An athlete at the gym holds a 3.5 kg steel ball in his hand. His arm is 76 cm long and has a mass of 4.1 kg . Assume the center of mass of the arm is at the geometrical center of the arm.
"What is the magnitude of the torque about his shoulder due to the weight of the ball and his arm if he holds his arm straight out to his side, parallel to the floor?
"What is the magnitude of the torque about his shoulder due to the weight of the ball and his arm if he holds his arm straight, but 45∘ below horizontal?

The magnetic flux through the circular cross-sectional area of the solenoid is 0.00066 Weber or (Tm²).

A wire tightly twisted in a lengthy, thin coil is a solenoid. Due to its design, the solenoid will have an electromagnet inside of it and a weak magnetic field surrounding it if we pass a current through it.

Equation of solenoid's magnetic field:

By utilizing the convolution operation as well as right hand rule, the magnetic field within a large solenoid is appropriately computed, but all of that can be condensed into:

B = (µ₀ × N × I )/ L

where

B = magnetic field (Tesla)

µ₀ = [tex]\pi[/tex]× 10^-7 (Tm/A ) is the vacuum permeability,

N = number of turns on solenoid,

I = electric current (Ampere)

L = length of the solenoid (m)

According to the question;

A diameter of solenoid 6.00 cm.

A radius of solenoid is 3 cm = 0.03m

Number of turns = 750

The length of solenoid is 10cm = 0.1m

Substitute all the values in equation to fine mangetic filed.

B = ([tex]\pi[/tex]×[tex]10^{-7}[/tex] × 750× 15 )/ 0.1

B = 0.035 Tesla

The formula for magnetic flux is

Ф = B×A

   = B×([tex]\pi[/tex][tex]r^{2}[/tex])

   = 0.035×[tex]\pi[/tex]×[tex].03^{2}[/tex]

Ф = 0.000099

Ф = 99×[tex]10^{-6}[/tex] Weber

Therefore, the magnetic flux through the circular cross-sectional area of the solenoid. is 99×[tex]10^{-6}[/tex] Weber.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \:E = \dfrac{hc}{\lambda} [/tex]

here,

____________________________________

[tex]\qquad \sf  \dashrightarrow \: E = \cfrac{1.99 \times 10 {}^{ - 25} }{7 \times 10 {}^{ - 12} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: E= \cfrac{1.99}{7} \times 10 {}^{ (- 25 + 12)} { } [/tex]

[tex]\qquad \sf  \dashrightarrow \:E= 0.284 \times 10 { }^{ - 13} [/tex]

[tex]\qquad \sf  \dashrightarrow \: E= 2.84 \times 10 { }^{ - 14\:\; } J\: \: [/tex]

so, correct choice is A

The frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.

The frequency heard by the observer is calculated by applying the principle of Doppler effect.

f₀ = f'[(v/v - vs)]

where;

f₀ = 500[(343 / 343 - 36)]

f₀ = 500(343/307)

f₀ = 558.6 Hz

Thus, the frequency heard by an observer in the moving car as he approaches the police car is 558.6 Hz.

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The force require to keep grouper submerged is 8.207N.

According to Archimedes principle  buoyant force of any object must equal to weight of fluid it displaced.

The expression for the force exerted to stay submerged in salt water is

           F = F(b) - w(fish)

 where F(b) = buoyant force

              w(fish) = weight

      now substitute w(b) for F(b)

   →  F = Vρg - w(fish)

where  V = volume of sea water

             ρ = density of sea water

Now by Archimedes principle   V = m(fish)  / ρ(fish)

    →    F = (m(fish) / ρ (fish) ) ρg - m(fish)g

           F =   (85 kg/1015 kg-m^-3) (1.025× 10³ kg-m^-3) (9.8 m/s^2)

                                  -   (85kg)  × 9.8 m/s^2

           F = 841.207N - 833N

           F = 8.207 N

  Hence, the force require to keep grouper submerged is 8.207N.

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When a man pushes a box across a floor, as he increases the force he applies horizontally to the box, then the kinetic friction remains the same.

To find the answer, we need to know about friction.

Thus, we can conclude that, kinetic friction remains the same when we increase the applied force.

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As a guy pushes a box across a floor, the kinetic friction stays constant no matter how much force is applied on the box horizontally.

We must understand friction if we are to find the solution.

We can therefore draw the conclusion that kinetic friction does not change as the applied force is increased.

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Since , e"(h) = M >0

hence ,  At p3 3ε/M  function e(h) has a minimum of function.

In mathematics, point at which the value of a function is less than or equal to the value at any nearby point (local minimum) or at any point (absolute minimum) or the minimum value of a function is the lowest point of a vertex

e(h) = ∈ /h +( [tex]h^{2}[/tex]/6) M

e'(h) = - ∈ /[tex]h^{2}[/tex] + (2h/6) M

putting , e'(h)  = 0

- ∈ /[tex]h^{2}[/tex] + (2h/6) M  = 0

h = [tex](3 /M)^{1/3}[/tex] *  (∈^(1/3))

e"(h) = 2∈ / [tex]h^{3}[/tex] + (2M)/6                          equation 1

substituting value of h in equation 1, we get

e"(h) = 2∈M / 3∈ + M/3

e"(h) = M >0

hence ,  At p3 3ε/M  function e(h) has a minimum

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Answer:

1. 571.43m/s

2. 142.9m and 342.9m

Explanation:

1.Take the difference in time.

1.2-0.7=0.7 seconds

Take the distance between them and divide with differnce in time.

400÷0.7=571.43 seconds.

2.Take the time of the two men and divide by two.

0.5÷2= 0.25 secs

1.2÷2= 0.6 secs

multiply each with the velocity.

0.25×571.43=142.9m

0.6×571.43=342.9m

The weight required to stretch the spring 12.5 cm is 7.5 N (Option A)

The new weight required to stretch the spring can be obtained as follow:

W₁ / L₁ = W₂ / L₂

3 / 5 = W₂ / 12.5

Cross multiply

W₂ × 5 = 3 × 12.5

Divide both sides by 5

W₂ = (3 × 12.5) / 5

W₂ = 7.5 N

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Answer:

Need quiet to concentrate

Are reflective

Are self-aware

Take time making decisions

Feel comfortable being alone

Don’t like group work

Prefer to write rather than talk

And maybe even feel tired after being in a crowd

Explanation:

(a) The diameter of the largest orbit just before the protons exit the cyclotron is 39 cm.

(b) The number of orbits completed by the proton during this 1.0 ms is 14000 revolutions.

What is  kinetic energy?

The kinetic energy of an object is the energy that it possesses due to its motion.

It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Formula of KE:

K.E = 1/2mv²

mv² = 2 K.E

v = sqrt( 2*KE / M)

Here,

(a)

The KE of the medical isotopes = 6.5 MeV

substituting the values,

v = sqrt( 2* 6.5* 1.6* 10^-13 / 1.67* 10^-27 )

v = 3.53 × 10⁷ m/s

Now the centripetal force:

mv² / R = qvB

r = q*v / mv²

r = ( 1.67* 10^-27 * 3.53 × 10⁷ ) / ( 1.9* 1.6* 10^-19 )

r = 0.19415 m

diameter d = 2r,

d= 2(0.19415  m)

d= 0.39 m ≅ 39 cm

(b)

The time period to complete a revolution around the spiral trajectory is:

T = 2πr / v

T = 2*3.14* 0.1941 / 3.53*10^7

T = 0.7 × 10⁻⁷ s

Thus, the number of orbits that the proton does to complete the revolution in 1 ms is:

n = t / T

n = 10^-3 / (0.7*10^-7)

n = 14285.71  ≅ 14000 revolutions

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Your question is incomplete, but most probably full question was:

A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.

(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous

(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?

Answer:

Virgo will be the highest zodiac constellations at night.

Answer:

R = ρ L / A     where R is the resistance and ρ the resistivity:

R2 / R1 = (L2 / A2) / (L1 / A1) = L2 * A1 / (L1 * A2)

R2 / R1 =  (2 L * A) / (L * 2 A) = 1

Their resistances should be the same.

The lion has a kinetic energy of 5000 j, the speed of the lion is  v = 100 / [tex]\sqrt{M1}[/tex]  m/s

Kinetic energy is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy or Kinetic energy is the energy that an object possesses due to its motion. It is basically the energy of mass in motion. Kinetic energy can never be negative and it is a scalar quantity i.e. it provides only the magnitude and not the direction.

given

kinetic energy = 5000 J

speed = ?

since , mass is not given in the question

Let mass of lion will be = M1

kinetic energy = 1/2 * M1 * [tex]v^{2}[/tex]

             5000 J = 1/2 * M1 *  [tex]v^{2}[/tex]

             [tex]v^{2}[/tex] = [tex]\sqrt{10,000 / M1}[/tex]  m/s

              v = 100 / [tex]\sqrt{M1}[/tex]  m/s

The speed of the lion =  v = 100 / [tex]\sqrt{M1}[/tex]  m/s

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The resultant magnitude and direction of the vectors are as follows:

The resultant magnitude and direction of the vectors are as follows:

A. A = √(5.7² + 3.4²)

A = 6.6

θ = tan⁻¹(3.4/5.7)

θ = 30.8° from the x-axis

B. B = √{(-10)² + (-3²)}

B 10.4

θ = tan⁻¹(3/10) + 180

θ = 16.7° + 180°

θ = 196.7° from the x-axis

C. C = √{(12)² + (-20²)}

C = 23.3

θ = 360° - tan⁻¹(20/12)

θ = 300° from the x-axis

D. D = √{(-30)² + (27²)}

D = 40.4

θ = 180 - tan⁻¹(27/30)

θ = 138° from the x-axis

E. E = √{(48)² + (12²)}

E = 49.5

θ = 360° - tan⁻¹(12/48)

θ = 346° from the x-axis

In conclusion, the resultant of the vectors and direction are obtained using the resultant vector formula.

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In order to use the efficiency of a car engine in an optimal way, a maximum engine speed of 2,500 rpm for shifting is recommended for gas engines.

The maximum thermal efficiency of modern gasoline engines is over 50%, but legal cars on the road are only about 20% to 35% when used to power cars.

Unfortunately, even with regular car maintenance such as tuning and oil changes, the efficiency of today's gasoline engines is about 30-35%. In other words, about 65 cents per dollar spent on gasoline is wasted.

EPA's 2020 Automotive Trend Report preliminary data shows that the average fuel economy of 2020 model light trucks has increased to 25.7 miles per gallon (MPG). If this preliminary data holds, it will mark the highest average fuel economy ever for a new light commercial vehicle.

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Increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.

Work is a measure of energy expended in moving an object. It is calculated by multiplying the force by the distance.

According to this question, work is required to move a car from one position to another.

The distance moved from 0 - 30mph is more than that moved from 50 - 60mph, therefore, increasing a car's speed from 0 mph to 30 mph requires more work than that of 50 mph to 60 mph.

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The magnitude of the electric potential difference between the plates is 37.63 V.

Given:

Distance between the plates, d = 9 cm

Surface charge density, ρ = 3.7 nC/m² = 3.7 × 10⁻⁹ C/m²

Calculation:

For two parallel plate conductors, the electric field is given as:

E = ρ/ε₀

where ρ is the charge density

           ε₀ is the permeability of free space

Applying values in the above equation we get:

E = ( 3.7 × 10⁻⁹ C/m²)/(8.85 × 10⁻¹² C²/m)

  = 418.08 V/m

Now, the potential difference between the plates separated by a distance 'd' is given as:

ΔV = Ed

where E is the electric field

           d is the distance of separation between the plates

Applying values in the above equation we get:

ΔV = (418.08 V/m) × (0.09 m)

     = 37.63 V

Therefore, the magnitude of the electric potential difference between the plates is 37.63 V.

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Answer: 37 Celsius and 310.15 K

Explanation:

C/5 = (F-32)/9 = (98.6-32)/9 = 66.6/9 = 7.4

C = 7.4 * 5 = 37 so the temperature is 37 Celsius

K = C + 273.15 = 37 + 273.15 = 310.15 K

Answer:

1.66m/s

Explanation:

here

initial velocity(u): 0m/s

final velocity (v):60km= 60×1000/60×60

:16.6m/s

time taken(t): 10s

now

acceleration:v-u/t

or a: 16.6-0/10

:16.6/10

acceleration: 1.66 m/s

In physics, acceleration is the rate at which the velocity of an object changes in relation to time. The sum of all forces exerted on an object results in its acceleration. The acceleration is  1.66 m/s².

The rate at which velocity, either in terms of speed or direction or both, varies over time is known as acceleration. A circle's motion accelerates despite its constant speed because its direction is continually shifting.

Here

initial velocity(u) = 0m/s

final velocity (v) = 60km

v = 60 × 1000 / 60 × 60

v = 16.6 m/s

Time taken(t) =  10s

Now.

acceleration =  v-u / t

a = 16.6-0/10

a = 16.6/10

a = 1.66 m/s²

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The pattern of organization Alicia chose for her speech outline is referred to as topical.

This type of organization involves the arrangement of subtopics within a large or broad topic.

Alicia talked about speech pathology and the different subtopics include challenges, therapy etc which depicts topical pattern.

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Answer:

80J

Explanation:

K.E = ½ mv²

k.e = ½ * 80*

100²

ke= 4*20

ke= 80 J

Answer: An object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.

Explanation: To find the answer, we need to know more about the kinetic and potential energies.

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

Thus, we can conclude that, an object at rest has no kinetic energy, but it may have potential energy resulting from its location or structure.

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In the pinball game, momentum is transferred from the plunger to the ball.

What is momentum?

Momentum is the quantity of motion of a moving body, measured as a product of its mass and velocity.

The formula of the momentum is: p = m*v

Here a pinball game machine is given.

We know that,

Hence,

In the pinball game, momentum is transferred from the plunger to the ball.

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The amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.

Given:

Depth of the well, h = 22.5m

Mass of heavy-duty steel chain, M = 17.9 kg

The combined mass of the water and bucket, m = 11.3 kg

time taken to raise the bucket out of the water, T = 1.75 min = 105 s

Calculation:

Consider that the center of mass of the steel chain is at the midpoint of the depth of the well.

Now, the work done during the lifting process can be calculated as:

W.D = (Work done in lifting bucket filled with water) + (work done to lift    

                                                                                              the steel chain)

W.D = mgh + Mg (h/2)      -( 1 )

where g is the acceleration due to gravity

Applying values in the above equation we get:

W.D = mgh + Mg (h/2)

       = (11.3 kg)(9.8 m/s²)(22.5 m) + (17.9 kg)(9.8 m/s²)(22.5 m / 2)

       = 2491.65 + 1973.475

       = 4465.125 J

We know that the average power is given as:

P_avg = W.D / T     - ( 2 )

where W.D is the work done during the lifting process

            T is the time taken to raise the bucket out of the well

Applying values in the above equation, we get:

P_avg = W.D / T

           = (4465.125 J)/(105 s)

           = 42.525 W

Therefore, the amount of work done during the lifting process is 4465.125 J and our average power will be 42.525 W.  

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Answer: A

Explanation:

SOLUTION:

Acceleration = Force/mass

= 100N / 2 kgs

= 50 m/s

.

.

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X and Y are two things that travel in the same direction. The mass of the things is the same. 5.0 m/s is the velocity of object x as it moves to the right. The velocity of object y to the left is 3.0 m/s. Objects x and y collide and adhere to one another. Following their collision, they both move at a speed of 1.0 m/s to the right.

Their velocity after colliding is 1.0 m / s to the right.

What is the velocity during the collision?

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The particle that was given off in the reaction beta rays is β–. Option C

A nuclear reaction will involve the change in the nucleus of an atom. It often leads to the production of new nucleus. As we can see the equation, there was a transformation from nitrogen nucleus to oxygen atom.

Thus, the particle that was given off in the reaction beta rays is β–. The fact that the mass number remained the same but the atomic number increased by one unit from left to right implies that a beta decay has occurred.

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Answer:

the answer to your question will be D

Explanation:

5 N* 3S =3.25