Gibbons, small Asian apes, move by brachiation, swinging below a handhold to move forward to the next handhold. A 9.0 kg gibbon has an arm length (hand to shoulder) of 0.60 m. We can model its motion as that of a point mass swinging at the end of a 0.60-m-long, massless rod. At the lowest point of its swing, the gibbon is moving at 3.2 m/s .

What upward force must a branch provide to support the swinging gibbon?

Express your answer to two significant figures and include the appropriate units.

(Textbook is College Physics by:Knight, Jones, and Field.)

Answer:

0.032 m

Explanation:

Consider the forces acting on the block

m = mass of the block = 1.50 kg

[tex]f_{s}[/tex] = Static frictional force

[tex]F_{n}[/tex] = Normal force on the block from the wall

[tex]F_{s}[/tex] = Spring force due to compression of spring

[tex]F_{g}[/tex] = Force of gravity on the block = mg = 1.50 x 9.8 = 14.7 N

k = spring constant = 860 N/m

μ = Coefficient of static friction between the block and wall = 0.54

x = compression of the spring

Spring force is given as

[tex]F_{s}[/tex] = kx

From the force diagram of the block, Using equilibrium of force along the horizontal direction, we get the force equation as  

[tex]F_{n}[/tex] = [tex]F_{s}[/tex]

[tex]F_{n}[/tex] = kx                                             eq-1

Static frictional force is given as

[tex]f_{s}[/tex] = μ [tex]F_{n}[/tex]

Using eq-1

[tex]f_{s}[/tex] = μ k x                                                eq-2

From the force diagram of the block, Using equilibrium of force along the vertical direction, we get the force equation as

[tex]f_{s}[/tex] = [tex]F_{g}[/tex]

Using eq-2

μ k x = 14.7

(0.54) (860) x = 14.7

x = 0.032 m

Answer:

Distance=538.51m

Explanation:

The echo is heard after covering double distance .

Therefore 2d=(t1+t2)×speed.

2d={(1.76+1.38)×343}

2d=743.02

d=1077.02÷2

=538.51m

Answer:

The speed of meteoroid is 21.61 km/s in south-east.

Explanation:

Given that,

A meteoroid is traveling through the atmosphere at 18.3 km/s. while descending at a rate of 11.5 km/s it means 11.5 km/s in south.

We need to draw a diagram

Using Pythagorean theorem

[tex]AC^2=AB^2+BC^2[/tex]

[tex]AC^2=(18.3)^3+(11.5)^2[/tex]

[tex]AC=\sqrt{(18.3)^2+(11.5)^2}[/tex]

[tex]AC=21.61\ km/s[/tex]

Hence, The speed of meteoroid is 21.61 km/s in south-east.

The speed of the meteoroid is calculated using the Pythagorean theorem and is approximately 21.62 km/s.

To calculate the speed (magnitude of the velocity), the equation is: speed = √(horizontal velocity)² + (vertical velocity)².

Thus, the speed = √(18.3 km/s)² + (11.5 km/s)² = √(335.29 + 132.25) km²/s² = √467.54 km²/s² = 21.62 km/s.

The meteoroid's speed through the atmosphere is approximately 21.62 km/s.

Answer:

a= 2 m/s^2

Explanation:

take to the right as positive

let Ftot be the total forces acting on the box , m be the mass of the box and a be the acceleration of the box.

Ftot = 10 - 2 = 8 N

and,

Ftot = ma

   a = Ftot/m

      = 8/4

      = 2 m/s^2

therefore, the acceleration of the box is of magnitude of 2 m/s^2.

Answer:

option (b)

Explanation:

Th weight of the body is equal to the product of mass of the body and acceleration due to gravity. So, it depends on the acceleration due to gravity.

Inertia is the inherent property of the body which always resists any change in the body. It does not depend on any factor. mass is the measure of inertia.

Momentum is the product of mass of body and the velocity of the body.

Force is the product of mass and the acceleration of the body.

Answer:

Length of pendulum, l = 1.74 meters

Explanation:

The time period of simple pendulum is, [tex]T=2\pi\sqrt{\dfrac{l}{g}}[/tex]

Where

l is the length of simple pendulum

The time period of  uniform thin rod is hung vertically from one end is, [tex]T=2\pi\sqrt{\dfrac{2l'}{3g}}[/tex]

l' is the length of uniform rod, l' = 2.6 m

It is given that the rod and pendulum have same time period. So,

[tex]2\pi\sqrt{\dfrac{l}{g}}=2\pi\sqrt{\dfrac{2l'}{3g}}[/tex]

After solving above expression, the value of length of the pendulum is, l = 1.74 meters. Hence, this is the required solution.

The meteorite's speed just before striking the sand is approximately 3836.82 m/s, calculated using conservation of energy principles from its initial potential energy at 750 km above Earth.

Let's break down the solution step by step:

Step 1: Calculate the initial potential energy of the meteorite when it is 750 km above the Earth's surface.

[tex]\[PE_{initial} = mgh\][/tex]

Where:

- [tex]\(m\)[/tex] is the mass of the meteorite,

- [tex]\(g\)[/tex] is the acceleration due to gravity, and

- [tex]\(h\)[/tex] is the height above the Earth's surface.

Given:

- [tex]\(h = 750 \, \text{km} = 750 \times 10^3 \, \text{m}\)[/tex] (converted to meters)

- [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex] (acceleration due to gravity)

[tex]\[PE_{initial} = mg \times h\][/tex]

[tex]\[PE_{initial} = (m)(9.8 \, \text{m/s}^2)(750 \times 10^3 \, \text{m})\][/tex]

Step 2: Calculate the final kinetic energy of the meteorite just before it strikes the sand.

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

Where:

- [tex]\(v\)[/tex] is the final velocity of the meteorite just before it strikes the sand.

Given:

- [tex]\(d = 3.35 \, \text{m}\)[/tex] (distance traveled while coming to rest)

Step 3: Apply the principle of conservation of energy.

Since energy is conserved, the initial potential energy of the meteorite is converted into kinetic energy just before it strikes the sand.

[tex]\[PE_{initial} = KE_{final}\][/tex]

[tex]\[mg \times h = \frac{1}{2}mv^2\][/tex]

[tex]\[9.8 \times 750 \times 10^3 = \frac{1}{2} \times v^2\][/tex]

[tex]\[v^2 = \frac{2 \times 9.8 \times 750 \times 10^3}{1}\][/tex]

[tex]\[v^2 = 2 \times 9.8 \times 750 \times 10^3\][/tex]

[tex]\[v^2 = 2 \times 7.35 \times 10^6\][/tex]

[tex]\[v^2 = 14.7 \times 10^6\][/tex]

[tex]\[v^2 = 1.47 \times 10^7\][/tex]

[tex]\[v = \sqrt{1.47 \times 10^7}\][/tex]

[tex]\[v \approx 3836.82 \, \text{m/s}\][/tex]

So, the speed of the meteorite just before striking the sand is approximately [tex]\(3836.82 \, \text{m/s}\)[/tex].

Answer:

Here, for parallel resisitors

Option D) all of the other choices are are true

is correct.

Explanation:

In parallel connection:

1) Voltage across each element connected in parallel remain same.

2) Kirchhoff's Current Law (KCL), sum of the current entering and leaving the junction will be zero

3) The equivalent resistance of the elements connected in parallel is always less than the individual resistance of any resistor in the circuit.

The equivalent resistance in a parallel circuit is given by:

[tex]\frac{1}{R_{eq}} = \frac{1}{R_1} +\frac{1}{R_2} +......+ \frac{1}{R_n}[/tex]

Final answer:

When resistors are connected in parallel, the voltage across each resistor is the same, the total current flowing from the battery equals the sum of the currents flowing through each resistor, and the equivalent resistance of the combination is less than the resistance of any one of the resistors.

Explanation:

When two or more resistors are connected in parallel to a battery:

The voltage across each resistor is the same. This is because in a parallel circuit, all the resistors have the same potential difference across them.

The total current flowing from the battery equals the sum of the currents flowing through each resistor. In a parallel circuit, the total current is divided among the different resistors.

The equivalent resistance of the combination is less than the resistance of any one of the resistors. This is because adding resistors in parallel decreases the overall resistance of the circuit.

Answer:

0.0667 m

Explanation:

λ = wavelength of light = 400 nm = 400 x 10⁻⁹ m

D = screen distance = 2.5 m

d = slit width = 15 x 10⁻⁶ m

n = order = 1

θ = angle = ?

Using the equation

d Sinθ = n λ

(15 x 10⁻⁶) Sinθ = (1) (400 x 10⁻⁹)

Sinθ = 26.67 x 10⁻³

y = position of first minimum

Using the equation for small angles

tanθ = Sinθ = y/D

26.67 x 10⁻³ = y/2.5

y = 0.0667 m

The first minimum in a single-slit diffraction pattern of light with a wavelength of 400 nm incident on a single slit of width 15 microns, 2.5 m from the screen, is approximately 66.67 mm from the central maximum.

The question asks for the distance of the first minimum from the central maximum in a single-slit diffraction pattern.

The distance to the first minimum from the central maximum in a single-slit diffraction pattern is calculated using the formula: [tex]y = \frac{\lambda X D}{d}[/tex]

where y - is the distance from the central maximum to the first minimum on the screen (meters), λ (lambda) - is the wavelength of light (meters), D - is the distance between the slit and the screen (meters), and d - the width of the slit (meters)

Given λ (lambda) = 400 nm = [tex]400 X 10^{-9} m[/tex], D = 2.5 m, d = 15 microns = [tex]15 X 10^{-6} m[/tex]

Calculation:

[tex]y = \frac{(400 X 10^{-9} m) X (2.5 m)}{(15 X 10^{-6} m)}\\y = 0.0667 \ meters (or 66.7 \ millimeters)[/tex]

The first minimum is 66.7 millimeters from the central maximum.

Answer:

f = 632 Hz

Explanation:

As we know that for destructive interference the path difference from two loud speakers must be equal to the odd multiple of half of the wavelength

here we know that

[tex]\Delta x = (2n + 1)\frac{\lambda}{2}[/tex]

given that path difference from two loud speakers is given as

[tex]\Delta x = 5.80 m - 3.90 m[/tex]

[tex]\Delta x = 1.90 m[/tex]

now we know that it will have fourth lowest frequency at which destructive interference will occurs

so here we have

[tex]\Delta x = 1.90 = \frac{7\lambda}{2}[/tex]

[tex]\lambda = \frac{2 \times 1.90}{7}[/tex]

[tex]\lambda = 0.54 m[/tex]

now for frequency we know that

[tex]f = \frac{v}{\lambda}[/tex]

[tex]f = \frac{343}{0.54} = 632 Hz[/tex]

Answer:

No we cannot perform any experiment that tells us weather we are moving or not at a constant speed.

Explanation:

Motion of any body is relative to other reference bodies. We can perceive motion only if our position with respect to a fixed object changes. This is the fundamental concept of reference frame in classical physics or Newtonian Physics  that motion is always from a reference.

We choose a fixed body as reference and ,measure the distance we cover from this fixed point and also our speed with respect to this fixed point. The choice of frame of reference is completely dependent on the observer.

Since in the given case a reference cannot be established outside the plane thus we cannot detect our motion.

Answer:

A) Apparent Weight = 590 N

Explanation:

As we know that frequency is given as

[tex]f = \frac{1}{30}[/tex]

[tex]f = 0.033 Hz[/tex]

now the angular speed is given as

[tex]\omega = 2\pi f[/tex]

[tex]\omega = 2\pi(0.033) = 0.21 rad/s[/tex]

now at the top position we will have

[tex]mg - N = m\omega^2 R[/tex]

[tex]N = mg - m\omega^2 R[/tex]

[tex]N = 600 - \frac{600}{9.8}(0.21)^2(4.0)[/tex]

[tex]N = 590 N[/tex]

The woman's apparent weight at the top of the Ferris wheel is less than her actual weight due to the centripetal force experienced during the uniform circular motion. This apparent weight can be calculated by subtracting the centripetal force from the gravitational force, yielding an answer of 590 N.

This problem revolves around the concepts of centripetal force and apparent weight in the context of uniform circular motion. The woman's apparent weight at the top of the Ferris wheel is less than her actual weight because of the centripetal force directed towards the center of the Ferris wheel.

To calculate the apparent weight, we should subtract the centripetal force from the gravitational force. The gravitational force is her actual weight, and since weight = mass * gravity, her mass equals 600N/9.8 m/s2 ~= 61.2 kg. The angular velocity of the Ferris wheel (ω) is 2π rad/30s since it makes one revolution every 30s. Using the formula centripetal force = m*ω2*r, we find that the centripetal force equals 61.2 kg * (2π rad/30s)2 * 4m = 10 N approximately.

Finally, the woman's apparent weight at the top is the gravitational force minus the centripetal force, or 600 N - 10 N, which equals 590 N. Therefore, the correct answer is A) 590 N.

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Answer:

Magnetic field, B = 1.84 T

Explanation:

It is given that,

Charge on alpha particle, q = +2e = [tex]3.2\times 10^{-19}\ C[/tex]

Mass of alpha particle, [tex]m=6.6\times 10^{-27}\ kg[/tex]

Speed of alpha particles, [tex]v=1.6\times 10^7\ m/s[/tex]

We need to find the magnetic field strength required to bend them into a circular path of radius, r = 0.18 m

So, [tex]F_m=F_c[/tex]

[tex]F_m\ and\ F_c[/tex] are magnetic force and centripetal force respectively

[tex]qvB=\dfrac{mv^2}{r}[/tex]

[tex]B=\dfrac{mv}{qr}[/tex]

[tex]B=\dfrac{6.6\times 10^{-27}\ kg\times 1.6\times 10^7\ m/s}{3.2\times 10^{-19}\ C\times 0.18\ m}[/tex]

B = 1.84 T

So, the value of magnetic field is 1.84 T. Hence, this is the required solution.

The magnetic field strength required to bend them into a circular path is 1.83 T.

The magnetic force on the emitted charge is given as;

F = qvB

The centripetal force of the emitted charge is given as;

F = mv²/r

The magnetic field strength required to bend them into a circular path is calculated as follows;

qvB = mv²/r

[tex]B = \frac{mv}{rq}[/tex]

[tex]B = \frac{6.6 \times 10^{-27} \times 1.6 \times 10^7}{(2\times 1.6 \times 10^{-19} ) \times 0.18} \\\\B = 1.83 \ T[/tex]

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Answer:

The second wavelength is 482 nm.

Explanation:

Given that,

Wavelength = 630 nm

Distance from central maxim = 0.51 m

Distance from central maxim of another wavelength = 0.39 m

We need to calculate the second wavelength

Using formula of width of fringe

[tex]\beta=\dfrac{\lambda d}{D}[/tex]

Here, d and D will be same for both wavelengths

[tex]\lambda[/tex] = wavelength

[tex]\beta [/tex] = width of fringe

The width of fringe for first wavelength

[tex]\beta_{1}=\dfrac{\lambda_{1} d}{D}[/tex]....(I)

The width of fringe for second wavelength

[tex]\beta_{2}=\dfrac{\lambda_{2} d}{D}[/tex]....(II)

Divided equation (I) by equation (II)

[tex]\dfrac{\beta_{1}}{\beta_{2}}=\dfrac{\lambda_{1}}{\lambda_{2}}[/tex]

[tex]\lambda_{2}=\dfrac{630\times10^{-9}\times0.39}{0.51}[/tex]

[tex]\lambda_{2}=4.82\times10^{-7}[/tex]

[tex]\lambda=482\ nm[/tex]

Hence, The second wavelength is 482 nm.

To find the second wavelength, we can use the formula for the wavelength of light from a diffraction grating. In this case, we know the first wavelength is 630 nm, the first bright spot is separated from the central maximum by 0.51 m, and we need to find the second wavelength.

To find the second wavelength, we can use the formula for the wavelength of light from a diffraction grating: wavelength = (m * d * sin(theta)) / n. In this case, we know the first wavelength is 630 nm, the first bright spot is separated from the central maximum by 0.51 m, and we need to find the second wavelength. The m and n values are the same for both cases, so we can set up the equation:

630 nm = (m * 0.51 m * sin(theta)) / n
wavelength = (m * 0.51 m * sin(theta)) / n

Next, we can solve for the second wavelength by rearranging the equation:

wavelength = (630 nm * n) / (m * 0.51 m * sin(theta))

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Answer:

Energy, [tex]E=9\times 10^{13}\ J[/tex]

Explanation:

It is given that,

Mass of matter, m = 1 g = 0.001 Kg

If this matter is completely converted into energy, we need to find the yield. The mass of an object can be converted to energy as :

[tex]E=mc^2[/tex]

c = speed of light

[tex]E=0.001\ kg\times (3\times 10^8\ m/s)^2[/tex]

[tex]E=9\times 10^{13}\ J[/tex]

So, the energy yield will be [tex]9\times 10^{13}\ J[/tex]. Hence, this is the required solution.

Answer:

the visible wavelength is 480 nm

Explanation:

Given data

thick film = 4.0 × 10² nm

n = 1.2

wavelength range = 380 nm to 750 nm

to find out

the visible wavelength in air

solution

we know that index of water is 1 and kerosene is 1.2

we can say that when light travel reflected path difference is = 2 n t

and for maximum intensity it will be k × wavelength

so it will be  2 n t = k × wavelength

2 × 1.2 × 4.0 × 10² = k × wavelength

wavelength = 2 × 1.2 × 4.0 × 10² / k

here k is 2 for visible

so wavelength = 2 × 1.2 × 4.0 × 10² / 2

wavelength  = 480 nm

the visible wavelength is 480 nm

Answer:

The temperature of hot reservoir is 669.24 K.

Explanation:

It is given that,

Efficiency of gasoline engine, [tex]\eta=35.3\%=0.353[/tex]

Temperature of cold reservoir, [tex]T_C=160^{\circ}C=433\ K[/tex]

We need to find the temperature of hot reservoir. The efficiency of Carnot engine is given by :

[tex]\eta=1-\dfrac{T_C}{T_H}[/tex]

[tex]T_H=\dfrac{T_C}{1-\eta}[/tex]

[tex]T_H=\dfrac{433}{1-0.353}[/tex]

[tex]T_H=669.24\ K[/tex]

So, the temperature of hot reservoir is 669.24 K. Hence, this is the required solution.

Answer:

The Magnetic field is 59.13 mT.

Explanation:

Given that,

Number of turns = 400

Radius = 1.0 cm

Frequency = 90 Hz

Emf = 4.2 V

We need to calculate the angular velocity

Using formula of angular velocity

[tex]\omega=2\pi f[/tex]

[tex]\omega=2\times3.14\times90[/tex]

[tex]\omega=565.2\ rad/s[/tex]

We need to calculate the magnetic flux

Relation between magnetic flux and induced emf

[tex]\epsilon=NA\omega B[/tex]

[tex]B=\dfrac{\epsilon}{NA\omega}[/tex]

Put the value into the formula

[tex]B=\dfrac{4.2}{400\times\pi\times(1.0\times10^{-2})^2\times 565.2}[/tex]

[tex]B=0.05913\ T[/tex]

[tex]B=59.13\ mT[/tex]

Hence, The Magnetic field is 59.13 mT.

Explanation:

It is given that,

Speed of the baseball, u = 44 m/s

Speed of the baseball, v = 53 m/s

Mass of the ball, m = 145 g = 0.145 kg

Time of contact between the ball and the bat, t = 2.2 ms = 0.0022 s

[tex]F=ma[/tex]

[tex]F=\dfrac{mv}{t}[/tex]

[tex]F_1=\dfrac{0.145\ kg\times 44\ m/s}{0.0022\ s}[/tex]

F₁ = 2900 N...........(1)

[tex]F=ma[/tex]

[tex]F=\dfrac{mv}{t}[/tex]

[tex]F_2=\dfrac{0.145\ kg\times 53\ m/s}{0.0022\ s}[/tex]

F₂ = 3493.18 N.........(2)

In average vector form force is given by :

[tex]F=F_1+F_2[/tex]

[tex]F=(2900i+(-3493.18)\ N[/tex]

[tex]F=(2900i-3493.18j)\ N[/tex]

Hence, this is the required solution.

Answer:

Explanation:

Let east be towards X-axis ant north be Y-axis. Let initial position of Dog be at

A . O be the police station (centre). Vector OA can be written as follows

OA = 1.2 Cos 33 + 1.2 Sin 33

O B =2 Cos 75 + 2 Sin 75.

Displacement A   → B = OB - OA  =2Cos75i +2 Sin 75j -1.2 Cos 33i -1.2 Sin 33j

= 2 x .2588 i+ 2x .966j - 1.2 x .8387i - 1.2 x .5446j = .5176i + 1.932 j- 1.0064i - .65356j

= -.4888 i + 1.27844j

Magnitude of displacement =√( .4888)² + ( 1.27844)²

= 1.405 km

Average velocity =1.405 / 57-23 km / min  = 1.405 /34 x 60 =2.48 km/h

angle with x-axis ( east towards north ) ∅

 Tan∅ =- 1.27844/.4888 = - 2.615

∅ = -69° or 111° towards north from east or 21° towards west from north.

Answer:

option (b)

Explanation:

Let the electric field is given by E.

mass of proton = mp

mass of electron = me

acceleration of proton = ap

acceleration of electron = ae

Charge on both the particle is same but opposite in nature.

The force on proton = q E

The force on electron = - q E

acceleration of proton, ap = q E / mp

acceleration of electron, ae = - q E / me

We observe that the force is same in magnitude but opposite in direction, acceleration is also different and opposite in direction.

Final answer:

The electron and proton experience the same magnitude of force but different accelerations due to their mass difference, and move in opposite directions because of their opposite charges.

Explanation:

When a proton and an electron are placed in a uniform electric field and released, they both experience the same magnitude of force, because they have equal and opposite charges of the same magnitude. However, their accelerations differ due to their masses. The electron has a much smaller mass compared to the proton, and according to Newton's second law (F = ma), a given force will produce a larger acceleration on an object with a smaller mass.

Therefore, while the magnitudes of the forces are the same, the electron will experience a greater magnitude of acceleration than the proton. Finally, they move in opposite directions because the electric field exerts a force in the direction of the field on positive charges and in the opposite direction on negative charges. Therefore, the electron moves in the opposite direction to the proton when released in the same electric field.

Answer:

The specific heat of the substance is c= 512.04 J/kg K

Explanation:

ΔQ= 2205 J

m= 0.03434 kg

ΔT= 125.4 ºC

ΔQ= m * c * ΔT

c= ΔQ / (m * ΔT)

c= 512.04 J/Kg K

Answer:

EMF = 1.20 V

Explanation:

It is given that,

Magnetic field used by the screwdriver, B = 13.5 T

Length of screwdriver, l = 10.5 cm = 0.105  m

Speed with which it is moving. v = 0.85 m/s

We need to find the maximum EMF induced in the screwdriver. It is given by :

[tex]\epsilon=BLv[/tex]

[tex]\epsilon=13.5\ T \times 0.105\ m \times 0.85\ m/s[/tex]

[tex]\epsilon=1.20\ V[/tex]

So, the maximum emf of the screwdriver is 1.20 V. Hence, this is the required solution.

Answer:

Length of the chain, l = 0.99 m

Explanation:

Given that,

A playground tire swing has a period of 2.0 s on Earth i.e.

T = 2 s

We need to find the length of this chain. The relationship between the length and the time period is given by :

[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]

Where

l = length of chain

g = acceleration due to gravity

[tex]l=\dfrac{T^2g}{4\pi^2}[/tex]

[tex]l=\dfrac{(2)^2\times 9.8}{4\pi^2}[/tex]

l = 0.99 meters

So, the length of the chain is 0.99 meters. Hence, this is the required solution.

Answer:

c. Throw the items away from the spaceship.

Explanation:

By the Principle of action and reaction yu can get back to your spacecraft throwing the items away from the spaceship.

Answer:

c. Throw the items away from the spaceship

Explanation:

The propulsion that throwing items away from the spaceship will propel you to the opposite direction in which you are throwing the objects, this means that if you throw the items away from the spaceship you will be getting force of rpopulsion towards the spaceship.

Answer:

The amplitude of oscillation for the oscillating mass is 0.28 m.

Explanation:

Given that,

Mass = 0.14 kg

Equation of simple harmonic motion

[tex]x(t)=(0.28\ m)\cos[(8\ rad/s)t][/tex]....(I)

We need to calculate the amplitude

Using general equation of simple harmonic equation

[tex]y=A\omega \cos\omega t[/tex]

Compare the equation (I) from general equation

The amplitude is 0.28 m.

Hence, The amplitude of oscillation for the oscillating mass is 0.28 m.

Answer:

374 N

Explanation:

N = normal force acting on the skier

m = mass of the skier = 82.5

From the force diagram, force equation perpendicular to the slope is given as

N = mg Cos18.7

μ = Coefficient of friction = 0.150

frictional force is given as

f = μN

f =  μmg Cos18.7

F = force applied by the rope

Force equation parallel to the slope is given as

F - f - mg Sin18.7 = 0

F - μmg Cos18.7 - mg Sin18.7 = 0

F = μmg Cos18.7 + mg Sin18.7

F = (0.150 x 82.5 x 9.8) Cos18.7 + (82.5 x 9.8) Sin18.7

F = 374 N

a. The resistance of the bulb is equal to 4.58 Ohms.

b. The fraction of the chemical energy transformed which appears as internal energy in the batteries is 8.4%.

Given the following data:

a. To find the resistance of the bulb:

First of all, we would determine the total electromotive force (E) of the electric circuit:

[tex]E = 2 \times 1.50[/tex]

E = 3.0 Volts

Total internal resistance = [tex]0.240 + 0.180 = 0.42 \;Ohms[/tex]

Mathematically, electromotive force (E) is given by the formula:

[tex]E = V + Ir[/tex]    ....equation 1.

Where:

According to Ohm's law, voltage is given by:

[tex]V = IR[/tex]    ....equation 2

Substituting eqn 2 into eqn 1, we have:

[tex]E = IR + Ir\\\\E = I(R + r)\\\\R + r = \frac{E}{I} \\\\R = \frac{E}{I} - r\\\\R = \frac{3}{0.6} - 0.42\\\\R = 5 - 0.42[/tex]

Resistance, R = 4.58 Ohms

b. To determine what fraction of the chemical energy transformed appears as internal energy in the batteries:

First of all, we would determine the electromotive force (E) in the batteries.

[tex]E_B = IR\\\\E_B = 0.6 \times 0.42[/tex]

[tex]E_B[/tex] = 0.252 Volt

[tex]Percent = \frac{E_B}{E} \times 100\\\\Percent = \frac{0.252}{3} \times 100\\\\Percent = \frac{25.2}{3}[/tex]

Percent = 8.4 %

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The resistance of the bulb and the fraction of the chemical energy transformed into internal energy in the batteries can be determined using Ohm's law and the power dissipation formula. The total resistance in the series circuit is the sum of the individual resistances, and the total voltage is the sum of the individual voltages.

The total voltage supplied by the batteries is the sum of their voltages, so Vtot = 1.5V + 1.5V = 3.0V. The total internal resistance of the batteries is the sum of their internal resistances, Rt = 0.240Ω + 0.180Ω = 0.420Ω. For the bulb's resistance, we can rearrange Ohm's law to R = V/I. Knowing the total voltage (3.0V) and the current (600 mA or 0.600 A), we can find the total resistance in the circuit.

Subtracting the total internal resistance gives us the resistance of the bulb. As for the second part of the question, the power dissipated in the internal resistances can be found using P = I²r for each battery, and then add these together. The total power supplied by the batteries is P = IV, using the total current and total voltage. The fraction of the chemical energy that appears as internal energy in the batteries is then Pinternal / Ptotal.

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Answer:

[tex]C_2=\frac{C_1}{4}[/tex]

Explanation:

Given:

Initial capacitance, C = C₁

Initial Frequency, F₁ = 600kHz

Final Frequency, F₂ = 1200kHz

let the adjusted capacitance be, C₂

Now

the  frequency (f) is given as:

[tex]f={\frac{1}{2\pi \sqrt{LC}}}[/tex]

where, L = inductance (same for the same material)

thus substituting the values we have

[tex]600={\frac{1}{2\pi \sqrt{LC_1}}}[/tex]     ...............(1)

and

[tex]1200={\frac{1}{2\pi \sqrt{LC_2}}}[/tex]        ..............(2)

dividing the equation 1 with 2, we get

[tex]\frac{600}{1200}=\frac{{\frac{1}{2\pi \sqrt{LC_1}}}}{{\frac{1}{2\pi \sqrt{LC_2}}}}[/tex]

or

[tex]\frac{1}{2}=\sqrt{\frac{C_2}{C_1}}[/tex]

or

[tex]\frac{C_2}{C_1}=\frac{1}{4}[/tex]

or

[tex]C_2=\frac{C_1}{4}[/tex]

hence, the new capacitance C, must be one-fourth times the initial capacitance

The capacitance for the frequency of 1200 kHz must be one-fourth times the capacitance for the frequency of 800 kHz.

Capacitance is the ability of a circuit to store energy in the form of an electrical charge.it is an energy-storing device. generally, it is defined by the ratio of electric charge stored to the potential difference.

Given:

Initial capacitance is C

Capacitance for the frequency of 1200 kHz is [tex]\rm{C=C_1}[/tex]

The capacitance for the frequency of 800 kHz is [tex]\rm{C=C_2}[/tex]

The  frequency (f) is given by

[tex]f=\frac{1}{2\pi \sqrt{LC} }[/tex]

The capacitance for the frequency of 1200 kHz finds by

[tex]f_1=\frac{1}{2\pi \sqrt{LC_1} }[/tex]

[tex]1200=\frac{1}{2\pi \sqrt{LC_1} }[/tex]        ------------------1

The capacitance for the frequency of 800 kHz

[tex]f_2=\frac{1}{2\pi \sqrt{LC_2} }[/tex]

[tex]600=\frac{1}{2\pi \sqrt{LC_2} }[/tex]         ------------------2

On dividing the equation 2 by 1

[tex]\frac{1}{2} =\sqrt{\frac{C_2}{C_1} }[/tex]

[tex]{\frac{C_2}{C_1} }=\frac{1}{4}[/tex]

[tex]C_2=\frac{C_1}{4}[/tex]

Hence the capacitance for the frequency of 1200 kHz must be one-fourth times the capacitance for the frequency of 800 kHz.

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Answer:

Explanation:

KE_s: Kinetic Energy Son

KE_f: Kinetic Energy Father.

Relationship

KE_f: =  (1/4) KE_s

m_s: = (1/3) m_f

v_f: = velocity of father

v_s: = velocity of the son

Relationship

1/2 mf (v_f + 1.2)^2 = 1/2 m_s (v_s)^2      Multiply both sides by 2.

mf (v_f + 1.2)^2 = m_s * (v_s)^2               Substitute for the mass of the m_s

mf (v_f + 1.2)^2 = (m_f/3) * (v_s)^2         Divide both sides by father's mass

(v_f + 1.2)^2 = 1/3 * (v_s)^2                      multiply both sides by 3

3*(v_f + 1.2)^2 = (v_s) ^2                         Take the square root both sides

√3 * (v_f + 1.2) = v_s

Note

KE_f = (1/4) KE_s                                                  Multiply by 4

4* KE_f = KE_s                                                     Substitute (again)

4*(1/2) m_f (v_f + 1.2)^2 = 1/2* (1/3)m_f *v_s^2   Divide by m_f

2* (v_f + 1.2)^2 = 1/6 * (v_s)^2                              multiply by 6

12*(vf + 1.2)^2 = (v_s)^2                                        Take the square root

2*√(3* (v_f + 1.2)^2) = √(v_s^2)

2*√3 * (vf + 1.2) = v_s

Use the second relationship to substitute for v_s so you can solve for v_f

2*√3 * ( v_f + 1.2) = √3 * (v_f + 1.2)                     Divide by sqrt(3)

2(v_f + 1.2) = vf + 1.2

Edit

2vf + 2.4 = vf + 1.2

2vf - vf + 2.4 = 1.2

vf = 1.2 - 2.4

vf = - 1.2

This answer is not possible, but 2 of us are getting the same answer. The other person is someone whose math I would never question. She rarely makes an error. And I do mean rarely. Could you check to see that you have copied this correctly?