Find the center of mass of a one-meter long rod, made of 50 cm of iron (density 8gcm3) and 50 cm of aluminum (density 2.7gcm3).

Hi there!

a)
When the motor is first turned on, the coils are initially stationary. Thus, there is no change in magnetic flux and, consequently, no induced emf.

Therefore:
[tex]iR = \epsilon - \epsilon_{back}[/tex]

Since there's no back emf:
[tex]iR = \epsilon[/tex]

Solving for i using Ohm's Law:
[tex]i = \frac{\epsilon}{R}\\\\i = \frac{120}{10} = \boxed{12.0 A}[/tex]

b)

We are given that at max speed, the back EMF is 70.0 V.

Using the same equation as above:
[tex]iR = \epsilon - \epsilon_{back}[/tex]

Plugging in the values:
[tex]10i = 120 - 70 \\\\10i = 50 \\\\[/tex]

Solving for current:
[tex]i = \frac{50}{10} = \boxed{ 5.0 A}[/tex]

The statement that water boils at a temperature below 100 degrees in a pressure cooker is correct

The term freezing refers to the temperature at which a liquid is turned into a solid.

The following is the sorting of the statements into those that are correct and incorrect.

Water boils at a temperature below 100 degrees at high altitudes - correct

Water expands on freezing - correct

Water contracts on freezing - incorrect

Water boils at a temperature below 100 degrees in a pressure cooker - correct

Water boils at 100 degrees under normal pressure - correct

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The speed of the second ball after impact is 1.43 m/s at 60.8⁰.

Apply the principle of conservation of linear momentum;

0.6(2) = 0.6(1.5 sin30) + 0.6(vy)

1.2 = 0.45 + 0.6vy

0.6vy = 0.75

vy = 0.75/0.6

vy = 1.25 m/s

0.6(2) = 0.6(1.5 cos30) + 0.6(vx)

1.2 = 0.78 + 0.6vx

0.6vx = 0.42

vx = 0.42/0.6

vx = 0.7 m/s

v = √(vy² + vx²)

v = √(1.25² + 0.7²)

v = 1.43 m/s

θ = arc tan(vy/vx)

θ = arc tan (1.25/0.7)

θ = 60.8⁰

Thus, the speed of the second ball after impact is 1.43 m/s at 60.8⁰.

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Answer:

It is the tendency

of an object to resist any change in its state of motion .

Explanation:

if I am right mark my answer as brainliest

The angle above the horizontal of the motion of mass A + B after the collision. as well as others are mathematically given as

According to the collision hypothesis of chemistry, chemical reactions happen when two molecules or atoms collide.

Generally, the equation for Collison equilibrium is  mathematically given as

For horizontal motion

mvAx+m2vAx = 2mvfx

For vertical motion

-mvAy+m2vAy = 2mvfy

vfy = 1/2 vAy

[tex]\tan \theta f = vfy/vfx \\\\\tan \theta f = 1/3 vAy/vAx \\\\\tan \theta f = vAy/vAx \\\\\theta f = tan-1 ( 1/3 tan (56) )\\\\[/tex]

[tex]\theta f = 26.3 \deg[/tex]

(b)

[tex]v fy = vf sin \theta f\\\\vAy = vA sin theta i\\\\vf/vA = vfy/vAy sin( \theta i)/sin(\theta f)\\\\vf/vA = 1/2 sin(56)/sin(26.3) \\\\[/tex]

vf/vA= 0.94

(c)

[tex]Ef/Ei = \frac{(1/2 * (2m) * (vf)^2) }{ (1/2 * m * (vA)^2) + 1/2*m*(2vA)^2) ]}[/tex]

2vf^2 / 5vA^2 = 0.35

In conclusion, The angle above the horizontal of the motion of mass A + B after the collision. as well as others

[tex]\theta f = 26.3 \deg[/tex]

vf/vA= 0.94

2vf^2 / 5vA^2 = 0.35

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Considering the definition of kinetic energy, the housefly has a kinetic energy of 0.00242 J.

Kinetic energy is a form of energy. It is defined as the energy associated with bodies that are in motion and this energy depends on the mass and speed of the body.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a given mass and in a rest position, until it reaches a given speed. Once this point is reached, the amount of accumulated kinetic energy will remain the same unless there is a change in speed or the body returns to its rest state by applying a force to it.

The kinetic energy is represented by the following expression:

Ec= ½ mv²

Where:

In this case, you know:

Replacing in the definition of kinetic energy:

Ec= ½ ×0.00100 kg× (2.20 m/s)²

Solving:

Ec= 0.00242 J

Finally, the housefly has a kinetic energy of 0.00242 J.

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(a)The acceleration of the 1,400-kg boat will be 0.425 m/sec²

(b) If it starts from rest, the distance through which the boat moves in 20.0 s will be 85 m.

(c)Velocity at the end of that time will be 8.5 m/sec.

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

Given data;

Forwad force acting on the boat,v₁ = 1,800-N

Resistive force acting on the boat,v₂ = 1,200-N

The acceleration of the boat,a

Mass of boat,m = 1,400-kg

Initial velocity of boat,u= 0 m/sec

Distance travelled by boat,S = ?

Time for the boat travels,t = 20.0 s

Final velocity,V = ? m/sec

The net force on the boat;

F = F₁ - F₂

F = 1800 N - 1200 N

F = 600 N

From the defination of force;

F= ma

a = F / m

a = 600 N / 1400 kg

a = 0.425 m/sec²

b)

The distance through which the boat moves is 20.0 s;

[tex]\rm x_f = x_ 0 + v_0 t + \frac{1}{2} at^2 \\\\ x_f = \frac{1}{2}at^2 \\\\ x_f = 0+0 + \frac{1}{2} at^2 \\\\ x_f = \frac{1}{2}\times 0.425 \times (20 )^ 2 \\\\ x_f = 85 \ m[/tex]

c)

The velocity at the end of that time is found as;

[tex]\rm v_f = v_ 0 + at \\\\ v_f =- 0+ at \\\\ v_f = 8.5[/tex] m/sec

Hence the acceleration of the boat, the distance through which the boat moves in 20.0 s, and velocity at the end of that time will be 0.425 m/sec²,85 m, and 8.5 m/sec.

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The election would be given to the members of the House of Representatives who would be able to select either O'Rourke, or Trump only, because they were the only candidates who received more than 15% of the available electoral votes.

The house of representatives are those that has been given the authority to make and pass federal laws.

They are supposed to handle and mischief during elections that may affect the process on order to ascertain the rightful leader.

From the excerpt given, since a recount of the votes where made and the three parties involved had a miscount, the final decision should be made by the house of representatives.

This is because, the house of representatives has the authority to elect the president from the three presidential candidates that received the highest votes.

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The action that will cause the magnetic force to push two magnets closer together: is that of attraction which happens when opposite poles of the magnets approach.

magnetic force can be defined as the effect that is felt by magnetic objects that causes attraction and repulsion.

A magnetic force attracts two magnets when they are in opposite poles and repels them if they are in the same pole.

In conclusion, The action that will cause the magnetic force to push two magnets closer together: is that of attraction which happens when opposite poles of the magnets approach.

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The specific gravity of the object’s material is 5.09.

Weight difference = 9 - 7.2 = 1.8 N = Buoyant force of water

Buoyant Force in water(Fb) = density of water x g x volume of the   body(Vb)

1.8 = 1000 x 9.81 x Vb

Vb = 1.8/9810 cubic meter

Now, in the air;

Weight of body = mg = 9 N

Mass of body,m = 9/9.81 Kg

So,

Density of body = m/ Vb

= 9/9.81 ÷ 1.8/9810

= 5094.44 kg per cubic meter

The specific gravity of body = density of body ÷ density of water

= 5094.44 ÷ 1000

= 5.09

Therefore, Specific gravity of body = 5.09

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Hello!

1.

To solve, we can use the work-energy theorem.

Initially, the rod is at rest. Its center of mass is some height above the surface, so it contains gravitational potential energy.

Finally, the rod has rotational kinetic energy.

To find the initial energy, we have to find where the center of mass is. It is located at the midpoint of the rod, or l/2. To find its height above, though, we have to find its sine component with respect to the angle:
[tex]E_i = mg{\frac{l}{2}}}sin(\theta)[/tex]

Its final energy:
[tex]E_f = \frac{1}{2}I\omega^2[/tex]

About the pivot point, a rod's moment of inertia (I) is 1/3ml².

[tex]E_f = \frac{1}{2}(\frac{1}{3}ml^2) = \frac{1}{6}ml^2\omega^2[/tex]

Now, solving for angular speed:

[tex]E_i = E_f\\\\mg\frac{l}{2}sin\theta = \frac{1}{6}ml^2 \omega^2\\\\3gsin\theta = l\omega^2 \\\\\omega = \sqrt{\frac{3gsin\theta}{l}}[/tex]

Plugging in the values and solving:
[tex]\omega = \sqrt{\frac{3(9.8)sin(70.4)}{2.1}} = \boxed{3.63 rad/s}[/tex]

2.

Let's determine where to place our pivot point. To minimize the number of torques to take into account, let's put the pivot point at the base of the rod.

Now, the only torque we must consider is that produced by the force of gravity.

Recall the equation for torque:
[tex]\tau = r \times F[/tex]

This is a cross-product, where 'r' is the lever arm of the force. This is the perpendicular distance between the line of action of the force and the pivot point.

In this instance, based on our reference angle, this would be the COSINE.

[tex]\tau = rFcos\theta[/tex]

r = distance from pivot point to center of the rod (1.05 m)

F = Force of gravity, mg (19.03 N)

θ = angle of rod from horizontal

Using the rotational equivalent of Newton's Second Law:
[tex]I\alpha = rFcos\theta[/tex]

'I' is the rod's moment of inertia about the pivot point. For a uniform rod, its moment of inertia at its end is 1/3ml².

Therefore:
[tex]I = \frac{1}{3}(1.94)(2.1^2) = 2.85 kgm^2[/tex]

Now, we can solve for the function for angular acceleration.

[tex]\alpha(\theta) = \frac{rF}{I}cos\theta\\\\\alpha(\theta) = \frac{(1.05)(19.03)}{2.85}cos\theta = 7cos\theta[/tex]

This is the angular acceleration of the rod as a function of theta.

Substituting in θ = 0°:
[tex]\alpha(0) = 7cos(0) = \boxed{7 rad/s^2}[/tex]

**Note, we couldn't just use rotational kinematics because the angular acceleration is NOT constant.

Answer:

A. 0.23 ms⁻²

Explanation:

Using the equation:

v² = u² + 2as

where:

v = final velocity (85 kmh⁻¹  =  85 x 0.278 = 23.6 ms⁻¹)

u = initial velocity (0 ms⁻¹)

a = acceleration (? ms⁻²)

s = displacement (1.20 km  =  1.2 x 1000  =  1200 m),

[tex](23.6)^2 = (0)^2 + 2 (a) (1200)[/tex]

⇒ [tex]a = \frac{23.6^2}{2(1200)}[/tex]

⇒ a = 0.23 ms⁻²

This question is health related and seeks to compute the details surrounding a traumatic head injury. See the explanation below.

Traumatic brain injury (TBI), a form of acquired brain injury, occurs when a sudden trauma causes damage to the brain.

TBI can result when the head suddenly and violently hits an object, or when an object pierces the skull and enters brain tissue

Final velocity before hitting the ground

V² = 2g*0.56

V² = 2 * 9.8 * 0.56

V = √10.976

V = 3.312 m/s

*** Note that g which is the acceleration of gravity is about 9.8 meters.

1a) Where there is a hardwood floor

-u^2 = -2as

a = 3.312^2/2*0.0019

a = 1,042.08 m/s^2

1b) Duration

t = u/a

= 3.312/1,042.08

t = 3.18 ms

2a) Where there is a carpet on the floor

a = 3.312^2/2*0.013

a = 713.01 m/s^2

t = u/a

=  3.312/713.01

t = 4.65 ms

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The strength of the electric field at that point and the force would this charge experiences at that point will be 4.587 N/C and  12.38 N.

The electric field strength is defined as the ratio of electric force to charge.

Given data;

q₁ = 5.4 C

F₁ is the electric force in case1

E is the electric field =?

F₂ is the electric force in case 2

q₂ is the charge 2

The strength of the electric field at that point is;

F₁=Eq₁

E₁=F/q₁

E₁=25.0 N / 5.4 C

E₁=4.587 N/C

The force would this charge experience at that point when the charge is 2.7 C;

F₂=Eq₂

F₂=4.587 N/C × 2.7 C

F₂ = 12.38 N

Hence the strength of the electric field at that point and the force would this charge experiences at that point will be 4.587 N/C and  12.38 N.

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Hydroelectric plants are used to produce electricity is the statement that best explains the relationship between energy and motion.

There is direct relationship between energy and motion in the process because if we increase the motion of the turbines, more electricity is produced in the generator and vice versa.

So we can conclude that the relationship between energy and motion in the process is directly proportional to each other.

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Answer:

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation.

Hope its helpful!

Answer:

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation.

Explanation:

Considering the Coulomb's Law, the force between the two ballons is 9.216×10⁻⁸ N.

Charged bodies experience a force of attraction or repulsion on approach.

From Coulomb's Law it is possible to predict what the electrostatic force of attraction or repulsion between two particles will be according to their electric charge and the distance between them.

From Coulomb's Law, the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them:

[tex]F=k\frac{Qq}{d^{2} }[/tex]

where:

The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.

In this case, you know that two balloons have a negative charge of 1.6×10⁻¹⁰ C and the balloons are 0.05 m apart.

Replacing in the Coulomb's Law, you get:

[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{(-1.6x10^{-10} C)x(-1.6x10^{-10} C)}{(0.05 m)^{2} }[/tex]

Solving:

[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } \frac{2.56x10^{-20} C^{2} }{(0.05 m)^{2} }[/tex]

[tex]F=9x10^{9} \frac{Nm^{2} }{C^{2} } 1.024x10^{-17}\frac{ C^{2} }{m^{2} }[/tex]

F= 9.216×10⁻⁸ N

Finally, the force between the two ballons is 9.216×10⁻⁸ N.

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Oxygen is used in spacecraft by the persons for respiration.

Rocket engines carry oxygen gas for combustion because combustion need oxygen. Rockets carry an  liquid oxygen up to space with them as a fuel.

Astronauts sealed in a spacecraft that need a continuous supply of oxygen for respiration. Without this oxygen, no person can survive in the spacecraft.

So we can conclude that oxygen is used in spacecraft by the persons for respiration.

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Oxygen is required in spacecrafts for the following:

Spacecraft refers to vehicles which are used to travel to space.

In space, their is little or no oxygen. Thus oxygen is used in the following ways:

In conclusion, oxygen is important for combustion of fuel of the spacecraft engines as well as for breathing by the astronauts.

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The solution to the given question is that the radius of the wire will be 0.378 millimetre approximately

At equilibrium,

Lets assume Tension T in the wire

mass of the block is given as 29 Kg

T sin 12° + T sin 12° = mg  

T sin 12° + T sin 12° = 29 × 9.8

2T sin 12° = 29 × 9.8

T = ( 29 × 9.8 )/2 sin 12°

T = 141.1 / sin 12°

T = 141.1 / 0.2

T = 705.5 Newton

Stress = K × Strain

where K is the elastic modulus of the metal

elastic modulus is given as 7.0 × 10¹⁰ N/m²

T/A = 7.0 × 10¹⁰ × (Δl/l)

A = T × (l/Δl) × (1/ (7.0 × 10¹⁰) )

A = π r² = T / ( (7.0 × 10¹⁰) × ( (1/cos 12°) - 1) )

π r² =  705.5 / ( (7.0 × 10¹⁰) × 0.02234 )

r = √( 705.5 / ( π × (7.0 × 10¹⁰) × 0.02234  ) ) metre

r = √( 705.5 / ( 4910.33 × 10⁶   ) ) metre

r = √( 0.1436 × 10⁻⁶ ) metre

r = ( 0.378 × 10⁻³ ) metre

r = 0.378 millimetre

Thus we have find the radius of the wire by applying stress strain relation which came out to be 0.378 millimetre.

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We obtain the magnitude of the acceleration as   1.55 m/s^2 while its component parallel to the ground is 0.775  m/s^2.

The acceleration refers to change of speed with time. From the question;

It the follows that;

v^2 = u^2 + 2as

And;

u = 0m/s  owing to the fact that motion started from rest

v^2 = 2as

a = v^2/2s

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

a = 1.55 m/s^2

For the acceleration component which is parallel to the ground;

ax = a sin θ

ax =  1.55 m/s^2 cos 60

ax = 0.775  m/s^2

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The average speed of the person over the entire trip is 3.75 m/s.

Average speed = total distance/total time

Average speed = (d + d)/(d/Va + d/Vb)

where;

Average speed = (2Vavb)/(Va + Vb)

Average speed = (2 x 5 x 3)/(5 + 3)

Average speed = 3.75 m/s

Thus, the average speed of the person over the entire trip is 3.75 m/s.

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Explained in the attachment !

The vertical weight carried by the builder at the rear end is F = 308.1 N

Given that:

The weight is carried up along the plane in rotational equilibrium condition

The torque equilibrium condition can be used to solve

We can note that the torque due to the force of the rear person about the position of the front person = Torque due to the weight of the block about the position of the front person

This would lead to:

F(W*cosθ) = mgsinθ(L/2) + mgcosθ(W/2)

F(1cos20)= 197/2(3.10sin20 + 2 cos 20)

Fcos20= 289.55

F= 308.1N

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The time is required for a sound to travel 1 mile (5,280.0 ft) if the air temperature is 0°C is 4.85 sec.

Velocity is largely a vector quantity. It is the fee of alternate distance. The speed of an item transferring can by no means be negative. The pace of a transferring item may be zero.

The velocity of sound waves at zero degrees Celsius is 1087 ft/sec.

Velocity = Distance/Time

Time= Distance/Velocity

The distance to be traveled by sound is 5280 ft

The velocity of sound is 1087 ft/sec

Time = 5280 ft/ 1087 ft/sec

Time = 4.85 sec.

The time required by sound to travel 1 mile at zero degrees Celsius is 4.85 sec.

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The amount that Mary will pay in social security taxes will be $1550.

It should be noted that the current tax for the social security is 6.2% for the employer and 6.2% for the employee.

In this case, let's assume that the income for Mary is $25000, the amount that Mary will pay will be:

= 6.2% × $25000

= 0.062 × $25000

= $1550

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Explanation:

Supernovae play a fundamental role in a great cosmic recycling program. We believe that almost all of the elements in the Universe that are heavier than hydrogen and helium are created either in the centres of stars during their lifetimes or in the supernova explosions that mark the demise of larger stars.

The percent of the braking distance is mathematically given as

P=91.5128%

Generally, the equation for is  mathematically given as

V^2=U^2+2as

Therefore

V^2=u^2+2(-a)s

[tex]s=\frac{u^2}{-2a}[/tex]

Hence.

u'=u-u×0.103

u'=0.206u

v^2=u^2+2as

0=(0.206)^2+2(-a)s'

Hence

[tex]s'=\frac{0.042436u^2}{a}[/tex]

In conclusion,The reduction percentage is

[tex]P=\frac{s-s'}{s}*100\\\\P=\frac{(\frac{u^2}{-2a})-(\frac{0.042436u^2}{a} )}{ \frac{u^}{-2a}}*100\\\\P=\frac{(0.5-0.042436 )}{ 0.5}*100[/tex]

P=91.5128%

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The weight of the person in the first case is 25759.44 N while in the second it is 790.86 N.

Weight is the product of mass and acceleration due to gravity. We have to find the acceleration due to gravity in both cases.

g = GM/r^2

g1 = 6.67 × 10^−11 m3 kg−1 s−2 * 5.98×10^24 kg/(1120 * 10^3 m)^2

g1 = 3.99 * 10^14/1.25 * 10^12

g1 = 319.2 m/s^2

g2 = 6.67 × 10^−11 m3 kg−1 s−2 * 5.98×10^24 kg/( 6370  * 10^3 m)^2

g2 = 3.99 * 10^14/4.06 * 10^13

g2 = 9.8 m/s^2

The weight of the person in the first case is;  80.7 kg * 319.2 m/s^2

= 25759.44 N

The weight of the person in the second case is; 80.7 kg *  9.8 m/s^2

= 790.86 N

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