Calculate the mass for an object with 5,000J of PE on top of a 200m tall building.

The volume of a gas in liters if 2.95 mol has a pressure of 0.760 atm at a temperature of 52oc is 116.584.

volume of a gas = 2.95 × 0.760 × 52 = 116.584

We understand temperature as the average translational kinetic energy linked to the disordered motion of atoms and molecules, and the kinetic temperature as derived from kinetic theory provides reasonable accuracy. In light of the fact that higher energy molecules are colliding with lower energy molecules and transferring energy to them, it follows naturally that the flow of heat is from a region of high temperature toward a region of lower temperature. Since temperature only measures the kinetic energy portion of internal energy, it is not directly proportional to internal energy, so two objects with the same temperature do not necessarily have the same internal energy (see water-metal example). The three commonly used temperature scales are used to measure temperatures (Celsius, Kelvin, and Fahrenheit).

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After solving the equation the cases according to total energy C<A<B= D

What is spring constant ?

A measure of the spring's stiffness is its spring constant, or k. Various springs and materials have different effects. The spring becomes stiffer and more challenging to extend the bigger the spring constant.

What is equilibrium  ?

When all external forces (including moments) acting on an item are balanced, the object is said to be in equilibrium in a reference coordinate system. Thus, all external moments and forces acting on this item result in zero as a net effect.

Case A; k effective = K

Case B ; strings connected in parallel

               K effective = 2A

Case c; strings connected in series

  K effective = k/2

Case D ; strings connected in parallel

K effective = 2K

So, C,<A<B= D

T= 2π[tex]\sqrt{m/Keffective}[/tex]

T∝ [tex]\sqrt{1/K effective }[/tex]

Accordingly time period ranking is C>A>B= D

E total = 1/2 K effective a²

E total ∝ k effective

so ranking will be

C<A<B= D

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The statement of dalton's law of partial pressures is the total pressure by a mixture of gases is equal to the sum of the partial pressures of each gas that makes up the mixture. The correct answer is B.

The pressure that each gas would produce if it occupied the same volume of the mixture at the same temperature alone is referred to as the partial pressure.

the law of partial pressure known as Dalton's Law A combination of gases exerts a pressure that is equal to the sum of the pressures that each gas exerts on its own. Each gas exerts pressure directly proportional to the amount of that gas present in the gas mixture.

In closed vessels over water, Dalton found that oxygen interacted with either one or two volumes of nitric oxide. This ground-breaking observation of integral multiple proportions served as crucial experimental support for his fledgling atomic theories.

Your question is incomplete but most probably your full question was

Which of the following is a statement of daltons law of partial pressure

A. The total pressure of a mixture of gases is the product of the partial pressures of each gas in the mixture

B. The total pressure of a mixture of gases is the sum of the partial presaure of each gas that makes up the mixture

C. gases can exist as mixtures at STP only

D. in a mixture of two gases, the pressure of each gas is 1/2 of the total pressure

E. the partial pressure of a gas is equal to the total pressure of the mixture

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The difference between the highest frequency heard by a student in the classroom and the initial frequency of the sound generator is =582.5 Hz and 619.2 Hz

F(s) = 600 Hz, the generator's frequency

The rope's length is r = 1 m.

rotating frequency, w = 100 rpm

First, we determine the generator's speed, v (g)

v(g) = r.w

However, it should be remembered that we must convert the whirling speed from rpm to rad/s.

100 rpm is 100*2/60 rad/s.

100 rpm = 200π/60

100 rpm = 620.4 / 60

10.47 rad/s for 100 rpm.

Now, we employ this to determine the generator's speed.

v(g) = r.w

v(g) = 1 * 10.47

v(g) = 10.47 m/s

The frequency is estimated when approaching the generator as

F(a) = F(s) / [(v(g)/v) - 1)]

F(a) = 600 / [1 - (10.47/343)]

F(a) = 600 / 0.969

F(a) = 619.2 Hz

On the other hand, the frequency of the retreating generator is

F(r)=F(s)/[1 + (v(g)/v)]

F(r) = 600 / [1 + (10.47/343)]

F(r) = 600 / 1.030

F(r) = 582.5 Hz

The highest and lowest frequencies are therefore 619.2 Hz and 582.5 Hz, respectively.

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Based on the information provided, the statement that correctly describes the magnetic fields from the wires in the region between the wires and provide evidence to support this claim is that the magnetic fields are in opposite directions, because the region is on opposite sides of the wires: to the right of wire 1 and to the left of wire 2. (Option B)

A magnetic field refers to a vector field that defines the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A current traveling through a loop of wire creates a magnetic field along the axis of the loop. The direction is obtained from the right-hand rule. Hence, the direction of the field inside the loop can be found by curling the fingers of the right hand in the direction of the current through the loop; the thumb then points in the direction of the magnetic field.

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Subcutaneous tissue fat functions similarly to insulation in your home in numerous areas of your body. This fat absorbs shock to underlying structures and aids in protecting the deep body systems like muscles and organs from temperature changes.

Which of the following causes a decrease in metabolism?

Crash dieting, starvation, or fasting all cause the body to reduce its metabolism in an effort to conserve energy. BMR can fall by up to 15%, and if lean muscle mass is lost as well, BMR is further decreased.

Which tissue serves as insulating material, a cushion of protection, and a source of energy?

The bottom layer of skin on your body is called the hypodermis. It has a variety of purposes, such as defending your body from injury, insulating your body, storing energy, and attaching your skin to your muscles and bones.

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The acceleration of the car when Vₓ = 16.7 m/s  is 8.05 m/s² .

In the question ,

it is given that ,

east ward component of the the car's velocity is Vₓ(t) = (0.970 m/s³)t²

To find the acceleration of the car, we differentiate velocity with respect to t ,

We get ,

aₓ = dVₓ/dt = d/dt (0.97 m/s³)t²

aₓ = (2 × 0.97 m/s³)t

aₓ = (1.94 m/s³)t    ...equation(1)

given that Vₓ = 16.7 m/s .

So , 16.7 = (0.97 m/s³)t²

t² = 16.7/0.97

t = 4.15 sec .

Substituting, time t = 4.15 in the  equation(1) , we get

aₓ = 1.94 × 4.15

= 8.05 m/s²

Therefore , the requires acceleration is 8.05 m/s²  .

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An ac voltage source is attached to an LCR series circuit. The phase difference between current and voltage is /3 when L is taken out of the circuit. The circuit has a power factor of one.

LCR series circuit, which stands for inductance-capacitance-resistance, can only function as one of the three components on its own. It is also employed to boost voltage and raise the voltage that travels through each component of the circuit individually. This voltage has the potential to be far higher than the external voltage that is applied to the electrical circuit.

IXc = sin (pi/4)

Xc = R

The phasor will look like this when C is eliminated.

Xl = Xc

The supplied circuit is therefore in resonance.

LCR circuit's power factor is 1 cos(o).

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a) The magnitude of the magnetic flux through the curved part of the surface is 0.70 mWb.

b) The magnetic flux through the curved part of the surface is 12.56 cm².

The direction of the magnetic flux through the curved part of the surface is outward.

The magnetic flux through a surface is given by the equation:

Φ = B × A

where Φ is the magnetic flux, B is the strength of the magnetic field, and A is the area of the surface.

In this case, the strength of the magnetic field is given as 0.30 T, and the area of the curved surface is given as the surface area of a hemisphere with a radius of 2.0 cm, which is:

A = 2 × π × r² = 2 × 3.14 × (2.0 cm)² = 12.56 cm²

Plugging these values into the equation gives us a magnetic flux of:

Φ = (0.30 T) × (12.56 cm²) = 0.70 mWb

The direction of the magnetic flux is given as outward for both the top and bottom faces, so the direction of the magnetic flux through the curved part of the surface is also outward.

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Moon Illusion is an Optical Phenomenon. This occurs because when the moon is near the horizon, Earthly things that resemble the moon on your retina generate a misunderstanding or inaccurate perception of distance and size.

The brain interprets the low moon as being bigger since it is lower in the sky than the higher moon.

The mechanism behind size-distance perception in everyday life, which transforms planar pictures that fall on the retina into a perception of hard objects moving in space, is related to the moon illusion.

What happens when the mechanism acts in an uncommon circumstance is what causes the moon illusion. In typical perception, the angular size of the light image stimulating our eyes expands or shrinks as rigid objects move in depth (distance).

The sense of hard objects with shifting depth perception is produced naturally by the brain in response to these changing stimuli. The ground and horizon make the moon appear comparatively close when it is close to the horizon.

Due to the moon's shifting apparent position in depth while the light stimulus stays constant, the moon appears extraordinarily huge due to the brain's size-distance mechanism.

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It is not desirable to have large areas of forest plants replaced by oil palms because animals and plants may be affected in regions of fragmented habitat, which is an important issue in ecosystem disturbance and loss of biodiversity.

Ecosystem disturbance is an ecological concept that makes reference to the different human activities and natural processes (such as earthquake catastrophes) that are to break the delicate internal homeostatic equilibrium of the ecosystems. Moreover, loss of biodiversity refers to the loss of variation due to the extinction of populations and even species.

Therefore, with this data, we can see that ecosystem disturbance and loss of biodiversity are fundamental processes and they have been associated with the process of replacement of native trees in natural forests with oil palms, which have negative outcomes for the surrounding environment.

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(a) The total distance of the bus is 10 m.

(b) The total displacement of the bus is 2.83 m.

(c) The average speed of the bus is 2 m/s.

(d) The average velocity of the bus is 0.57 m/s.

The total distance of the bus is the sum of all the distance covered by the bus and it is calculated as follows;

distance = 2 m + 5 m + 3 m = 10 m

The total displacement of the bus is calculated as follows;

resultant horizontal displacement = 2 m east

resultant vertical displacement = 5 m - 3 m = 2 m North

Total displacement = √ ( 2² + 2² )

Total displacement = 2.83 m

The average speed is calculated as;

average speed = 10 m / 5 s = 2 m/s

The average velocity is calculated as;

average velocity = 2.83 m / 5 s = 0.57 m/s

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The sun can fuse hydrogen for over ten billion years, while a star twice as massive runs out of hydrogen in two billion years.

Given that they have more fuel than stars with smaller masses, you may assume that big stars would endure longer. However, the cores of these monsters burn through fuel more quickly because they are much hotter and fuse elements at far faster rates.

For more than 10 billion years, a star like a sun can happily burn hydrogen into helium. But in under two billion years, a star twice as massive as the sun exhausts its supply of hydrogen. In just a few hundred million years, a star eight times as massive as the Sun will run out of fuel. Additionally, the speed of each phase in the fusion process increases over time.

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larger in a rope with a smaller angle.

When nellie newton dangles by a pair of ropes, each at different angle from the vertical, the rope tension will be greater in the rope having the larger in a rope with a smaller angle.

The pulling force transmitted axially by a string, rope, chain, or other similar object, or by each end of a rod, truss member, or other similar three-dimensional object is referred to as tension. The action-reaction pair of forces acting at each end of said elements can also be referred to as tension. The polar opposite of compression might be tension.

The ends of a string or other object that transmits tension will apply forces in the direction of the string at the point of attachment to the objects to which it is connected.

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A jet of water squirts out horizontally from a hole near the bottom of the tank shown in the figure. If the hole has a diameter of 3.80 mm, the height h of the water level in the tank is 44.1 cm

The height of the water level can be calculate as follows:

According to kinematics, if the water's initial velocity when it exits the tank is, its horizontal range is given by

d = v√(2y/y)

where, y is the acceleration caused by gravity and is the vertical distance from the ground to the hole.

Torricelli's law provides the velocity of the fluid flowing out of the hole. the velocity  of water coming out of the hole is

v=√(2gh)

where,h is the tank's top-to-bottom distance, as depicted in the picture.

The horizontal range equation is used to calculate the water's exit velocity from the hole:

d= v√(2y/g)

v= d x √(g/2y)

and since d= 0.600 m an y= 1 m

v= 0.600  x √(9.8/2(1))

v= 0.600 x 4.9

v= 2.94 m/s

Now, we can  use Torricelli's theorem to find the height

v=√(2gh)

h = v²/2g

h = (2.94)² / 2 (9.8)

h = 0.441 m = 44.1 cm

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Answer:

ΔS= -1 J/K

Explanation:

Using this data

Heat Q= -256.0J

Temperature T=420.0 K

To find

Entropy change ΔS

Solution

We know that the entropy change of system is ΔS is given by

ΔS=Q/T

We have take heat value Q as negative because the heat is removed from heat reservoir

So

ΔS=(-256J/470K)

ΔS= -1 J/K

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The centripetal force is 7.3 m/s and tension  is 7.30 m/s .

What is tension ?

Any two physical objects in touch have the ability to exert forces on one another. Based on the kinds of objects in touch, we give these contact forces various names. When a rope, string, chain, or cable is one of the things applying the force, the force is referred to as tension.

What is speed ?

Speed is the rate of change in location of an item, expressed in metres per second. For instance, the speed of an item is one metre per second if it starts at the origin and goes three metres in three seconds. Speed is easily calculated by dividing a distance by a time.

Tension (force) in string = mv²/R = 0.90v²/0.80 = 1.125v²

Tension (force) in string = 60.0 N

set Tensions equal:

1.125v² = 53.33

v = v53.33

v = 7.30 m/s (speed of mass at which string breaks)

circumference of path mass travels = 2pR = 5.02 m

time of one rev that gives a tangential speed of 7.3 m

T = 5.02/7.3 = 0.69 sec

rev/sec = 1/0.69 = 1.45 rps

60 x 1.45 = 87 rpm

centripetal force = Tension

mv^2/r = T

0.9xv^2/0.8 =60

v=7.3 m/s

Therefore, the centripetal force is 7.3 m/s and tension  is 7.30 m/s .

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Using theory on the Cartesian method, starting with the smallest problem and progressing to the most complex, refers to the rule known as synthesis.

This has been a method developed by René Descartes with which he sought to find what was the truth.

The method established by René Descartes contains four fundamental rules or principles that are:

Among all these rules, the synthesis is the one that indicates that you should start with the smallest problem and progress to the most complex.

The performance of a digital communication system is quantified by the probability of bit detection problems in the presence of thermal noise.

In the context of wireless communications, the major source of thermal noise is the addition of random signals arising from the vibration of atoms in the receiver electronics.

Gaussian: The probability distribution of the noise samples is Gaussian with a zero mean, i.e., in the time domain, the samples can acquire both negative and positive values in addition.

the values near zero have a higher chance of occurrence while the values far away from zero are less likely to appear.

As a result, the time domain average of a greater number of noise samples is equal to zero.

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Don is attempting to build muscle mass for his first body-building competition. According to the American College of Sports Medicine, he should be eating 1.5 to 1.7 grams per kilogram of body weight of protein per day.

Muscle is a system of coordinated contractile tissues that is used to perform tasks more effectively. The physical appearance and cell location of the muscular systems in humans are used to classify them. Strained (or skeletal), cardiac, and smooth muscles are the three categories (or nonstriated). The majority of the muscular tissue in the body is striated muscle, which is mostly connected to the skeleton. The somatic nervous system directs the multinucleated fibers, which cause stresses on the skeleton like those produced by pulleys and levers to cause movement. Sinoatrial node, the pacemaker of the heart, controls the rhythmic contraction of cardiac muscle. Cardiovascular muscle is a particular striated muscle with several centrally positioned nuclei that is made up of elongated cells, however it is not controlled voluntarily. Blood lines the smooth muscle of the viscera.

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 The speed of a bobsled is increasing because it has an acceleration of 2.4 m/s2. at a given instant in time 1363.6N.

Acceleration refers to the rate at which the velocity and direction of a moving object change over time. Anything is said to be sped when it goes straighter and faster or slower. Therefore, even though the speed is constant, travel on a circle increases due to the constant change in direction.

The rate at which a displacement varies is measured by its velocity. Speed changes occur at an accelerated rate. Its magnitude and orientation are both present, making it a vector quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.

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The payback period of the new equipment is closest to 17.8%

Simple rate of return is equal to annual operating income minus the initial investment.

=$65000/365000    

=17.8%

The payback period describes how long it will take to return the cost of an investment. The time it takes for an investment to break even can be summed up in this way. The payback period is important because people and businesses invest money primarily to be compensated. The payback period is the amount of time an investor would need to invest in a project before they would be able to repay their initial investment. The investment's break-even point is closely related to it.

Instead of using the units of a break-even analysis, Payback Period employs years to quantify investment opportunities and risk in a rapid and straightforward manner.

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It's called the Phantom because the galaxy's surface brightness is low.

Because of the galaxy's low surface brightness, it is known as the Phantom. Of all the Messier objects that amateur astronomers view using tiny telescopes, it is the most challenging to locate. The galaxy almost faces Earth, which accounts for the low surface brightness.

M74 is a star in the constellation Pisces that is around 32 million light-years from Earth. Through modest telescopes, the galaxy appears as a dim patch of light with an apparent magnitude of only 10. The ideal time to view it is around November. A spiral galaxy with a majestic pattern, M74 is the ideal illustration.

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The height of the cliff that a stone is dropped from the top, the splash it made as it hit the water below was heard 5.0 s later is 857.5 m.

Sound can bounce when it hits an object that has a hard surface and is not easily penetrated by waves. Examples of objects that can reflect sound are glass walls, iron, zinc, cave walls, and seabeds.

This reflected sound can be used to measure the depth of the sea or the distance of the walls of the cave passage. One of the uses of sound reflection is to know the depth of the sea or the distance of the cave walls.

The equation to determine the distance is:

s = ½ (v) (t)

s = distance or height

t = time

v = velocity of the sound wave (343 m/s)

We have,

Time  = 5.0 s

Velocity of the sound wave = 343 m/s

So, the height of the cliff:

s = ½ (v) (t)

= ½ (343) (5)

= 857.5 m

The question is incomplete, it should be:

A stone is dropped from the top of a cliff. The splash it makes when striking the water below is heard 5.0 s later. How high is the cliff?

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The speed of the glider when it reaches the bottom of the track is 4.71 m/s.

[tex]V^{2}[/tex] = μ² + 2as

μ = 0

ν = [tex]\sqrt{2as}[/tex] = √2 × 7.55 × 1.47 = 4.71 m/s

This glider can create lift equal to its weight and can soar into the air at any speed greater than 30 kts. If the aircraft is launched into the wind at, let's say, a surface wind speed of 10 kts, it just needs to travel 20 kts above the ground before taking off. A winch launch is one of the most popular ways of launch, accelerating a glider from zero to sixty miles per hour in less than two seconds using a very powerful winch and lengthy steel cables. Slowest - normally 25 to 60 km/h for recreational gliders (above 50 km/h necessitates use of a safety device), these steel lines (and the glider linked to them) represent a very serious risk to everyone on the grounds.

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The final velocity of the second puck will be 20.61 m/s [S 30.95 E] and the collision will be non-perfectly inelastic.

We know that since there is no external force applied to the system of two pucks, So after the collision, Momentum will remain conserved,

Using Momentum conservation in x-direction:

Px(initial) = Px(final)

[tex]m1*u1x + m2*u2x = m1*v1x + m2*v2x[/tex]

[tex]m1 = m2 = m[/tex] (given)

u1 = Initial speed of m1

= 20.0 m/s at S 45 E

= 20.0 m/s at 45 deg below the positive x-axis

u2 = Initial speed of m2

= 15.0 m/s at S 45 W

= 15.0 m/s at 45 deg below the negative x-axis

v1 = final speed of m1

= 10.0 m/s at S 45 W

= 10.0 m/s at 45 deg below the negative x-axis

u1x = Initial velocity of m1 in x-direction

= [tex]20.0*cos 45[/tex]°

= 14.14 m/s

u2x = Initial velocity of m2 in x-direction

= [tex]-15.0*cos 45[/tex]°

= -10.61 m/s

v1x = Final velocity of m1 in x-direction

= [tex]-10.0*cos 45[/tex]°

= -7.07 m/s

v2x = Final velocity of m2 in x-direction = ?

So,

[tex]m*14.14 + m*(-10.61) = m*(-7.07) + m*v2x[/tex]

[tex]v2x = 14.14 - 10.61 + 7.07[/tex]

[tex]v2x= 10.6 m/s[/tex]

Now Using Momentum conservation in the y-direction:

Px(initial) = Px(final)

[tex]m1*u1y + m2*u2y = m1*v1y + m2*v2y[/tex]

u1y = Initial velocity of m1 in y-direction

= [tex]-20.0*sin 45[/tex]°

= -14.14 m/s

u2y = Initial velocity of m2 in y-direction

= [tex]-15.0*sin 45[/tex]°

= -10.61 m/s

v1y = Final velocity of m1 in y-direction

= [tex]-10.0*sin 45[/tex]°

= -7.07 m/s

v2y = Final velocity of m2 in y-direction = ?

So,

[tex]m*(-14.14) + m*(-10.61) = m*(-7.07) + m*v2y[/tex]

[tex]v2y = -14.14 - 10.61 + 7.07[/tex]

[tex]v2y= -17.68 m/s[/tex]

So we have

v2x = 10.6 m/s and v2y = -17.68 m/s

the final speed of puck 2 will be:

[tex]|v2| = sqrt (10.6^2 + (-17.68)^2)[/tex]

[tex]|v2| = 20.61 m/s[/tex]

the final direction of puck 2 will be:[tex]Direction = arctan (\frac{v2y}{v2x} ) = arctan (\frac{-17.68}{10.6})[/tex]

Direction = 59.05 deg below positive x-axis (Since v2x > 0 and v2y < 0, So puck 2 will be moving in 4th quadrant)

Direction = 90 - 59.05

= 30.95 deg

= S 30.95 E

b) Since both pucks did not stick together after the collision, So this is not a perfectly inelastic collision

Now Using energy conservation:

[tex]KE = KEf - KEi[/tex]

[tex]KE = (\frac{1}{2})*m*v1^2 + (\frac{1}{2})*m*v2^2 - (\frac{1}{2})*m*u1^2 - (\frac{1}{2})*m*u2^2[/tex]

[tex]KE = (\frac{1}{2})*m*[10.0^2 + 20.6^2 - 20.0^2 - 15.0^2][/tex]

[tex]KE = -50.32*m[/tex]

So some amount of energy was lost during the collision, which means the above collision is (non-perfectly) inelastic

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a) The magnitude of the final velocity of the second puck  is 20.61 m/s in the direction 50.3° east-south.

b) This collision is (non-perfectly) inelastic.

According to the rule of conservation of momentum, absent an external force, the combined momentum of two or more bodies operating upon one another in an isolated system remains constant. As a result, momentum cannot be gained or lost.

Let the final velocity of the second puck = v i + V j

Now, applying law of conservation of momentum along x axis:

m × 20.0 × cos45° + m × 10.0 ×(- cos45°) = m × 10 × ( - cos45°) + mv

⇒ v =10.6 m/s.

Applying law of conservation of momentum along y axis:

m × 20.0 × (-sin45°) + m × 10.0 ×(- sin45°) = m × 10 × ( - sin45°) + mV

⇒ V = - 17.68 m/s.

Hence, the final velocity of the second puck = 10.6 i - 17.8 j m/s.

The magnitude of the final velocity of the second puck  

= √{(10.6)² + (-17.8)²} m/s

= 20.61 m/s.

and the direction is = tan⁻¹(-17.8/10.6) = - 59.22°

b) The amount of loss in kinetic energy = 1/2 × m ( 20.0² + 15.0² - 10.0² - 20.61²) joule

= 50.36m joule.

Hence, as loss of kinetic energy happens,  this collision is (non-perfectly) inelastic.

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The magnitude of the horizontal component of the ball's initial velocity is 4.7 m/s .

In the question ,

it is given that ,

the velocity of the ball is ⇒ 5 m/s .

the angle between horizontal and the direction of 5 m/s decreases from 30 degrees to 20 degrees .

Now , θ = 20° .

We know that ,the trigonometric ratio ,  Cos θ is = (Adjacent side)/(Hypotenuse)

given velocity = 5 m/s .

So , Cos(20°) = Vₓ/(5)     ....Vₓ is the horizontal component .

Simplifying further ,

we get ,

Vₓ = 4.7 m/s .

Therefore , The magnitude of horizontal component is 4.7 m/s .

The given question is incomplete , the complete question is

The ball being kicked by a foot and rising at an angle of 30 degrees from the horizontal. The ball has a velocity of 5.0 meters per second. (Neglect Friction) If the angle between the horizontal and the direction of the 5.0 meters per second decreases from 30 degrees to 20 degrees,

What is the magnitude of the horizontal component of the ball's initial velocity ?

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Answer:16

Explanation:

as F=BIL so by placing value's B is magnetic field 4 and i is current 2A and l is length that js 2 m so answer is

Given: i=10A,B=0.15 T,θ=45

∘

and l=2 m

Force on a current carrying wire of finite length =

F

=l(

i

×

B

)

Hence, magnitude of force, F=Bilsinθ

=0.15×10×2×sin45

∘

=

2

3

N

The angular speed of the gate just after it is struck by the unfortunate raven is 2.4375rad/s and during the collision, the angular momentum is conserved but not the linear momentum.

Given mass of square (m) =4kg

length of solid wooden gate (l) =1.5m

mass of raven (m1) = 1.3kg

speed of raven (v1) = 5m/s

speed of bouncing back (v2) = 2.5m/s

Impulse on gate (I) = 1/3ml^2 = 1/3x4x1.5x1.5 = 3kgm^2

(a) using conservation of angular momentum  Li = Lf

1/2mv1L/2 = mv2L/2+Iω

m(v1+v2)L/2 = 3xω

1.3x(5+2.5)x1.5/2 = 3xω

ω = 2.4375rad/s

(b)As momentum is conserved there is no external torque

initial kinetic energy (KE) = 1/2mv1^2 = 1/2x1.3x5x5 = 16.25J

final kinetic energy (KEf) = 1/2mv2^2+Iω^2/2

KEf = 1x1.3x2x2/2+3x2.4375x2.4375/2 = 2.6+ 8.9 = 11.5J

As Kinetic energy is not conserved, the collision is inelastic.

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Complete question: a uniform, 4.0 kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. a 1.3 kg raven flying horizontally at 5.0 m/s flies into this door at its center and bounces back at 2.5 m/s in the opposite direction. (a) What is the angular speed of the gate just after it is struck by the unfortunate raven? (b) During the collision, why is the angular momentum conserved but not the linear momentum?