It is well known that for a hollow, cylindrical shell rolling without slipping on a horizontal surface, half of the total kinetic energy is translational and half is rotational. What fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface?Part AA uniform solid cylinder.Part BA uniform sphere.Part CA thin-walled hollow sphere.Part DA hollow, cylinder with outer radius R and inner radius R/2.

Answer:

FALSE

Explanation:

The earth's lithosphere is divided into 2 types, namely the continental and the oceanic crust. The continental crust is comprised of lighter rock minerals such as silicate minerals, alkali and potash feldspar, and some oxide minerals, whereas, the oceanic crust is comprised of olivine, pyroxene and some feldpars that are comparatively denser than the minerals present in the continental crust. Due to this composition, the oceanic lithosphere is denser than the continental lithosphere.

During the convergent plate motion, the oceanic lithosphere (plate) subducts below the continental lithosphere due to its greater density.

Thus, the above given statement is False.

Answer:

The speed v of the particle at t=5.00 seconds = 43 m/s

Explanation:

Given :

mass m = 5.00 kg

force f(t) = 6.00t2−4.00t+3.00 N

time t between t=0.00 seconds and t=5.00 seconds

From mathematical expression of Newton's second law;

Force = mass (m) x acceleration (a)

F = ma              

[tex]a = \frac{F}{m}[/tex]      ...... (1)

acceleration (a) [tex]= \frac{dv}{dt}[/tex]   ......(2)

substituting (2) into (1)

Hence, F [tex]= \frac{mdv}{dt}[/tex]

[tex]\frac{dv}{dt} = \frac{F}{m}[/tex]

[tex]dv = \frac{F}{m} dt[/tex]

[tex]dv = \frac{1}{m}Fdt[/tex]

Integrating both sides

[tex]\int\limits {} \, dv = \frac{1}{m} \int\limits {F(t)} \, dt[/tex]

The force is acting on the particle between t=0.00 seconds and t=5.00 seconds;

[tex]v = \frac{1}{m} \int\limits^5_0 {F(t)} \, dt[/tex]     ......(3)

Substituting the mass (m) =5.00 kg of the particle, equation of the varying force f(t)=6.00t2−4.00t+3.00 and calculating speed at t = 5.00seconds into (3):

[tex]v = \frac{1}{5} \int\limits^5_0 {(6t^{2} - 4t + 3)} \, dt[/tex]

[tex]v = \frac{1}{5} |\frac{6t^{3} }{3} - \frac{4t^{2} }{2} + 3t |^{5}_{0}[/tex]

[tex]v = \frac{1}{5} |(\frac{6(5)^{3} }{3} - \frac{4(5)^{2} }{2} + 3(5)) - 0|[/tex]

[tex]v = \frac{1}{5} |\frac{6(125)}{3} - \frac{4(25)}{2} + 15 |[/tex]

[tex]v = \frac{1}{5} |\frac{750}{3} - \frac{100}{2} + 15 |[/tex]

[tex]v = \frac{1}{5} | 250 - 50 + 15 |[/tex]

[tex]v = \frac{215}{5}[/tex]

v = 43 meters per second

The speed v of the particle at t=5.00 seconds = 43 m/s

Answer:

frictional force = 0.52 N

Explanation:

diameter of turn table (D1) = 30 cm = 0.3 m

mass of turn table (M1) = 1.2 kg

diameter of shaft (D2) = 1.2 cm = 0.012 m

mass of shaft (M2) = 450 g = 0.45 kg

time (t) = 15 seconds

acceleration due to gravity (g) = 9.8 m/s^{2}

radius of turn table (R1) = 0.3 / 2 = 0.15 m

radius of shaft (R2) = 0.012 / 2 = 0.006 m

total moment of inertia (I) = moment of inertia of turn table + moment of inertia of shaft

I = 0.5(M1)(R1)^{2} + O.5 (M2)(R2)^{2}

I =  0.5(1.2)(0.15)^{2} + O.5 (0.45)(0.006)^{2}

I = 0.0135 + 0.0000081 = 0.0135081

ω₁ = 33 rpm = 33 x \frac{2π}{60} = 3.5 rad/s

α = -ω₁/t = -3.5 / 15 = -0.23 rad/s^{2}

torque = I x α

torque = 0.0135081 x (-0.23) = - 0.00311 N.m

torque = frictional force x R2

- 0.00311 = frictional force x 0.006

frictional force = 0.52 N

The amount of friction force that the brake pad applied to the shaft is 0.52 N

To determine how much friction force does the brake pad applied to the shaft, we need to first know the moment of inertia of the solid turntable, followed by the angular acceleration of the turntable.  

The moment of inertia can be computed by using the formula:

[tex]\mathbf{I = \dfrac{1}{2} MR^2}[/tex]

where;

[tex]\mathbf{I = \dfrac{1}{2} \times (1.2 \ kg) (\dfrac{0.3}{2})^2}[/tex]

I = 0.0135 kgm²

The angular acceleration of the solid turntable is also estimated by using the formula:

[tex]\mathbf{\alpha = \dfrac{\omega _f - \omega _i}{t}}[/tex]

where;

∴

[tex]\mathbf{\alpha = \dfrac{0 -33 rpm \times( \dfrac{2 \pi \ rad/s}{60 rpm})}{15\ s}}[/tex]

[tex]\mathbf{\alpha = -0.23 rad/s^2}[/tex]

Finally, determining the friction force by using the equation of torque;

[tex]\mathbf{\sum \tau = I \times \alpha}[/tex]

From dynamics of rotational motion;

[tex]\mathbf{r \times f= I \times \alpha}[/tex]

[tex]\mathbf{ f= \dfrac{I \times \alpha}{r}}[/tex]

where;

[tex]\mathbf{ f= \dfrac{0.0135 \ kg.m^2 \times 0.23 \ rad/s^2}{(\dfrac{1.2 }{2} \times 10^{-2} m)}}[/tex]

f ≅ 0.52 N

Therefore, we can conclude that the amount of friction force that the brake pad applied to the shaft is 0.52 N.

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If the specific heat capacity of copper is three times that of lead, then it would require three times the amount of heat to cause the same temperature change in equal masses of copper and lead.

The amount of heat added to copper, whose specific heat capacity is three times the specific heat capacity of lead, is indeed three times the amount of heat given to lead when equal masses of copper and lead are heated from room temperature to the temperature of boiling water. This is because the specific heat, which is the heat required to raise the temperature of 1 gram of the substance 1 degree, is directly proportional to the amount of heat. Therefore, a substance with a higher specific heat capacity, like copper, would require more heat to obtain the same temperature change as a substance with a lesser specific heat capacity, like lead.

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The maximum distance the truck can travel without the box sliding can be calculated by finding the maximum static friction force and using it to determine the distance.

To find the maximum distance the truck can travel without the box sliding, we need to determine the maximum static friction force and then use it to calculate the distance. The maximum static friction force can be found by multiplying the coefficient of static friction (0.24) by the weight of the box (20 kg multiplied by the acceleration due to gravity, 9.8 m/s²).

The equation to find the maximum distance is: distance = (1/2) * acceleration * time². Plugging in the values into the equation, we get: distance = (1/2) * 0.24 * 20 kg * 9.8 m/s² * (3.0 s)². Solving the equation gives us the maximum distance the truck can travel without the box sliding.

Answer:

Speed of proton = 1.69 x 10⁷ m/s to the left

Speed of carbon = 3.08 x 10⁶ m/s to the right

Explanation:

Elastic collision means momentum and kinetic energy are conserved.

Mass of carbon = 12 x Mass of proton.

Initial velocity of proton = 2 x 10⁷ m/s

Initial velocity of Carbon = 0 m/s

Final velocity of proton = u

Final velocity of carbon = v

Initial momentum = Final momentum.

m x 2 x 10⁷ + 12m x 0 = m x u + 12m x v

               u + 12v = 2 x 10⁷

               u = 2 x 10⁷ - 12v

Initial K.E = Final K.E

0.5 x m x (2 x 10⁷)² + 0.5 x 12m x 0² = 0.5 x m x u² + 0.5 x 12m x (v)²

               u² + 12v² = 4 x 10¹⁴

              (2 x 10⁷ - 12v)² + 12v² = 4 x 10¹⁴

               4 x 10¹⁴ - 48 x 10⁷v + 144v² + 12v² = 4 x 10¹⁴

                                      156v² = 48 x 10⁷v

                                             v = 3.08 x 10⁶ m/s

                   u + 12 x 3.08 x 10⁶ = 2 x 10⁷  

                     u = -1.69 x 10⁷ m/s

Speed of proton = 1.69 x 10⁷ m/s to the left

Speed of carbon = 3.08 x 10⁶ m/s to the right

In a head-on perfectly elastic collision between a proton and a carbon atom, the speed of each particle remains the same after the collision, but their directions are reversed.

An elastic collision between a proton and a carbon atom can be analyzed using the conservation of momentum and kinetic energy.

First, we need to determine the initial momentum of the proton and the carbon atom. The momentum of an object is calculated by multiplying its mass by its velocity.

Given that the mass of the carbon atom is 12 times the mass of the proton, the initial momentum of the proton is equal to the momentum of the carbon atom.

After the collision, the total momentum of the system must still be conserved. Since the collision is head-on and elastic, only the directions of the velocities of both particles will change. The speed of each particle will remain the same.

Therefore, after the collision, the speed of the proton will still be 2.0 * 10^7 m/s, but its direction will be reversed to the left. The carbon atom will also have a speed of 2.0 * 10^7 m/s, but it will be traveling in the right direction.

Answer:

Explanation:

The tendency of the automobile running on a circular path at high speed to turn towards left or right around one of its wheels , is due to torque by centripetal force acting at its centre of mass about that wheel .

Suppose the automobile tends to turn in clockwise direction about its wheel on the outer edge . A rotational angular momentum is created . To counter this effect , we can take the help of a rotating wheel or flywheel . We shall have to keep its rotation in anticlockwise direction so that it can create rotational angular momentum in direction opposite to that created by centrifugal force on fast moving automobile. Each of them will nullify the effect of the other . In this way , rotating flywheel will save the automobile from turning upside down .

Final answer:

To counteract the tendency for a car to roll over when rounding curves at high speed, a flywheel should be mounted horizontally and perpendicular to the travel direction, with a sense of rotation that produces gyroscopic precession force downward on the inside wheels.

Explanation:

When an automobile rounds a curve at high speeds, the loading on the wheels changes, with the tendency to lighten the load on the inside wheels, which can lead to the car rolling over. To combat this, a large spinning flywheel can help equalize the loading on the wheels. The flywheel should be mounted such that its axis of rotation is horizontal and perpendicular to the direction of the car's travel. The sense of rotation should be such that when the car turns, the gyroscopic precession of the flywheel produces a force that pushes down on the inside wheels. This force counteracts the effect of the weight transfer to the outside wheels, reducing the risk of the car tipping over.

This concept exploits the conservation of angular momentum and the phenomenon known as gyroscopic precession. In a closed system, any attempt to change the direction of the axis of rotation of the spinning flywheel produces a force perpendicular to the direction of the applied force (precession). If the top of the flywheel is tilted outward, the precession force acts downward on the side of the flywheel closest to the inside of the turn, creating a stabilizing effect on the inside wheels.

Answer:

[tex]w_f=1.143\frac{rev}{s}[/tex]

Explanation:

1) Notation

[tex]I_{i}=0.8kgm^2[/tex] (Inertia with arms and legs in)

[tex]I_{f}=3.5kgm^2[/tex] (Inertia with arms out and one leg extended)

[tex]w_{i}=5\frac{rev}{s}[/tex]

[tex]w_{f}=?[/tex]  (variable of interest)

2) Analysis of the situation

For this case we can assume that there are no external forces acting on the skater, so based on this assumption we don’t have any torque from outside acting on the system. And for this reason, we can consider the angular momentum constant throughout the movement.

On math terms then the initial angular momentum would be equal to the final angular momentum.

[tex]L_i =L_f[/tex]   (1)

The angular momentum of a rigid object is defined "as the product of the moment of inertia and the angular velocity and is a vector quantity"

3) Formulas to use

Using this definition we can rewrite the equation (1) like this:

[tex]I_{i}w_{i}=I_{f}w_{f}[/tex] (2)

And from equation (2) we can solve for [tex]w_f[/tex] like this:

[tex]w_f=\frac{I_i w_i}{I_f}[/tex]   (3)

And replacing the values given into equation (3) we got:

[tex]w_f=\frac{0.8kgm^2 x5\frac{rev}{s}}{3.5kgm^2}=1.143\frac{rev}{s}[/tex]

And that would be the final answer [tex]w_f=1.143\frac{rev}{s}[/tex].

Angular speed ( in rev/s ) when arms out and one leg open extended outward is 1.14 rev/s

moment of inertia, I is the measure of distibution of the mass of the body along the axis of rotatiton.

I = angular momentum, L  / angular velocity, ω

L = I * ω

L1 = L2

L1 = angular momentum arms and leg in

L2 = angular momentum arms out and one leg extended

I1 * ω1 = I2 * ω2 conservation of angular momentum

0.8 * 5 = 3.5 * ω2

ω2 = 4 / 3.5

ω2 = 1.14 rev/s

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Most stars have one or more terrestrial planets orbiting within their habitable zones is the correct answer.  

Explanation:                    

According to the science, the  habitable zones  are the region around the stars where one or more terrestrial planets can orbit. A terrestrial planet orbits inhabitable zone is called potentially habitable zone which have  roughly comparable conditions to those of earth.

This situation is a proof stating that most of the stars have one or more terrestrial planets orbiting within their habitable zone.

Answer: E.  and Electroweak in 1961 the only other, as

Explanation:

This is more an English grammar question than a physics question, so taking that perspective, one should look for the answer that best completes the sentence.

Based on the word "first" in the sentence, implying the need for a conjunction to join the two theories and the last part of the sentence does not give a reason but further supports the determination of the theory being the first unified theory.

So, to complete the sentence, the best option is;

Maxwell’s theory of Electromagnetism in 1865 was the first "unified field theory" and Electroweak in 1961 the only other, as no further theory has united the electroweak field with either the Strong (Hadronic) force or Gravity.

Answer:

[tex]v = 0.085 m/s[/tex]

Explanation:

First when man throws the ball then the speed of the man is given as

[tex]m_1v_1 = m_2v_2[/tex]

[tex]97 v = 0.365 \times 11.3[/tex]

[tex]v = 0.042 m/s[/tex]

now ball will rebound after collision with the wall

so speed of the ball will be same as initial speed

now again by momentum conservation we will have

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

[tex]97 \times 0.042 + 0.365 \times 11.3 = (97 + 0.365) v[/tex]

[tex]v = 0.085 m/s[/tex]

Answer:midbrain

diencephalon

cerebrum

medulla oblongata

Explanation:

First-order neurons are sensory neurons with cell bodies in a ganglion, and they carry sensory information to the CNS.

The true statement regarding first-order neurons is b. First-order neuron cell bodies reside in a ganglion.

First-order neurons are sensory neurons, which means they carry sensory information from the periphery of the body to the central nervous system (CNS). They have their cell bodies located in the dorsal root ganglia of the spinal cord or in the sensory ganglia of the cranial nerves.

Option a is incorrect because first-order neurons originate in the periphery of the body, not in the CNS. Option c is incorrect because first-order neurons are sensory neurons, not motor neurons. Option d is incorrect because first-order neurons generally synapse in the spinal cord or brainstem before ascending to the thalamus.

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Answer:

The magnitude of the acceleration of the boy toward the girl is [tex]1.31\ m/s^2[/tex]

Explanation:

It is given that,

Mass of the boy, [tex]m_1=62\ kg[/tex]

Mass of the girl, [tex]m_2=37\ kg[/tex]

The acceleration of the girl toward the boy is, [tex]a_2=2.2\ m/s^2[/tex]

To find,

The acceleration of the boy toward the girl.

Solution,

Let [tex]a_1[/tex] is the magnitude of the acceleration of the boy toward the girl. We know that force acting on one object to other are equal in magnitude but opposite in direction. So,

[tex]F_1=-F_2[/tex]

[tex]m_1a_1=-m_2a_2[/tex]

[tex]a_1=-\dfrac{m_2a_2}{m_1}[/tex]

[tex]a_1=-\dfrac{37\times 2.2}{62}[/tex]

[tex]a_1=-1.31\ m/s^2[/tex]

[tex]|a_1|=1.31\ m/s^2[/tex]

So, the magnitude of the acceleration of the boy toward the girl is [tex]1.31\ m/s^2[/tex]

Answer:[tex]180.86^{\circ}C[/tex]

Explanation:

Properties of Fluid at [tex]100^{\circ}C[/tex]

[tex]P_r=0.711[/tex]

[tex]\rho =0.9458 kg/m^3[/tex]

[tex]c_p=1009 J/kg/k[/tex]

[tex]Flux =6100 W/m^2[/tex]

Drag force [tex]F_d=0.3 N[/tex]

[tex]A=0.2\times 0.5=0.1 m^2[/tex]

drag force is given by

[tex]F_d=c_f\cdot A\rho \frac{v^2}{2}[/tex]

[tex]c_f=\frac{2F_d}{\rho Av^2}[/tex]

[tex]c_f=\frac{2\times 0.3}{0.9458\times 0.1\times 100^2}[/tex]

[tex]c_f=\frac{0.6}{945.8}[/tex]

[tex]c_f=0.000634[/tex]

we know average heat transfer coefficient is

[tex]h=\frac{c_f}{2}\times \frac{\rho vc_p}{P_r^{\frac{2}{3}}}[/tex]

[tex]h=\frac{0.000634}{2}\times \frac{0.9458\times 100\times 1009}{(0.711)^{\frac{2}{3}}}[/tex]

[tex]h=37.92 W/m^2-K[/tex]

Surface Temperature of metal Foil

[tex]\dot{q}=h(T_s-T{\infty })[/tex]

[tex]T_s=\frac{\dot{q}}{h}[/tex]

[tex]T_s[/tex] is the surface temperature and T_{\infty }[/tex] is ambient temperature

[tex]T_s=\frac{6100}{37.92}+20=180.86^{\circ}C[/tex]

Answer:

Nebulae are made of dust and gases—mostly hydrogen and helium. The dust and gases in a nebula are very spread out, but gravity can slowly begin to pull together clumps of dust and gas.

Explanation:

Answer:

See explanation.

Explanation:

Nebulae are interstellar cloud of dust, hydrogen, helium and other ionized gases.

Nebulae are the places where stars are born. Nebulae formed when portions of the interstellar medium undergo gravitational collapse.

Nebulae are made of dust and gases; mostly hydrogen(about seventy-five percent) and helium(about twenty-five percent).

The interstellar gases are very dispersed and the amount of matter adds up over the vast distances between the stars.

Answer:

Angular acceleration will be [tex]1135.5rad/sec^2[/tex]

Explanation:

We have given initial angular speed of a particular disk [tex]\omega _i=646.1rad/sec[/tex]

And it finally comes to rest so final angular speed [tex]\omega _f=0rad/sec[/tex]

Time is given as t = 0.569 sec

From third equation of motion we know that

[tex]\omega _f=\omega _i+\alpha t[/tex]

So angular acceleration [tex]\alpha =\frac{\omega _f-\omega _i}{t}=\frac{0-646.1}{0.569}=1135.5rad/sec^2[/tex]

Answer:

Option E is the correct answer.

Explanation:

Velocity of boat = 10.8 m/s

Velocity of river = 2 m/s

Relative velocity upstream = 10.8 - 2 = 8.8 m/s

            Displacement = Velocity x Time

            1100 = 8.8 x t₁

        Time in upstream, t₁ = 125 s  

Relative velocity downstream = 10.8 + 2 = 12.8 m/s

            Displacement = Velocity x Time

            1100 = 12.8 x t₂

        Time in downstream, t₂ = 86 s  

Total time = t₁ + t₂ = 125 + 86 = 211 s

Option E is the correct answer.           

Final answer:

To find the total time for a complete round trip, we calculate the time taken for both the upstream and downstream trips. The effective speeds for both directions are determined by considering the boat's speed and the river current's speed. The total time for the round trip is 211 seconds.

Explanation:

To determine the time taken for the boat to make a complete round trip in the river, we need to calculate the time taken for each leg of the journey (upstream and downstream) separately and then sum those times. The boat's speed relative to the water is 10.8 m/s, and the river current's speed is 2.00 m/s.

For the upstream trip, the boat's effective speed is reduced by the current, so the boat's speed relative to the riverbank is 10.8 m/s - 2.00 m/s = 8.8 m/s. The distance for the upstream trip is 1100 m, so the time taken upstream is:
Time_upstream = Distance / Speed_upstream = 1100 m / 8.8 m/s = 125 seconds.

For the downstream trip, the boat's effective speed is increased by the current, so the boat's speed relative to the riverbank is 10.8 m/s + 2.00 m/s = 12.8 m/s. The distance for the downstream trip is also 1100 m, so the time taken downstream is:
Time_downstream = Distance / Speed_downstream = 1100 m / 12.8 m/s = 85.9375 seconds, which can be rounded to 86 seconds.

The total time for a complete round trip is the sum of the upstream and downstream times:
Total time = Time_upstream + Time_downstream = 125 seconds + 86 seconds = 211 seconds.

Answer:

6.5 seconds.

Explanation:

Given: h=-16t²+679

When the object reaches the ground, h=0.

∴ 0=-16t²+679

collecting like terms,

⇒ 16t²=679

Dividing both side of the equation by the coefficient of t² i.e 16

⇒ 16t²/16 = 679/16

⇒ t² = 42.25

taking the square root of both side of the equation.

⇒ √t² =√42.25

⇒ t = 6.5 seconds.

Answer:

Total load = 2999.126 kg

Explanation:

Let the spring constant of the shock absorber be k.

We know that the force applied on a spring is directly proportional to elongated length and the constant of proportionality is called spring constant.

Thus

Force, F = kx

where,

x = elongation = 9.1 cm 0.091 m

mass of the people, m = 127 kg

F = weight of the people = mg = 127 x 9.8 = 1244.6 N

substituting these values in the first equation,

1244.6 = k x 0.091

thus, k = 13,676.923 N/m

Now we know that the time period, T of an oscillating spring with a load of mass m is

[tex]T = 2\pi \sqrt{\frac{m}{k} }[/tex]

[tex]\frac{m}{k} = \frac{T^{2} }{4\pi ^{2} }[/tex]

thus,

[tex]m = k\frac{T^{2} }{4\pi ^{2}}[/tex]

T = 1.66s

substituting these values in the equation,

[tex]m =13,676.923\frac{1.66^{2} }{4\pi ^{2}  }[/tex]

m = 2999.126 kg

Answers:

a) [tex]W_{g}=mgh[/tex]

b) [tex]\Delta K=mgh[/tex]

c) [tex]K_{f}=\frac{1}{2}mV_{o}^{2}+mgh[/tex]

d) No

Explanation:

We have the following data:

[tex]m[/tex] is the mass of the projectile

[tex]V_{o}[/tex] is the initial speed of the projectile

[tex]h[/tex] is the height at which the projectile was fired

[tex]\theta=0\°[/tex] is the angle (it was fired horizontally)

[tex]g[/tex] is the acceleration due gravity

a) The Work when the applied force and the distance (height [tex]h[/tex]) are parallel is:

[tex]W_{g}=F_{g} hcos \theta[/tex] (1)

Where [tex]F_{g}=mg[/tex] is the force exerted by gravity on the projetile (its weight)

So:

[tex]W_{g}=mg h cos (0\°)[/tex] (2)

[tex]W_{g}=mgh[/tex] (3) This is the work done by gravity

b) According to Conservation of energy principle the initial total mechanical energy [tex]E_{o}[/tex] is equal to the final mechanical energy  [tex]E_{f}[/tex]:

[tex]E_{o}=E_{f}[/tex] (4)

Where:

[tex]E_{o}=K_{o}+U_{o}[/tex] (5)

Being [tex]K_{o}=\frac{1}{2}mV_{o}^{2}[/tex] the initial kinetic energy and [tex]U_{o}=mgh[/tex] the initial gravitational potential energy

[tex]E_{f}=K_{f}+U_{f}[/tex] (6)

Being [tex]K_{f}=\frac{1}{2}mV_{f}^{2}[/tex] the final kinetic energy and [tex]U_{f}=mg(0)[/tex] the final gravitational potential energy

So: [tex]K_{o}+U_{o}=K_{f}+U_{f}[/tex] (7)

[tex]K_{f}-K_{o}=U_{o}-U_{f}[/tex] (8)

Where [tex]\Delta K=K_{f}-K_{o}[/tex] is the change in kinetic energy.

Hence:

[tex]\Delta K=U_{o}-U_{f}[/tex]

[tex]\Delta K=mgh-mg(0)[/tex]

[tex]\Delta K=mgh[/tex] (9) This is the change in kinetic energy

c) Isolating [tex]K_{f}[/tex] from (8):

[tex]K_{f}=U_{o}-U_{f}+K_{o}[/tex] (10)

[tex]K_{f}=mgh-mg(0)+\frac{1}{2}mV_{o}^{2}[/tex]

Hence:

[tex]K_{f}=mgh+\frac{1}{2}mV_{o}^{2}[/tex] (11) This is the final kinetic energy of the projectile

d)These results will not change if we change the angle, since these equations do not depend on the angle.

The work done by the force of gravity is m*g*h. The change in kinetic energy is also m*g*h. The final kinetic energy is 1/2*m*v0² + m*g*h. These answers don't change with an initial angle change.

(a) The work done by the force of gravity on a projectile is equal to the force of gravity acting downwards (which is m*g, where m is the mass and g is gravity) times the distance over which this force acts, which is h (the initial height above the ground). Therefore the work done by the force of gravity is m*g*h.

(b) The change in kinetic energy is equal to the work done by the force (work-energy theorem). Therefore, the change in kinetic energy is also m*g*h.

(c) The projectile is initially fired horizontally so it only has horizontal kinetic energy. The vertical kinetic energy just before it hits the ground can be found using the energy equation where it is equal to the work done by gravity. The total final kinetic energy would therefore be the initial kinetic energy (1/2*m*v0²) plus the work done by gravity. So the final kinetic energy is 1/2*m*v0² + m*g*h.

(d) The answers to parts (a), (b) and (c) would not change if the initial angle is changed because the vertical and horizontal motions are independent of each other in a projectile motion.

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Answer:

[tex]1.13\times10^{-8} T[/tex]

Explanation:

[tex]E_{o}[/tex] = magnitude of electric field at the point in space = 3.40 Vm⁻¹

[tex]B_{o}[/tex] = magnitude of magnetic field at the point in space = ?

[tex]c[/tex] = speed of electromagnetic wave in vacuum = 3 x 10⁸ ms⁻¹

Magnitudes of electric and magnetic field are related to each other as

[tex]c B_{o} = E_{o}\\B_{o} = \frac{E_{o}}{c} \\B_{o} = \frac{3.40}{(3 \times10^{8} )}\\B_{o} = 1.13\times10^{-8} T[/tex]

Answer:

D. activation, signal transduction, response

Explanation:

The correct sequence for cell signaling given as

1.Signal

2.Reception

3.Transduction

4.Response

In the diagram form

Signal  ⇒  Reception  ⇒  Transduction  ⇒ Response

These should be in the above sequence , except option D all other option does not have a proper sequence.

Therefore option D is correct.

D. activation, signal transduction, response

The correct order of steps in cell signaling is receptor activation, signal transduction, and response.

In the process of cell signaling, the correct order of steps is: receptor activation, signal transduction, and response. This process begins when a signaling molecule binds to a receptor on the cell surface, activating it (receptor activation).

The signal is then converted, or transduced, into a form that can bring about a specific cellular response (signal transduction). Finally, the cell responds to the signal (response). Each of these steps is crucial for proper communication between cells.These sequential steps are fundamental to the proper functioning of cell signaling and are integral to various physiological processes, ensuring cells can appropriately perceive and respond to extracellular signals.

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The equivalent resistance is calculated by taking the inverse of the sum of the reciprocals of each resistance.

The smallest resistance you can obtain by connecting a 36.0-ohm, a 50.0-ohm, and a 700-ohm resistor together can be found by connecting them all in parallel. When resistors are connected in parallel, the equivalent resistance (Requivalent) is smaller than the smallest individual resistance in the network. The formula for the equivalent resistance of parallel resistors is:

1/Requivalent = 1/R1 + 1/R2 + 1/R3

Substituting the given values gives us:

1/Requivalent = 1/36 + 1/50 + 1/700

Calculating the sum of inverses and then taking the inverse of that sum gives us the equivalent resistance for our parallel network. The smallest resistance value, which is Requivalent, can be calculated using this method.

Answer:

Tension in the string, F = 6.316 N

Explanation:

It is given that,

Mass of the Yo - Yo, m = 0.2 kg

Length of the string, l = 0.8 m

It makes a complete revolution each second, angular velocity, [tex]\omega=2\pi\ rad[/tex]

Let T is the tension exist in the string. The tension acting on it is equal to the centripetal force acting on it. Its expression is given by :

[tex]F=\dfrac{mv^2}{r}[/tex]

[tex]F=m\omega^2 r[/tex]

[tex]F=0.2\times (2\pi )^2 \times 0.8[/tex]

F = 6.316 N

So, the tension must exist in the string is 6.316 N. Hence, this is the required solution.

Answer:

Your answer is D) 30 L

Explanation:

(Here's the explanation that I found on a website so Dont copy). You can estimate the fluid deficit by. Body weight in kg x% dehydration = Liters needed to re-establish hydration. 950 pounds / 2.2 pounds per kilogram ( pounds cancel out) = 431.8 kg ( will round up to 432 kg) Then multiply by percent dehydrated: 432kg x 0.07 ( which 7%) = 30 Liters.

Answer:

7.30523 m/s

Explanation:

t = Time taken

u = Initial velocity = 0

v = Final velocity

s = Displacement = 2.72 m

g = Acceleration due to gravity = 9.81 m/s² = a

Equation of motion

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times 9.81\times 2.72+0^2}\\\Rightarrow v=7.30523\ m/s[/tex]

The speed which a quarter would have reached before contact with the ground is 7.30523 m/s

Final answer:

The speed at which the quarter would have reached before contact with the ground if dropped from rest from the top of Robert Wadlow's head is approximately 7.3 m/s.

Explanation:

To determine the speed at which a quarter would have reached before contact with the ground if dropped from rest from the top of Robert Wadlow's head, we can use the principle of conservation of mechanical energy.

Let's denote the height of Robert Wadlow's head as h and the mass of the quarter as m. We are given that h = 2.72 meters.

The potential energy (PE) of the quarter at the top of Robert Wadlow's head is:

PE = m * g * h

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

The kinetic energy (KE) of the quarter just before it hits the ground is:

KE = (1/2) * m * v^2

where v is the speed of the quarter just before it hits the ground.

According to the principle of conservation of mechanical energy, the total mechanical energy at the top of Robert Wadlow's head is equal to the total mechanical energy just before the quarter hits the ground:

PE = KE

Substituting the expressions for PE and KE, we get:

m * g * h = (1/2) * m * v^2

Solving for v^2, we get:

v^2 = 2 * g * h

Substituting the given values for g and h, we get:

v^2 = 2 * 9.8 m/s^2 * 2.72 m

v^2 ≈ 53.2 m^2/s^2

Taking the square root of both sides, we get:

v ≈ 7.3 m/s

So, the speed at which the quarter would have reached before contact with the ground if dropped from rest from the top of Robert Wadlow's head is approximately 7.3 m/s.

Answer:

A 0.083 m/s approx 0

Explanation:

mass of the man is 720 N, the mass of the shoe is 4 N, and the man and the shoe were initially at rest. After throwing the shoe, the shoe had a velocity of 15 m/s. Using conservation of momentum:

since the man and the shoe were initially at rest, their initial momentum is zero

0 = M1V1 + M2V2 where M1 is the mass of the shoe ( 4 / 9.81), V1 is the velocity of the shoe 15m/s, M2 is mass of the man ( 720 / 9.81), V2 is the velocity of the man

MAKE V2 subject of the formula

- M1V1 = M2V2

- M1V1 / M2

substitute the values into the equation

- ((4/9.8) × 15) /( 720 / 9.81) = V2

V2 = - 0.0833 m/s approx 0  

The man moves to the left at approximately 0 m/s.

To solve this problem, we can use the principle of conservation of momentum. The man and the shoe are initially at rest on the frictionless ice, so the initial momentum is zero. When the man throws the shoe to the right, it gains momentum in that direction. According to the conservation of momentum, the man must gain an equal and opposite momentum in the left direction. Since the man weighs more than the shoe, his velocity will be significantly less than the shoe's velocity. Therefore, the man moves to the left at approximately 0 m/s.

Answer: Option (A) is the correct answer.

Explanation:

A corrective action is defined as the action with the help of which a person can avoid a difficulty or problem that he/she was facing earlier.

For example, when the chef checked the temperature of soup using thermometer then it was 120 but his operation's critical limit was 135.

So, to avoid this problem he heated the soup to 165 at 15 seconds following which he got the result as desired.

Therefore, reheating the soup was his corrective action.

Thus, we can conclude that reheating the soup was the corrective action.

In this context, the corrective action taken by the chef was reheating the soup because it was not meeting the operation's critical safe temperature limit.

In the provided scenario, the corrective action referring to steps taken to rectify a situation that does not meet specified standards, is reheating the soup. When the chef figured out the soup was below the operation's critical limit, prompt correction was made to ensure food safety by reheating the soup to 165 for 15 seconds. This measure ensures that any potential harmful microorganisms in the food are eliminated, thus making the food safe to consume.

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Answer:

2442.5 Nm

Explanation:

Tension, T = 8.57 x 10^2 N

length of rope, l = 8.17 m

y = 0.524 m

h = 2.99 m

According to diagram

Sin θ = (2.99 - 0.524) / 8.17

Sin θ = 0.3018

θ = 17.6°

So, torque about the base of the tree is

Torque = T x Cos θ x 2.99

Torque = 8.57 x 100 x Cos 17.6° x 2.99

Torque = 2442.5 Nm

thus, the torque is 2442.5 Nm.

Answer:

A. reduces the magnitude of the force required to stop the ball.

C. increases the contact time of the hand with the ball.

D. does neither increase nor decrease the impulse required to stop the ball.

Explanation:

As we know that the force required to stop the ball is given as

[tex]F = \frac{\Delta P}{\Delta t}[/tex]

here we know that

[tex]impulse = \Delta P[/tex]

so we have

[tex]impulse = m(v_f - v_i)[/tex]

now we know that time to stop the ball is increased due to which the force to stop the ball is decreased

so we have correct answer will be

A. reduces the magnitude of the force required to stop the ball.

C. increases the contact time of the hand with the ball.

D. does neither increase nor decrease the impulse required to stop the ball.