A roller coaster starts from rest at its highest point and then descends on its (frictionless) track. Its speed is 26 m/s when it reaches ground level. What was its speed when its height was half that of its starting point?

Answer:

μ = 1

F = P√2

Explanation:

The parabola equation is: y = ½ x².

The slope of the tangent is dy/dx = x.

The angle between the tangent and the x-axis is θ = tan⁻¹(x).

At x = 1, θ = 45°.

Draw a free body diagram of the block.  There are three forces:

Weight force P pulling down,

Normal force N pushing perpendicular to the surface,

and friction force Nμ pushing up tangential to the surface.

Sum of forces in the perpendicular direction:

∑F = ma

N − P cos 45° = 0

N = P cos 45°

Sum of forces in the tangential direction:

∑F = ma

Nμ − P sin 45° = 0

Nμ = P sin 45°

μ = P sin 45° / N

μ = tan 45°

μ = 1

Draw a new free body diagram.  This time, friction force points down tangential to the surface, and applied force F pushes up tangential to the surface.

Sum of forces in the tangential direction:

∑F = ma

F − Nμ − P sin 45° = 0

F = Nμ + P sin 45°

F = (P cos 45°) μ + P sin 45°

F = P√2

Answer:

A) Workdone = 223.57 N-m

B) 22357 J of energy

C) Number of donuts = 10.7 donuts

Explanation:

A) The work done is calculated from the formula;. Work done = Force × Distance

We are given;

Mass; m = 43 kg

Distance = 0.53 m

Force(weight) = mg = 43 × 9.81

Thus;

Work done = 43 × 9.81 × 0.53

Workdone = 223.57 N-m

B) We are told she does 23 repetitions a day.

Thus, we assume 23% efficiency.

So, Work = Energy

Thus;

At 100% efficiency;

Energy = (223.57/100%) × 23 repetitions = 5142.11 J

Now, since she is only 23% efficient, she will expend; 5142.11/0.23 J = 22357 J of energy to do 5390 J of work.

C) from conversions; 4.18 J = 1 calorie

Thus;

22357 J ÷ 4.18 J/cal = 5348.565 calories

We how many 500 calorie donuts she can eat in a day to supply that energy.

Thus;

Number of donuts = 5348.565 cal ÷ 500 cal /donut

Number of donuts = 10.7 donuts

Answer:

2035

Explanation:

The doctor does not travel with the woman, and therefore, he won't experience any relativistic effect on his time. The doctor will judge time by the time here on earth. Technically, the last new year's day the doctor, who is here on earth, would expect the woman to celebrate will be in 2020 + 15 years = 2035

Answer:

Explanation:

C. The temperature of the coffee will decrease while the temperature of the table increases.

Answer:

The question is not clear enough. So i have attached a copy of the correct question.

A) B = V/c

B) c = Lv

Explanation:

A) we know that formula for magnetic flux is;

Φ = BA

Where B is magnetic field and A is area

Now,

Let's differentiate with B being a constant;

dΦ/dt = B•dA/dt

From faradays law, the EMF induced is given as;

E = -dΦ/dt

However, we want to express it in terms of V and E.M.F is also known as potential difference or Voltage.

Thus, V = -dΦ/dt

Thus, we can now say that;

-V = B•dA/dt

Now from the question, we are told that dA/dt = - c

Thus;

-V = B•-c

So, V = Bc

Thus, B = V/c

B) according to Faraday's Law or Lorentz Force Law, an electromotive force, emf, will be induced between the two ends of the sidelength:

Thus;

E =LvB or can be written as; V = LvB

Where;

V is EMF

L is length of bar

v is velocity

From the first solution, we saw that;

V = Bc

Thus, equating both of the equations, we have;

Bc = LvB

B will cancel out to give;

c = Lv

Explanation:

Answer:

The glove takes 1.02s to return to the pitchers hand.

Explanation:

Given;

initial velocity the pitcher's glove, u = 5 m/s

Apply kinematic equation

s = ut - ¹/₂gt²

where;

g is acceleration due to gravity = 9.8 m/s²

t is the time takes the glove to return to the pitchers hand

s is the displacement of the glove, which will be equal to zero when the glove returns to the pitchers hand. (s = 0)

0 = ut - ¹/₂gt²

ut = ¹/₂gt²

u = ¹/₂gt

gt = 2u

t = (2u) / g

t = (2 x 5) / 9.8

t = 1.02 s

Therefore, the glove takes 1.02s to return to the pitchers hand.

Answer:

The width of Center bright fringe is 10.2mm

Explanation:

Given that if

Y/ L << 1 then

Sin theta will be approx Y/L

So sin theta approx Y/L = lamda/a

Y= a x lambda/a

By substituting

1.9x 10^ -3m x 550*10^-9/ 0.2 x 10^-3m

= 5.2mm

But

Change in y = 2y = 10.4mm

Answer:

The new time period is  [tex]T_2 = 3.8 \ s[/tex]

Explanation:

From the question we are told that

  The period of oscillation is  [tex]T = 5 \ s[/tex]

   The  new  length is  [tex]l_2 = 0.76 \ m[/tex]

Let assume the original length was [tex]l_1 = 1 m[/tex]

Generally the time period is mathematically represented as

         [tex]T = 2 \pi \sqrt{ \frac{ I }{ mgh } }[/tex]

Now  I is the moment of inertia of the stick which is mathematically represented as

           [tex]I = \frac{m * l^2 }{12 }[/tex]

So

        [tex]T = 2 \pi \sqrt{ \frac{ m * l^2 }{12 * mgh } }[/tex]

Looking at the above equation we see that

        [tex]T \ \ \ \alpha \ \ \ l[/tex]

=>    [tex]\frac{ T_2 }{T_1} = \frac{l_2}{l_1}[/tex]

=>    [tex]\frac{ T_2}{5} = \frac{0.76}{1}[/tex]

=>     [tex]T_2 = 3.8 \ s[/tex]

Answer:

C. 450v

Explanation:

Using

Voltage= B*distance of separation*velocity

3mm x 0.3T x 5E5m/s

= 450v

Answer:

Explanation:

The e.m.f induced in the coil depend on the following :

(a) No. of turns in the coil

(b) Cross-sectional Area of the coil

(c) Magnitude of Magnetic field

(d) Angular velocity of the coil

Answer:

A. Using displacement =Ut + 1/2gt²

=> 0 + 1/2 (-9.8)t²

= -4.9t²

So

h(t) = 50+ displacement

= 50 - 4.9t²

B. To reach the ground

h(t) = 0

So

50-4.9t²= 0

t = √ (50/4.9)

= 3.2s

C. Using

V = u+ gt

U= 0

V= - 9.8(3.2)

= 31.4m/s

D. If u = -9m/s

Then s = ut + 1/2gt²

5t- 1/2gt²

But distance from the ground is

=.> 50-5t- 4.8t²= 0

So t solving the quadratic equation

t= 3.58s

(a) The distance of the stone above the ground level at time t is [tex]h(t) = 50 - 4.9t^2[/tex]

(b) The time taken for the stone to strike the ground is 3.19 s.

(c) The velocity of the stone when it strikes the ground is 31.4 m/s.

(d) The time taken for the stone to reach the ground when thrown at the given speed is 2.41 s.

The given parameters;

The distance of the stone above the ground level at time t is calculated as;

[tex]h(t) = h_0 - ut - \frac{1}{2} gt^2\\\\h(t) = 50 - 0 -0.5\times 9.8t^2\\\\h(t) = 50 - 4.9t^2[/tex]

The time taken for the stone to strike the ground is calculated as;

[tex]t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2\times 50}{9.8} } \\\\t = 3.19 \ s[/tex]

The velocity of the stone when it strikes the ground is calculated as;

[tex]v =u + gt\\\\v = 0 + 3.2 \times 9.8\\\\v = 31.4 \ m/s[/tex]

The time taken for the stone to reach the ground when thrown at speed of 9 m/s is calculated as;

[tex]50 = 9t + \frac{1}{2} (9.8)t^2\\\\50 = 9t + 4.9t^2\\\\4.9t^2 + 9t - 50 = 0\\\\a = 4.9 \, \ b = 9, \ \ c = -50\\\\solve \ the \ quadratic \ equation\ using \ formula \ method\\\\t = \frac{-b \ \ + /- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\t = \frac{-9 \ \ + /- \ \ \sqrt{(9)^2 - 4(4.9 \times -50)} }{2(4.9)} \\\\t = 2.41 \ s \ \ or \ \ - 4.24 \ s[/tex]

Thus, the time taken for the stone to reach the ground when thrown at the given speed is 2.41 s.

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Answer:

Explanation:

We can conclude that the forces of the two teams are equal and opposite and hence they cancel each other. Therefore none of the teams won as the rope did not move.

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Answer:

R = 0.992 Ω

Explanation:

En esta pregunta, dada la información que contiene, debemos calcular la resistencia de la varilla de grafito.

Matemáticamente,

Resistencia = (resistividad * longitud) / Área De la pregunta;

Resistividad = 3,5 * 10 ^ -5 Ωm

longitud = 170 cm = 1,7 m

Área = 60 mm ^ 2 = 60/1000000 = 6 * 10 ^ -5 m ^ 2

Conectando estos valores a la ecuación anterior, tenemos;

Resistencia = (3.5 * 10 ^ -5 * 1.7) / (6 * 10 ^ -5) =

(3.5 * 1.7) / 6 = 0.992 Ω

Answer:

The number of  fringe pattern shift is   m  = 40

Explanation:

 From the question we are told that

      The  Michelson interferometer is moved 20 wavelengths i.e  [tex]20 \lambda[/tex]

Generally the distance which the  Michelson interferometer is moved is mathematically represented as

         [tex]d = \frac{m * \lambda}{2}[/tex]

Here [tex]m[/tex] is the number of  fringe pattern shift

     So

         [tex]20 \lambda = \frac{m * \lambda}{2}[/tex]

         [tex]40 \lambda = m * \lambda[/tex]

        m  = 40

Answer:

D) True. In this case the thumb goes up the page, the fingers are extended out of the page and the palm points to the left

Explanation:

The magnetic force on a conductor is given by

        F = i L x B

bold letters indicate vectors. We can write this expression in the form of magnitudes

         F = i L B sin θ

The direction of the force can be found by the rule of the right hand, the thumb points in the direction of the current, the fingers extended in the direction of the magnetic field and the palm gives the direction of the force

Let's apply this expression to the case presented.

A) False. In this case the force is out of the page and is in contradiction with the real force

B) False. In this case the force is zero since the displacement of the current and the field would be parallel

C) False. In this case the force is to the left

D) True. In this case the thumb goes up the page, the fingers are extended out of the page and the palm points to the left

Answer:

352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.

Explanation:

The decay of radioisotopes are represented by the following ordinary differential equation:

[tex]\frac{dm}{dt} = -\frac{t}{\tau}[/tex]

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]\tau[/tex] - Time constant, measured in seconds.

[tex]m[/tex] - Mass of the radioisotope, measured in grams.

The solution of this expression is:

[tex]m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]

Where [tex]m_{o}[/tex] is the initial mass of the radioisotope, measured in kilograms.

The ratio of current mass to initial mass is:

[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]

The time constant is now calculated in terms of half-life:

[tex]\tau = \frac{t_{1/2}}{\ln2}[/tex]

Where [tex]t_{1/2}[/tex] is the half-life of the radioisotope, measured in seconds.

Given that [tex]t_{1/2} = 88\,s[/tex], the time constant of the radioisotope is:

[tex]\tau = \frac{88\,s}{\ln 2}[/tex]

[tex]\tau \approx 126.957\,s[/tex]

Now, if [tex]\frac{m(t)}{m_{o}(t)} = \frac{1}{16}[/tex] and [tex]\tau \approx 126.957\,s[/tex], the time is:

[tex]t = -\tau \cdot \ln\frac{m(t)}{m_{o}}[/tex]

[tex]t = -(126.957\,s)\cdot \ln \frac{1}{16}[/tex]

[tex]t \approx 352\,s[/tex]

352 seconds are needed for the radioisotope to decay to one-sixteenth of its original mass.

Answer:

a) 1.35 x 10^11 m

b) 0.53 µs

c) 8 ns

Explanation:

Radar involves the use of radio wave which has speed c = 3 x 10^8 m/s

a) for 900 s,

The distance for a round trip = v x t

==>  (3 x 10^8) x 900 =  2.7 x 10^11 m

The distance of Venus is half this round trip distance = (2.7 x 10^11)/2 = 1.35 x 10^11 m

b) for a 80.0 m distance of the car from the radar source, the radar will travel a total distance of

d = 2 x 80 = 160 m

the time taken = d/c = 160/(3 x 10^8) = 5.3 x 10^-7 s = 0.53 µs

c) accuracy in distance Δd = 11.5 m

Δt = accuracy in time = Δd/c = 11.5/(3 x 10^8) = 3.8 x 10^-8 = 38 ns

Answer:

a) 60000 N

b) 35000 N

Explanation:

Force from locomotive = 100000 N

mass of first car = 80000 kg

mass of second car = 50000 kg

mass of third car = 70000 kg

friction is neglected in this system

Total mass of the cars = 80000 + 50000 + 70000  = 200000 kg

All the car in the system will accelerate at the same rate since they are pulled by the same force

We know that force F = ma

where

a is the acceleration of the cars

m is the total mass in the system

from this we can say that

a = F/m

a = 100000/200000 = 0.5 m/s^2

a) The total mass involved in this case = mass of the last two cars after the 80000 kg car =  50000 + 70000 = 120000 kg

therefore force exerted F = ma

F = 0.5 x 120000 = 60000 N

b) The total mass in this case = mass of the third car only = 70000 kg

F = ma

F = 70000 x 0.5 = 35000 N

Answer:

Explanation:

Answer:

quantum entanglement is thought to be one of the trickiest concepts in science, but the core issues are simple. And once understood, entanglement opens up a richer understanding of concepts such as the “many worlds” of quantum theory.

Explanation:

Answer:

1.1micro meter

Explanation:

Given that

Constructive interference is

ma = alpha x sin theta

Alpha = 1 x 594 x10^ -9/ sin 32.8°

= 1.1 x 10^ -6m

Explanation:

Answer:

D. evacuated tube collector due to reduced heat loss

Explanation:

Evacuated tube collectors has vacuum which reduces the loss of heat and increase the efficiency of the collector. It has a major application in solar collector, and converts solar energy to heat energy. It can also be used for heating of a definite volume of water majorly for domestic purpose.

During cold weather, the conservation and efficient use of heat is required. Therefore, evacuated tube collector is preferred so as to reduce heat loss and ensure the maximum use of heat energy.

Answer:

C) radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays

Explanation:

radio waves have lowest  energy , lowest  frequency and highest  wavelength

gamma rays  have highest  energy , highest  frequency and least  wavelength

Answer: C

Explanation:

Answer:

9.82 × [tex]10^{-35}[/tex] Hz

Explanation:

De Broglie equation is used to determine the wavelength of a particle (e.g electron) in motion. It is given as:

λ = [tex]\frac{h}{mv}[/tex]

where: λ is the required wavelength of the moving electron, h is the Planck's constant, m is the mass of the particle, v is its speed.

Given that: h = 6.63 ×[tex]10^{-34}[/tex] Js, m = 2.50 kg, v = 2.70 m/s, the wavelength, λ, can be determined as follows;

λ = [tex]\frac{h}{mv}[/tex]

  = [tex]\frac{6.63*10^{-34} }{2.5*2.7}[/tex]

 = [tex]\frac{6.63 * 10^{-34} }{6.75}[/tex]

 = 9.8222 × [tex]10^{-35}[/tex]

The wavelength of the object is 9.82 × [tex]10^{-35}[/tex] Hz.

Answer:

Explanation:

The lens equation is expressed as;

1/f = 1/u+1/v where;

f is the focal length of the lens

u is the object distance

v is the image distance

Since the near sighted person wants focus the starts at nigt, the stars at night are the images located that infinity. Hence the image distance v = ∞.

The object distance u = 130cm

Substituting the given parameters in the formula to get the focal length f

[tex]\frac{1}{f} = \frac{1}{\infty} + \frac{1}{130} \\\\As \ x \ tends \ to \ \infty, \, \frac{a}{x} \ tends \ to \ 0 \ where\ 'a' \ is \ a\ constant \\\\} \\\\[/tex]

[tex]\frac{1}{f} = 0+ \frac{1}{130}\\\\[/tex]

[tex]\frac{1}{f} =\frac{1}{130}\\cross\ multiply\\\\f = 130*1\\\\f = 130cm[/tex]

Hence the focal length of contact lenses that would allow a nearsighted person with a 130 cm far point to focus on the stars at night is 130cm

Answer: no u

Explanation: no u

Answer:

a)   Δt = 24.96 s , b)  τ = 0.078 N m

Explanation:

This is a rotational kinematics exercise

        θ = w₀ t - ½ α t²

Let's reduce the magnitudes the SI system

       θ = 60 rev (2π rad / 1 rev) = 376.99 rad

       w₀ = 7.0 rot / s (2π rad / 1 rpt) = 43.98 rad / s

      α = (w₀ t - θ) 2 / t²

let's calculate the annular acceleration

      α = (43.98 10 - 376.99) 2/10²

      α = 1,258 rad / s²

Let's find the time it takes to reach zero angular velocity (w = 0)

        w = w₀ - alf t

         t = (w₀ - 0) / α

         t = 43.98 / 1.258

         t = 34.96 s

this is the total time, the time remaining is

         Δt = t-10

         Δt = 24.96 s

To find the braking torque, we use Newton's law for angular motion

        τ = I α

the moment of inertia of a circular ring is

       I = M r²

we substitute

         τ = M r² α

we calculate

        τ = 0.625  0.315²  1.258

        τ = 0.078 N m

The total time taken by the wheel to come to rest is 25.18 s and the magnitude of the frictional torque is 25.18 N-m.

Given data:

The initial angular speed of wheel is, [tex]\omega = 7.0 \;\rm rps[/tex]   (rps means rotation per second).

The time interval is, t' = 10.0 s.

The number of rotations made by wheel is, n = 60.0.

The mass of bike wheel is, m = 0.625 kg.

The radius of wheel is, r = 0.315 m.

The problem is based on rotational kinematics. So, apply the second rotational equation of motion as,

[tex]\theta = \omega t-\dfrac{1}{2} \alpha t'^{2}[/tex]

Here, [tex]\theta[/tex] is the angular displacement, and its value is,

[tex]\theta =2\pi \times 60\\\\\theta = 376.99 \;\rm rad[/tex]

And, angular speed is,

[tex]\omega = 2\pi n\\\omega = 2\pi \times 7\\\omega = 43.98 \;\rm rad/s[/tex]

Solving as,

[tex]376.99 = 43.98 \times 10-\dfrac{1}{2} \alpha \times 10^{2}\\\\\alpha = 1.25 \;\rm rad/s^{2}[/tex]

Apply the first rotational equation of motion to obtain the value of time to reach zero final velocity.

[tex]\omega' = \omega - \alpha t\\\\0 = 43.98 - 1.25 \times t\\\\t = 35.18 \;\rm s[/tex]

Then total time is,

T = t - t'

T = 35.18 - 10

T = 25.18 s

Now, use the standard formula to obtain the value of braking torque as,

[tex]T = m r^{2} \alpha\\\\T = 0.625 \times (0.315)^{2} \times 1.25\\\\T = 0.0775 \;\rm Nm[/tex]

Thus, we can conclude that the total time taken by the wheel to come to rest is 25.18 s and the magnitude of the frictional torque is 25.18 N-m.

Learn more about the rotational motion here:

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Answer:

C. planetary accretion

Explanation:

Astronomers think planets formed from interstellar dust gases that clumped together in a process called planetary accretion.

Answer:

[tex]\boxed{\sf C. \ planetary \ accretion }[/tex]

Explanation:

Astronomers think planets formed from interstellar dust and gases that clumped together in a process called planetary accretion.

Planetary accretion is a process in which huge masses of solid rock or metal clump together to produce planets.

Answer:

Hey there!

PE=mgh, so as height decreases, so does the potential energy.

KE=mv^2, so as velocity increases, kinetic energy increases.

Thus, the correct answer would be Decreases, Increases.

Let me know if this helps :)

Answer:

e. The torque is the same for all cases.

Explanation:

The formula for torque is:

τ = Fr

where,

τ = Torque

F = Force = Weight (in this case) = mg

r = perpendicular distance between force an axis of rotation

Therefore,

τ = mgr

a)

Here,

m = 200 kg

r = 2.5 m

Therefore,

τ = (200 kg)(9.8 m/s²)(2.5 m)

τ = 4900 N.m

b)

Here,

m = 20 kg

r = 25 m

Therefore,

τ = (20 kg)(9.8 m/s²)(25 m)

τ = 4900 N.m

c)

Here,

m = 8 kg

r = 62.5 m

Therefore,

τ = (8 kg)(9.8 m/s²)(62.5 m)

τ = 4900 N.m

Hence, the correct answer will be:

e. The torque is the same for all cases.

Answer: Only Tech B is correct.

Explanation:

First, tech A is wrong.

The circuits that can be compared with links in a chain are the series circuit, and it can be related to the links in a chain because if one of the elements breaks, the current can not flow furthermore (because the elements in the circuit are connected in series) while in a parallel circuit if one of the branches breaks, the current still can flow by other branches.

Also in a parallel circuit, the sum of the currents of each path is equal to the current that comes from the source, so Tech B is correct, the total current is equal to the sum of the currents flowing in each branch of the circuit.