A 13-kg (including the mass of the wheels) bicycle has 1-m-diameter wheels, each with a mass of 3.1 kg. The mass of the rider is 38 kg. Estimate the fraction of the total kinetic energy of the rider-bicycle system is associated with rotation of the wheels?

Answer:

The force constant for each elastic band is 77.93 N/m

Explanation:

Hooke's law of a spring or an elastic band gives the relation between elastic force (Fe) and stretching (x), the magnitude of that force is:

[tex] F_{e}= kx [/tex] (1)

With k, the elastic force constant. The three elastic bands support the child’s weight (W) and maintain him at rest, so by Newton’s second law for one of the elastic bands:

[tex] \sum F=0 [/tex] (2)

[tex]\frac{W}{3}-F_{e}=0\Rightarrow F_{e}=\frac{W}{3} [/tex] (3)

Using (1) on (3):

[tex] kx=\frac{W}{3}\Rightarrow k=\frac{mg}{3x} [/tex](4)

[tex] k=\frac{7.15\,kg*9.81\,\frac{m}{s^{2}}}{3*0.300\,m}\simeq\mathbf{77.93\frac{N}{m}} [/tex]

The force constant of each elastic band is 77.87 N/m.

To find the force constant for each elastic band, we use Hooke's law

Hooke's law states that the force applied to an elastic material is directly proportional to its extension provided the elastic limit is not exceeded

Where:

Make k the subject of the equation

From the question,

Given:

Substitute these values into equation 2

Hence, The force constant of each elastic band is 77.87 N/m.
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Answer:

1.5 W/kg, 3.47 W/kg

6 dogs

Explanation:

[tex]m_d[/tex] = Mass of dog = 38 kg

[tex]v_d[/tex] = Pulling speed of dog = 2.2 m/s

[tex]F_d[/tex] = Force on sled = 60 N

[tex]P_h[/tex] = Power of horse = 750 W

[tex]m_h[/tex] = Mass of horse = 500 kg

Power is given by

[tex]P_d=F_dv_d\\\Rightarrow P_d=60\times 2.2\\\Rightarrow P_d=132\ W[/tex]

Specific power is given by

[tex]P_{sh}=\frac{P_h}{m_h}\\\Rightarrow P_{sh}=\frac{750}{500}\\\Rightarrow P_{sh}=1.5\ W/kg[/tex]

Specific power of horse is 1.5 W/kg

[tex]P_{sd}=\frac{P_d}{m_d}\\\Rightarrow P_{sd}=\frac{132}{38}\\\Rightarrow P_{sh}=3.47\ W/kg[/tex]

Specific power of dog is 3.47 W/kg

We have the relation

[tex]nP_d=P_h\\\Rightarrow n=\frac{P_h}{P_d}\\\Rightarrow n=\frac{750}{132}=5.68\ dogs\approx 6\ dogs[/tex]

The number of dogs is 6

(1) The specific power of the horse is 1.5 W/kg and the specific power of the dog is 3.5 W/kg.

(2) The minimum number of dogs needed to provide the same power as one horse is 6 dogs.

The specific power of the horse is calculated as follows;

Cp = P/m

Cp = 750/500

Cp = 1.5 W/kg

The specific power of the dog is calculated as follows;

Cp = P/m

Cp = (Fv)/m
Cp = (60 x 2.2)/38

Cp = 3.5 W/kg

n(Fv) = 750

n = (750)/(60 x 2.2)

n = 6 dogs

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Answer:

Part a)

[tex]U = 13 J[/tex]

Part b)

[tex]v = 2.28 m/s[/tex]

Part c)

[tex]v = 177.66 m/s[/tex]

Part d)

[tex]W = 1012.7 J[/tex]

Part e)

[tex]v = 2.1 m/s[/tex]

Part f)

[tex]E = 1037.2 J[/tex]

Explanation:

Part a)

As we know that the maximum angle deflected by the pendulum is

[tex]\theta = 38^o[/tex]

so the maximum height reached by the pendulum is given as

[tex]h = L(1 - cos\theta)[/tex]

so we will have

[tex]h = L(1 - cos38)[/tex]

[tex]h = 1.25(1 - cos38)[/tex]

[tex]h = 0.265 m[/tex]

now gravitational potential energy of the pendulum is given as

[tex]U = mgh[/tex]

[tex]U = 5(9.81)(0.265)[/tex]

[tex]U = 13 J[/tex]

Part b)

As we know that there is no energy loss while moving upwards after being stuck

so here we can use mechanical energy conservation law

so we have

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

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

[tex]v = \sqrt{2(9.81)(0.265)}[/tex]

[tex]v = 2.28 m/s[/tex]

Part c)

now by momentum conservation we can say

[tex]mv = (M + m) v_f[/tex]

[tex]0.065 v = (5 + 0.065)2.28[/tex]

[tex]v = 177.66 m/s[/tex]

Part d)

Work done by the bullet is equal to the change in kinetic energy of the system

so we have

[tex]W = \frac{1}{2}mv^2 - \frac{1}{2}(m + M)v_f^2[/tex]

[tex]W = \frac{1}{2}(0.065)(177.66)^2 - \frac{1}{2}(5 + 0.065)2.28^2[/tex]

[tex]W = 1012.7 J[/tex]

Part e)

recoil speed of the gun can be calculated by momentum conservation

so we will have

[tex]0 = mv_1 + Mv_2[/tex]

[tex]0 = 0.065(177.6) + 5.50 v[/tex]

[tex]v = 2.1 m/s[/tex]

Part f)

Total energy released in the process of shooting of gun

[tex]E = \frac{1}{2}Mv^2 + \frac{1}{2}mv_1^2[/tex]

[tex]E = \frac{1}{2}(5.50)(2.1^2) + \frac{1}{2}(0.065)(177.6^2)[/tex]

[tex]E = 1037.2 J[/tex]

Final answer:

The acceleration of the crate on the frictionless ramp is 2.39 m/s², while the acceleration on the ramp with friction is 0.49 m/s².

Explanation:

To find the acceleration of the crate, we first need to determine the force component parallel to the incline. This can be done using the formula F_parallel = F * sin(theta), where F is the applied force and theta is the angle of the ramp. Substituting the values, we have F_parallel = 7.0 N * sin(20°) = 2.39 N. The acceleration can then be found using the equation a = F_parallel / m, where m is the mass of the crate. Substituting the values, we have a = 2.39 N / 1.0 kg = 2.39 m/s².

If the ramp has a friction force of 1.9 N, it will oppose the motion of the crate. In this case, we need to subtract the friction force from the parallel force to find the effective force. The effective force, Feff, is given by Feff = F_parallel - friction force. Substituting the values, we have Feff = 2.39 N - 1.9 N = 0.49 N. The acceleration can then be found using the equation a = Feff / m. Substituting the values, we have a = 0.49 N / 1.0 kg = 0.49 m/s².

Answer:

Nuclear fusion reactions produce more energy.( basic difference)

Explanation:

Nuclear fusion reactions are different from nuclear fusion reactions :- In nuclear fission one heavy and unstable nuclear breaks into two parts(smaller) and produce energy( very high energy than normal reaction). whereas in nuclear fusion two small and unstable nuclei fuse and produce very high amount of energy( even higher than nuclear fusion).

Answer:

they are different because nuclear fission is  one heavy and unstable nuclear breaks into two parts, or half, and produce very high energy. nuclear fusion two small fuse and produce very high amount of energy

Explanation:

Answer:The gravitational field on Saturn can be calculated by the following formula;

Explanation:

Answer:

Explanation:

Given

mass of body A [tex]m_a=2 kg[/tex]

mass of body [tex]m_b=2 kg[/tex]

Velocity before Collision is [tex]u_a=15\hat{i}+30\hat{j}[/tex]

[tex]u_b=-10\hat{i}+5\hat{j} m/s[/tex]

after collision [tex]v_a=-5\hat{i}+20\hat{j} m/s[/tex]

let [tex]v_b_x[/tex] and [tex]v_b_y[/tex] velocity of B after collision in x and y direction

conserving momentum in x direction

[tex]m_a\times 15+m_b\times (-10)=m_a\times (-5)+m_b\times (v_b_x)[/tex]

as [tex]m_a=m_b[/tex] thus

[tex]15-10=-5+v_b_x[/tex]

[tex]v_b_x=10 m/s[/tex]

Conserving momentum in Y direction

[tex]m_a\times 30+m_b\times 5=m_a\times 20+m_b\times (v_b_y)[/tex]

[tex]30+5=20+v_b_y[/tex]

[tex]v_b_y=15 m/s[/tex]

thus velocity of B after collision is

[tex]v_b=10\hat{i}+15\hat{j}[/tex]

(b)Change in total Kinetic Energy

Initial Kinetic Energy of A  And B

[tex]K.E._a=\frac{1}{2}\times 2(\sqrt{15^2+30^2})^2=1125 J[/tex]

[tex]K.E._b=\frac{1}{2}\times 2(\sqrt{10^2+5^2})^2=125 J[/tex]

Total initial Kinetic Energy =1250 J

Final Kinetic Energy of A  And B

[tex]K.E._a=\frac{1}{2}\times 2(\sqrt{5^2+20^2})^2=425 J[/tex]

[tex]K.E._b=\frac{1}{2}\times 2(\sqrt{10^2+15^2})^2=325 J[/tex]

Final Kinetic Energy [tex]=425+325=750 J[/tex]

Change [tex]\Delta K.E.=1250-750=500 J[/tex]

The acceleration at the bottom of the loop is 34m/[tex]\bold{s^2}[/tex]

Explanation:

Given:  

Mass=52kg

Force=1750N

To calculate:

The acceleration at the bottom of the loop

Formula:

Force=Mass x Acceleration

1750=52 x Acceleration

1750/52=Acceleration

Therefore acceleration at the bottom of the loop is 34m/[tex]s^2[/tex]

Roller coasters are mainly based upon acceleration theory they have two types of acceleration one is at the top of the loop and the other is at the bottom of the loop.

Then the net forces and the values are given. In many problems the roller coaster concept is included and it gives another level of clarity to the problems including the net forces

Answer:

429 J  joules of heat are needed to raise the temperature of 5.00 g

Explanation:

given data

specific heat capacity = 2.20 j/g-k

methane = 5.00 g

temperature range = 36.0°c to 75.0°c

to find out

How many joules of heat are needed to raise the temperature of 5.00 g

solution

we will apply here formula for heat that needed to raise the temperature

Q = m × S × Δt     ..............................1

m is mass of methane and  S is specific heat capacity and Δt is change in temperature

put here value we get

Q = m × S × Δt  

Q = 5 × 2.2 × ( 75 - 36 )

Q = 5 × 2.2 × 39

Q =  429 J

so  429 J  joules of heat are needed to raise the temperature of 5.00 g

Answer:

b. isothermal

Explanation:

When a thermodynamic process occurs and the temperature remains constant, it is said to be an isothermal process.

The prefix "iso" means "equal", so the word isothermal indicates that the temperature remains equal in the process, and that is what happens in the situation described, the volume is varied (compressed) while maintaining the sample of nitrogen gas remains at a constant temperature.

Impulse : 7.5.10⁻¹⁰N.s

Momentum is the product of the mass of an object and its velocity

Whereas impulse is defined is the product of the force with the time interval when the force is acting on the object.

the pollen grains to be ejected out of the flower in 0.30 ms and acceleration of 2.5 × 10⁴ m/s², then

Δt = 0.3 ms = 3.10⁻⁴ s

a = 2.5 × 10⁴ m/s²

mass of pollen: 1.0 × 10⁻⁷g = 1.0 x 10⁻¹⁰ kg

then:

A force that works according to Newton's second law:

[tex]\rm F=1.0\times 10^{-10}\times 2.5\times 10^4\\\\F=2.5\times 10^{-6}\:N[/tex]

Impulse (I) :

[tex]\rm I=2.5 \times 10^{-6}\times 3\times 10^{-4}\\\\I=7.5\times 10^{-10}N.s[/tex]

Collisions between 2 objects  

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The distance of the elevator  

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Final answer:

To calculate the impulse delivered to a pollen grain, the mass is converted to kilograms and then multiplied with the given acceleration to find the force. This force is then multiplied by the time over which it acts to obtain the impulse, which is 75 in units of 10⁻¹⁰ kgm/s.

Explanation:

The question asks us to calculate the impulse delivered to a pollen grain by the forceful opening of a bunchberry plant flower. To find the impulse (I), which is the change in momentum, we can use the formula I = Ft, where F is the force and t is the time that the force is applied. Alternatively, since the question provides the acceleration (a) and initial time, we can utilize the link between force, mass, and acceleration (F = ma) and then apply that result to find the impulse using the time.

Firstly, we need to convert the mass of the pollen grain to kilograms (kg) which is the standard unit of mass in physics equations:
1.0 × 10⁻⁷ g = 1.0 × 10⁻¹⁰ kg.
Now, we calculate the force on the pollen grain:
F = ma = (1.0 × 10⁻¹⁰ kg) × (2.5 × 10⁴ m/s²) = 2.5 × 10⁻⁵ N.
Next, with force and the time of application known, we can find the impulse:
I = Ft = (2.5 × 10⁻⁵ N) × (0.30 × 10⁻³ s) = 7.5 × 10⁻⁹ kg·m/s.
In terms of 10⁻¹⁰ kg·m/s, the impulse is 75.

Answer:

(a) Potential energy of the child is converted into the kinetic energy at the bottom off the slide and a part of which is lost into friction generating heat between the contact surfaces.

(b) [tex]U=668.16\ J[/tex]

Explanation:

Given:

(a)

∴The initial potential energy of the child is converted into the kinetic energy at the bottom off the slide and a part of which is lost into friction generating heat between the contact surfaces.

Initial potential energy:

[tex]PE=m.g.h[/tex]

[tex]PE=24\times 9.8\times 3.3[/tex]

[tex]PE=776.16\ J[/tex]

Kinetic energy at the bottom of the slide:

[tex]KE=\frac{1}{2} m.v^2[/tex]

[tex]KE= 0.5\times 24\times 3^2[/tex]

[tex]KE= 108\ J[/tex]

(b)

Now, the difference in the potential and kinetic energy is the total change in the thermal energy of the slide and the seat of her pants.

This can be given as:

[tex]U=PE-KE[/tex]

[tex]U=776.16-108[/tex]

[tex]U=668.16\ J[/tex]

Answer:

1. [tex]v=14.2259\ m.s^{-1}[/tex]

2. [tex]F_T=25.8924\ N[/tex]

3. [tex]\lambda=29.6373\ m[/tex]

Explanation:

Given:

1.

[tex]\rm Speed\ of\ wave\ pulse=Length\ of\ slinky\div time\ taken\ by\ the\ wave\ to\ travel[/tex]

[tex]v=\frac{6.8}{0.478}[/tex]

[tex]v=14.2259\ m.s^{-1}[/tex]

2.

Now, we find the linear mass density of the slinky.

[tex]\mu=\frac{m}{L}[/tex]

[tex]\mu=\frac{0.87}{6.8}\ kg.m^{-1}[/tex]

We have the relation involving the tension force as:

[tex]v=\sqrt{\frac{F_T}{\mu} }[/tex]

[tex]14.2259=\sqrt{\frac{F_T}{\frac{0.87}{6.8}} }[/tex]

[tex]202.3774=F_T\times \frac{6.8}{0.87}[/tex]

[tex]F_T=25.8924\ N[/tex]

3.

We have the relation for wavelength as:

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

[tex]\lambda=\frac{14.2259}{0.48}[/tex]

[tex]\lambda=29.6373\ m[/tex]

Answer:

Part a)

[tex]T = 9.8 N[/tex]

Part b)

[tex]T = 9.8 N[/tex]

Part c)

If elevator is accelerating upwards then we have

So tension will be more than the weight

Now if the elevator is moving with uniform velocity

tension will be equal to the weight of the block

Explanation:

Part a)

As we know that rope 1 is connected to block 1 at its lower end

So here we have elevator is moving at constant velocity in upward direction

so we have

[tex]T - mg = 0[/tex]

[tex]T = mg[/tex]

[tex]T = 1\times 9.8[/tex]

[tex]T = 9.8 N[/tex]

Part b)

now for block II we have

[tex]T - mg = ma[/tex]

[tex]T - mg = 0[/tex]

[tex]T = 1 \times 9.8[/tex]

[tex]T = 9.8 N[/tex]

Part c)

If elevator is accelerating upwards then we have

[tex]T - mg = ma[/tex]

[tex]T = mg + ma[/tex]

So tension will be more than the weight

Now if the elevator is moving with uniform velocity

[tex]T - mg = 0[/tex]

[tex]T = mg[/tex]

so tension will be equal to the weight of the block

The hot gases produce their own characteristic pattern of spectral lines, which remain fixed as the temperature increases moderately.

A continuous light spectrum emitted by excited atoms of a hot gas with dark spaces in between due to scattered light of specific wavelengths is termed as an atomic spectrum. A hot gas has excited electrons and produces an emission spectrum; the scattered light forming dark bands are called spectral lines.

Fraunhofer closely observed sunlight by expanding the spectrum and a huge number of dark spectral lines were seen.  "Robert Bunsen and Gustav Kirchhoff" discovered that when certain chemicals were burnt using a Bunsen burner, atomic spectra with spectral lines were seen. Atomic spectral pattern is thus a unique characteristic of any gas and can be used to independently identify presence of elements.

The spectrum change does not depend greatly on increasing temperatures and hence no significant change is observed in the emitted spectrum with moderate increase in temperature.

Answer:

Jupiter and Saturn have high temperatures and they have very large gravitational pull compared to Uranus and Neptune.

Explanation:

Jupiter and Saturn have high densities meaning any methane on them is dragged down to their hot surface which prevents methane from ever forming  clouds.

Answer:

Jupiter and Saturn have high temperatures and they have very large gravitational pull compared to Uranus and Neptune.

Explanation:

The ratio is found by dividing the gravitational force, determined by the universal law of gravitation, by the weight of the lighter sphere, which is the product of its mass and the acceleration due to gravity.

The ratio of the gravitational force between the spheres to the weight of the lighter sphere can be found by dividing the gravitational force by the weight of the lighter sphere. The gravitational force (F) between two objects can be found using the universal law of gravitation: F = G * (m1*m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them. Plugging in the given values, we can find the gravitational force. The weight of the lighter sphere can be found by multiplying its mass by the acceleration due to gravity (9.8 m/s^2). Divide the former by the latter to get the answer.

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The ratio of the gravitational force to weight can be calculated using Newton's law of gravitation and the definition of weight. The gravitational constant G used in the calculations was accurately measured by Henry Cavendish in 1798. This allows the measurement of minute gravitational attractions, pivotal in understanding the strength of gravitation.

The ratio of the gravitational force between the two spheres to the weight of the lighter sphere is obtained through the gravitational law and the definition of weight. The universal gravitational constant G was accurately measured by English scientist Henry Cavendish in 1798 using an incredibly sensitive balance. The gravitational force (F) among the two spheres is computed through: F = G * m1 * m2 / r², where m1 and m2 are the masses of the spheres and r is the distance between the centers of the spheres, and G is the gravitational constant (6.67 × 10−11 N·m²/kg²).

Weight (W) is calculated as the mass (m) of an object multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s² on Earth. Thus, the weight of the lighter sphere is: W = m * g. Therefore, the ratio of the gravitational force to the weight of the lighter sphere is calculated by dividing the gravitational force by the weight of the lighter sphere. The tiny gravitational attraction between ordinary-sized masses measured by Cavendish is significant in the world of physics, as it determines the strength of one of the nature's fundamental forces.

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Answer:

[tex]5.9527559\times 10^3\ W[/tex]

Explanation:

Q = Heat

t = Thickness = d = 0.635 cm

[tex]k_g[/tex] = Heat conduction coefficient of glass = 0.84 W/m °C (general value)

[tex]\Delta T[/tex] = Change in temperature

A = Area = 3 m²

Power is given by

[tex]P=\frac{dQ}{dt}=\frac{kA\Delta T}{d}\\\Rightarrow P=\frac{k_gA\Delta T}{d}\\\Rightarrow P=\frac{0.84\times 3(5-(-10))}{0.00635}\\\Rightarrow P=5.9527559\times 10^3\ W[/tex]

The rate of conduction in watts through the window is [tex]5.9527559\times 10^3\ W[/tex]

The rate of heat conduction out of a window is calculated by using Fourier's law. Substituting the given values into Fourier's law yields a heat transfer rate of around 1.97 × 10⁴ W. This represents a significant amount of heat loss through the windows.

The heat conduction rate can be calculated using Fourier's law, which states that the rate of heat transfer per time, or heat flux, is proportional to the temperature gradient. The formula for this law is Q = k*A*(T1-T2)/d, where Q is the heat transfer rate in watts, k is the thermal conductivity, A is the surface area in square meters, T1 and T2 are the temperatures of the two surfaces, and d is the thickness of the material. Given that glass has a thermal conductivity of about 0.84 W/mºC, when we substitute these values into Fourier's law, we obtain:

Q = 0.84 W/mºC * 3.00 m² * (5.00ºC - (-10.0ºC))/0.635 cm, whereby this yields around 1.97 × 10⁴ W.

This indicates that a significant amount of heat is being lost through the windows, contributing to the chilling of the air in the room.

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The two possible frequencies could be ; 642 Hz or 712 Hz

Explanation:

For beats; f₁-f₂=fb where f₁=frequency of the first guitar, f₂=frequency of the second guitar, fb =frequency of beat

In this case, the two possibilities are;

f₁-f₂=fb or f₂-f₁=fb

f₁=677 Hz  and fb=35 Hz

then;

f₁-x=fb

677-x=35

x=677-35=642 Hz

or

x-f₁=fb

x-677=35

x=35+677 =712 Hz

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The object initially had potential energy of 108,410 Joules when placed 6.5 meters higher. Since it maintains the same speed, this energy was used to overcome friction. Thus, the object lost 108,410 Joules to friction.

To answer your question, we first need to calculate the initial potential energy of the object when it was 6.5 m higher. Potential energy (PE) is given by PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height. So, the initial potential energy is PE = (1700 kg)(9.8 m/s²)(6.5 m) = 108,410 Joules.

Since the object reaches the top of the loop with the same velocity in both scenarios, we can say that its kinetic energy remained the same. This implies all of the initial potential energy went into overcoming friction. Therefore, the object lost 108,410 Joules of energy to friction.

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The object lost 111,230 joules of energy to friction during its ascent.

The question is asking how much energy, in joules, the object lost to friction if it starts 6.5 m higher than the previous part and still reaches the top of the loop with the same velocity. To calculate this, we need to find the change in gravitational potential energy, which is given by the formula: ΔPE = mgh.

The mass of the object is 1700 kg, and the change in height is 6.5 m. Substituting these values into the equation, we have:

ΔPE = (1700 kg)(9.8 m/s^2)(6.5 m) = 111,230 J.

Therefore, the object lost 111,230 joules of energy to friction during its ascent.

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Answer:

12.64968 Hz

Explanation:

v = Velocity of sound in seawater = 1522 m/s

u = Velocity of dolphin = 7.2 m/s

f' = Actual frequency = 2674 Hz

From Doppler effect we get the relation

[tex]f=f'\frac{v-u}{v}\\\Rightarrow f=2674\frac{1522-7.2}{1522}\\\Rightarrow f=2661.35032\ Hz[/tex]

The frequency that will be received is 2661.35032 Hz

The difference in the frequency will be

[tex]2674-2661.35032=12.64968\ Hz[/tex]

Final answer:

The difference between the observed frequency and the actual frequency of clicks emitted by the dolphin, calculated using the Doppler Effect, is approximately 12.7 Hz.

Explanation:

The question involves calculating the observed frequency of sound due to the Doppler Effect, which occurs when the source of the sound is moving relative to the observer. In this case, the dolphin is the source of sound waves (clicks), moving away from the marine biologist, who acts as the observer.

The formula for the Doppler Effect for a source moving away from the observer is given by:

f' = f * (v / (v + vs))

Where:

f' is the observed frequency

f is the actual frequency emitted by the source

v is the speed of sound in the medium (1522 m/s in seawater)

vs is the speed of the source relative to the medium (7.2 m/s)

The marine biologist measures the observed frequency (f') as 2674 Hz. We can rearrange the formula to solve for the actual frequency (f):

f = f' * (v + vs) / v

f = 2674 Hz * (1522 m/s + 7.2 m/s) / 1522 m/s

After performing the calculation:

f ≈ 2686.7 Hz

The difference in frequency is then:

Δf = f - f'

Δf ≈ 2686.7 Hz - 2674 Hz

Δf ≈ 12.7 Hz

Therefore, the difference between the observed frequency and the actual frequency of clicks emitted by the dolphin is approximately 12.7 Hz.

Answer:

W = 8085.064 J

Explanation:

given,

mass of the cheerleaders partner = 37.4 Kg

distance above which she was lift = 0.817 m

acceleration due to gravity = 9.8 m/s²

number of time she was picked = 27 times

work he done = ?

now,                                    

Work done will be equal to the potential energy into number times she was lifted.                                          

Work done =  N m g h                    

              W = 27 x 37.4 x 9.8 x 0.817

              W = 8085.064 J                                  

work done by his partner is equal to W = 8085.064 J

Answer: Minimum global acc when you substitute t = 0 in equation 2

Acc = 23.52m/s^2.

Global max acc = 35.595684524m/s^2

Explanation:

(t)= 0.001490833t^3-.08389t^2+23.52t+7.3(in feet per second). ...equation 1.

Equation 1 is the model showing the velocity pathway..

To derive the equation of acceleration.

We differentiate equation 1

DV(t)/Dt = acc. = .004472499t^2 - 0.16778t + 23.52...equ 2

Minimum global acc when you substitute t = 0 in equation 2

Acc = 23.52m/s^2.

Maximum global acc when you substitute the = 74s

Acc = 24.491404524 -12.41572 +23.52

Global max acc = 35.595684524m/s^2

To find the global maximum and minimum values of the acceleration of a rocket, we compute the second derivative of the velocity function, which is the acceleration function. We then evaluate the acceleration function at the given time points and at any critical points within this period.

To find the global maximum and minimum values of the acceleration of a rocket, we first need to determine the function for the acceleration, a(t), which is the second derivative of the given velocity function, v(t). The given velocity function v(t) = 0.001490833t^3 - 0.08389t^2 + 23.52t + 7.3. The first derivative, v'(t), gives us the acceleration function and can be computed as v'(t) = 0.004472499t^2 - 0.16778t + 23.52. Computing the second derivative, v''(t), we get a(t) = 0.008944998t - 0.16778.

To find the maximum and minimum values of this acceleration within the given time frame (0 to 74 sec), we evaluate the function at these time points and at any critical points within this interval. The critical points are obtained by solving the equation a'(t) = 0, which yield the value for which the acceleration is maximum or minimum.

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Answer:

No change in the specific heat.

Explanation:

Specific heat is an intrinsic property that it has not depend upon on the amount of substance or energy added, it depends upon the material.

So, when twice the amount of energy is transferred, specific heat of the material does not change rather the energy that is twice in the amount to 1 kg of that material cause it to warm 2.0° C.

Answer:

The velocity of the student and skateboard together [tex]=1.82\ ms^{-1}[/tex]

Explanation:

Given:

Mass of student [tex]m_1=71\ kg[/tex]

Mass of skateboard [tex]m_2=2.8\ kg[/tex]

Distance between student and skateboard [tex]d=2.75\ m[/tex]

Acceleration of student [tex]a=0.65\ ms^{-2}[/tex]

Finding velocity [tex]v_1[/tex] of the student  before jumping on skateboard

Using equation of motion

[tex]v_1^2=v_0^2+2ad[/tex]

here [tex]v_0[/tex] represents the initial velocity of the student which is [tex]=0[/tex] as he starts from rest.

So,

[tex]v_1^2=0^2+2(0.65)(2.75)[/tex]

[tex]v_1^2=3.575[/tex]

Taking square root both sides:

[tex]\sqrt{v_1^2}=\sqrt[1.7875}[/tex]

∴ [tex]v_1=1.89[/tex]

Finding velocity [tex]v[/tex] of student and skateboard.

Using law of conservation of momentum.

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]

Where [tex]v_2[/tex] is initial velocity of skateboard which is [tex]=0[/tex] as it is at rest.

Plugging in values.

[tex]71(1.89)+(2.8)(0)=(71+2.8)\ v[/tex]

[tex]134.19=73.8\ v[/tex]

Dividing both sides by [tex]73.8[/tex]

[tex]\frac{134.19}{73.8}=\frac{73.8\ v}{73.8}[/tex]

∴ [tex]v=1.82[/tex]

The velocity of the student and skateboard together [tex]=1.82\ ms^{-1}[/tex]

Answer:

(a)

[tex]\lambda _{m}=9.332 \times 10^{-6}m[/tex]

(b)

[tex]\lambda _{m}=1.632 \times 10^{-6}m[/tex]

(c) [tex]\lambda _{m}=4.988 \times 10^{-7}m[/tex]

Explanation:

According to the Wein's displacement law

[tex]\lambda _{m}\times T = b[/tex]

Where, T be the absolute temperature and b is the Wein's displacement constant.

b = 2.898 x 10^-3 m-K

(a) T = 37°C = 37 + 273 = 310 K

[tex]\lambda _{m}=\frac{b}{T}[/tex]

[tex]\lambda _{m}=\frac{2.893\times 10^{-3}}{310}[/tex]

[tex]\lambda _{m}=9.332 \times 10^{-6}m[/tex]

(b) T = 1500°C = 1500 + 273 = 1773 K

[tex]\lambda _{m}=\frac{b}{T}[/tex]

[tex]\lambda _{m}=\frac{2.893\times 10^{-3}}{1773}[/tex]

[tex]\lambda _{m}=1.632 \times 10^{-6}m[/tex]

(c) T = 5800 K

[tex]\lambda _{m}=\frac{b}{T}[/tex]

[tex]\lambda _{m}=\frac{2.893\times 10^{-3}}{5800}[/tex]

[tex]\lambda _{m}=4.988 \times 10^{-7}m[/tex]

Answer:

1.19cm^3 of glycerine

Explanation:

Let Vo= 150cm^3 for both aluminum and glycerine, using expansion formula:

Volume of spill glycerine = change in volume of glycerine - change in volume of aluminum

Volume of glycerine = coefficient of volume expansion of glycerine * Vo* change in temperature - coefficient of volume expansion of Aluminum*Vo* change temperature

coefficient of volume expansion of aluminum = coefficient of linear expansion of aluminum*3 = 23*10^-6 * 3 = 0.69*10^-4 oC^-1

Change in temperature = 41-23 = 18oC

Volume of glycerine that spill = (5.1*10^-4) - (0.69*10^-4) (150*18) = 4.41*10^-4*2700 = 1.19cm3

Answer:

B:the changes in the characteristics within a population that lead to survival.

Explanation:

Answer:

B

Explanation:

study Island

Answer:

a≅3.33

Explanation:

Answer:

The acceleration of the block down the incline is 3.23 m/s²

Explanation:

Fk = frictional force

m = mass

g = acceleration due to gravity

F1 = force in direction of motion

theeta = inclination angle

For Force on inclined plane

F1 = m*g*sin(theeta)

F1 = (1.2)*(9.8)*sin(30)

F1 = 5.88-N

now,

Fnet = F1 - Fk

Fnet = 5.88 - 2

Fnet = 3.88-N

now for acceleration,

Fnet = m*a

a = Fnet / m

a = 3.88 / 1.2

a = 3.23 m/s²

Answer:

20 kg

Explanation:

Kinetic energy=½*Mass * velocity²

4000= ½* m*20²

8000=400m

m=8000/400

m=20 kg