

Hence, the distance car moves with an average speed of 75 km/hr from town P to town Q in 2 hours is 149,760 m.

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The angular frequency of the oscillation is determined as 2.7 rad/s.

ω = √k/m

With respect to spring constant k1 and k2

k1 + k2 = 9.5 N/m + 5 N/m = 14.5 N/m

ω = √14.5/2 = 2.7 rad/s

Thus, the angular frequency of the oscillation is determined as 2.7 rad/s.

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c. Sodium and potassium

Perspiration, water given off by the intact skin, either as vapor by simple evaporation from the epidermis or as sweat, a form of cooling in which liquid actively secreted from sweat glands evaporates from the body surface.

When our body is sweating sodium and potassium is lost from the body along with water.

In order to maintain the integrity of the cells in the body ,Sodium and potassium are very important.

Sweat is also known as perspiration.

So,

By maintaining  the proper cell functioning and cell vitality optimum level of sodium and potassium should be maintained in the body.

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The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other.

We know that graphite is composed of layers. These hexagonal layers are held together by weak Van Der Walls forces and as such are able to slide over each other. The carbon atom in each layer are held together by strong covalent bonds.

The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other and as such make the graphite fluid.

Thus, the image that shows these layers of graphite is attached to this an answer

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Answer:it’s B

Explanation:

The answers are as follows;

a) the inductive reactance is 322 ohm

b) The maximum voltage is 387.5 V

c) The rms and maximum currents in the inductor are 1.2 A and 0.85 A.

The reactance is obtained from;

XL = 2πfL

XL = 2 * 3.14 * 57.0 * 0.900

XL = 322 ohm

The maximum voltage is obtained as;

Vo = Vrms * √2

Vo =  274 V * √2

Vo = 387.5 V

Io = Vo/XL

Io =  387.5 V/ 322 ohm

Io = 1.2 A

Irms = 274 V/322 ohm

Irms = 0.85 A

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The acceleration is  1.55 m/s^2 while is component that is parallel to the ground is 0.775  m/s^2.

The term acceleration is the rate of change of speed. Given that the distance covered is 35.0 m and the final velocity is 10.43 m/s it the follows that;

v^2 = u^2 + 2as

u = 0 because he started from rest

v^2 = 2as

a = v^2/2s

a = (10.43 m/s)^2/2 * 35.0 m

a = 1.55 m/s^2

The component of this acceleration which is parallel to the ground is;

ax = a sin θ

ax =  1.55 m/s^2 cos 60

ax = 0.775  m/s^2

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The Sketch  of the figure will bear the parameters of the charge that lies   at (4,0,0)

Generally, the equation for is  mathematically given as

1)

Since both of the other points, "q1"<"q2," are on the x-axis, the third one must also be on the x-axis, and it must be close to the charge of lesser magnitude. off q1 by x cm

Now, forces on q3 due to q1

[tex]\vec{F}_{1}=\frac{k q_{1} q_{3}}{x^{2}} \hat{x}[/tex]

Force on q3 due to q2

[tex]\vec{F}_{2}=\frac{k q_{2} q_{3}}{(6+x)^{2}}(-\hat{x})[/tex]

[tex]\quad \vec{F}_{1}+\vec{G}_{2}=0$[/tex]

[tex]&\frac{k q_{1} q_{3}}{x^{2}}-\frac{k q_{2} q_{3}}{(x+6)^{2}}=0 \\&\frac{2}{x^{2}}=\frac{8}{(x+6)^{2}} \Rightarrow \frac{x+6}{x}=\sqrt{\frac{8}{2}}=2 \\&x+6=2 x \Rightarrow x=6 \mathrm{~cm}[/tex]

In conclusion, the charge lies at (4,0,0)

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The length of the filament is 0.2 m.

To find the answer, we need to know about the Stefan - Boltzmann law.

L= power/(π×d×e×σ×T⁴)

= 40/(π×0.0001×0.35×5.67×10^(-8)×2500⁴)

= 0.2m

Thus, we can conclude that the length of the filament is 0.2 m.

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For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive

Kinetic energy can be defined as the ability assumed by an object in motion.

Kinetic energy is also said to be a form of mechanical energy that is possessed by an object to be in motion.

In conclusion, For a ball that starts rolling down a ramp the value of the change in its kinetic energy, ΔEk is: Positive

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The force constant of the spring is determined as 14,222.2 N/m.

Apply the principle of conservation of energy,

K.E = U

where;

¹/₂mv² = ¹/₂kx²

mv² = kx²

k = mv²/x²

Where;

k = (2000 x 8²)/(3²)

k = 14,222.2 N/m

Thus, the force constant of the spring is determined as 14,222.2 N/m.

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Answer:

Given,

Frame rate = 25 frames per second

To find,

Time interval between one frame and the next.

Solution,

We can simply solve this numerical problem by using the following process.

Now,

Number of frames = 25

Total time taken to display the given number of frames (ie. 25 frames) = 1 second

To calculate the time interval between one frame and next, we need to divide the time taken to display total number of frames by total number of frames.

So,

Time interval between one frame and next :

= Time taken to display total number of frames / Total frames

= 1/25

= 0.04 second

Hence, time interval between one frame and next is 0.04 second.

Answer:

35000 KJ

Explanation:

The equation for the kinetic energy is given by the formula :

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

[tex]E_{k} = \frac{1}{2} (700)(10)^{2}[/tex]

[tex]E_{k} = \frac{1}{2} (700)(100)[/tex]

[tex]E_{k} = (350)(100)[/tex]  OR [tex]E_{k} = \frac{1}{2} (70000)[/tex]

[tex]E_{k} = 35000[/tex]

Units will be kilojoules since the units of mass was kilograms .

Our final answer is 35000 KJ

Hope this helped and have a good day

(a)The acceleration of the ball, while it is in flight, will be 9.81 m/s².

(b) The velocity of the ball when it reaches its maximum height will be 0 m/sec.

(c) The initial velocity of the ball is 20.30 m/s upward.

(d) The maximum height it reaches will be 21.00 m

The change of displacement with respect to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.

The given data in the problem is;

u is the initial velocity of fall = ? m/sec

h is the distance of fall = ? m

g is the acceleration of free fall = 9.81 m/sec²

a.

The acceleration of the ball, while it is in flight, is equal to the acceleration due to gravity,g=9.81 m/s².

b.

The ball's velocity will be zero when it has reached its highest point.

c.

The initial velocity of the ball is;

v=u-gt

0=u-gt

u=gt

u=9.81 m/s² × 2.07 sec

u=20.30 m/s

d.

The maximum height it reaches is found by the formula as;

[tex]\rm u^2 = - 2gh \\\\ (20.30)^2 = -2 \times (-9.8) \times h \\\\ 412.09 = 19.6 \times h\\\\ h = 412.09/19.6\\\\ h = 21.00 m[/tex]

Hence the acceleration of the ball,s the velocity of the ball when it reaches its maximum height, the initial velocity of the ball, and the maximum height it reaches will be 9.81 m/s²,0 m/sec,20.30 m/s, and 21.00 m respectively.

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It reasonable to expect that anyone would be able to make good sense of a filing system as it reduces the overall storage space occupied by the records.

This is the process of keeping document safely and being able to easily retrieve them.

The new filing system is based on their volume which is why the space is reduced thereby reducing the ambiguity.

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