Nowdothesameproblemwiththepivotatthe toes. A Ballet dancer puts all her weight on the toes of one foot. If her mass is 60 kg, what is the force that has to be exerted by her leg muscle to hold that pose? Assume the pivot is at the toes.

Answer:

v = 1.4 m/s

Explanation:

This problem is about an inelastic collision. The total momentum before the collision is equal to total momentum after (because of the conservation of momentum law):

[tex]m_1v_1-m_2v_2=(m_1+m_2)v[/tex]  (1)

m1: mass of the toy car = 2 kg

m2: mass of the toy truck = 3 kg

v1: speed of the toy car = 1 m/s

v2: speed of the truck car = 3 m/s

v: speed of both car and truck after the collision = ?

In the equation (1) the negative sign of m2v2 is because of the opposite direction of the toy truck respect to the toy car.

You solve the equation (1) for v, and you replace the values of all variables involved:

[tex]v=\frac{m_1v_1-m_2v_2}{m_1+m_2}\\\\v=\frac{(2kg)(1m/s)-(3kg)(3m/s)}{2kg+3kg}=-1.4\frac{m}{s}[/tex]

this velocity is negative, then, the direction of motion of both car and truck is in the direction of the truck

Hence, the speed of both car and truck toys is 1.4 m/s

Answer:

The answer is option 2.

Explanation:

Both sides are pulling the rope with equal force where the rope doesn't move. So they have a balanced forces.

Answer:

λ1 = 0.0129m = 1.29cm

λ2 = 0.00923m = 0.92 cm

Explanation:

To find the distance between the first order bright fringe and the central peak, can be calculated by using the following formula:

[tex]y_m=\frac{m\lambda D}{d}[/tex]    (1)

m: order of the bright fringe = 1

λ: wavelength of the light = 660 nm, 470 nm

D: distance from the screen = 5.50 m

d: distance between slits = 0.280mm = 0.280 *10^⁻3 m

ym: height of the m-th fringe

You replace the values of the variables in the equation (1) for each wavelength:

For λ = 660 nm = 660*10^-9 m

[tex]y_1=\frac{(1)(660*10^{-9}m)(5.50m)}{0.280*10^{-3}m}=0.0129m=1.29cm[/tex]

For λ = 470 nm = 470*10^-9 m

[tex]y_1=\frac{(1)(470*10^{-9}m)(5.50m)}{0.280*10^{-3}m}=0.00923m=0.92cm[/tex]

Answer:

a.  4 V

b. 0.697 A

Explanation:

Magnetic field strength B =  0.732 T

length of rod l = 0.362 m

velocity of rod v = 15.1 m/s

a.  EMF can be calculated as

E = Blv = 0.732 x 0.362 x 15.1 = 4 V

b. If the rod is connected to a conducting rail, with resistance R = 5.74Ω

current I = V/R = 4/5.74 = 0.697 A

the current flows in a clockwise direction

Answer:

Explanation:

12.)

A. Opposite poles attract

B. Same poles repel

13.)

IDK

Answer:

N₂ / N₁ = 13.3

Explanation:

A transformer is a system that induces a voltage in the secondary due to the variation of voltage in the primary, the ratio of voltages is determined by the expression

           ΔV₂ = N₂ /N₁  ΔV₁

where ΔV₂ and ΔV₁ are the voltage in the secondary and primary respectively and N is the number of windings on each side.

In this case, they indicate that the primary voltage is 9.0 V and the secondary voltage is 120 V

therefore we calculate the winding ratio

         ΔV₂ /ΔV₁ = N₂ / N₁

         N₂ / N₁ = 120/9

         N₂ / N₁ = 13.3

s good clarify that in transformers the voltage must be alternating (AC)

Answer:

Explanation:

Let the point source have power P .

At distance r , the intensity I

I = P / 4πr² . If intensity at 6 m and 2 m be I₁ and I₂

I₁ = P / 4π x 6²

I₂ =  P / 4π x 2²

I₁ / I₂ = 2² / 6²

= 1 / 9

I₂ = 9 I₁

Intensity will be 9 times that at 6 m .

Answer

The rate at which the magnetic field is changing is  [tex][\frac{dB}{dt} ] = 0.000467 T/s[/tex]

Explanation

From the question we are told that

   The electric field strength is [tex]E = 3.5mV/m = 3.5 *10^{-3} \ V/m[/tex]

    The radius is  [tex]r = 1.5 \ m[/tex]

The rate of change of the  magnetic  field  is mathematically represented as

        [tex]\frac{d \phi }{dt} = \int\limits^{} {E \cdot dl}[/tex]

Where [tex]dl[/tex] is change of a unit length

     [tex]\frac{d \phi}{dt} = A * \frac{dB}{dt}[/tex]

Where A is the area which is mathematically represented as

     [tex]A = \pi r^2[/tex]

    So

    [tex]E \int\limits^{} { dl} = ( \pi r^2) (\frac{dB}{dt} )[/tex]  

  [tex]E L = ( \pi r^2) (\frac{dB}{dt} )[/tex]  

where L is the circumference of the circle which is mathematically represented as

     [tex]L = 2 \pi r[/tex]

So

     [tex]E (2 \pi r ) = (\pi r^2 ) [\frac{dB}{dt} ][/tex]

      [tex]E = \frac{r}{2} [\frac{dB}{dt} ][/tex]

       [tex][\frac{dB}{dt} ] = \frac{E}{ \frac{r}{2} }[/tex]

substituting values

      [tex][\frac{dB}{dt} ] = \frac{3.5 *10^{-3}}{ \frac{15}{2} }[/tex]

      [tex][\frac{dB}{dt} ] = 0.000467 T/s[/tex]    

Answer:

(a) v-bullet = 399.04 m/s

(b) I = 2.38 kg m/s

(c) T = 2.59 N

Explanation:

(a) To calculate the initial speed of the bullet, you first take into account that the kinetic energy of both wood block and bullet, just after the bullet impacts the block, is equal to the potential gravitational energy of block and bullet when the cord is at 60° respect to the vertical.

The potential energy is given by:

[tex]U=(M+m)gh[/tex]       (1)

U: potential energy

M: mass of the wood block = 1 kg

m: mass of the bullet = 6g = 6.0*10^-3 kg

g: gravitational constant = 9.8m/s^2

h: distance to the ground

The distance to the ground is calculate d by using the information about the length of the cord and the degrees of the cord respect to the vertical:

[tex]h=l-lsin\theta\\\\h=2.2m-2,2m\ sin60\°=0.29m[/tex]

The potential energy is:

[tex]U=(1kg+6*10^{-3}kg)(9.8m/s^2)(0.29m)=2.85J[/tex]

Next, the potential energy is equal to kinetic energy of the block and the bullet at the beginning of its motion:

[tex]U=\frac{1}{2}(M+m)v^2\\\\v=\sqrt{2\frac{U}{M+m}}=\sqrt{2\frac{2.85J}{1kg+6*10^{-3}kg}}=2.38\frac{m}{s}[/tex]

Next, you use the momentum conservation law, in order to calculate the speed of the bullet before the impact:

[tex]Mv_1+mv_2=(M+m)v[/tex]    (2)

v1: initial velocity of the wood block = 0m/s

v2: initial speed of the bullet

v: speed of bullet and block = 2.38m/s

You solve the equation (2) for v2:

[tex]M(0)+mv_2=(M+m)v[/tex]    

[tex]v_2=\frac{M+m}{m}v=\frac{1kg+6*10^{-3}kg}{6*10^{-3}kg}(2.38m/s)\\\\v_2=399.04\frac{m}{s}[/tex]

The speed of the bullet before the impact with the wood block is 399.04 m/s

(b) The impulse is gibe by the change in the velocity of the block, multiplied by the mass of the block:

[tex]I=M\Delta v=M(v-v_1)=(1kg)(2.38m/s-0m/s)=2.38kg\frac{m}{s}[/tex]

The impulse is 2.38 kgm/s

(c) The force on the cord after the impact is equal to the centripetal force over the block and bullet. That is:

[tex]T=F_c=(M+m)\frac{v^2}{l}=(1.006kg)\frac{(2.38m/s)^2}{2.2m}=2.59N[/tex]    

The force on the cord after the impact is 2.59N

Answer:

Explanation:

Apply the law of conversion of energy

[tex]V_f = \sqrt{2gh}[/tex]

where,

h = height of which the bullet and block rise after impact

[tex]h = L - Lcos\theta\\\\h = 2.2 - (2.2*cos60)\\\\h = 1.1m[/tex]

Therefore,

[tex]V_f = \sqrt{2gh}\\\\V_f = \sqrt{2*9.8*1.1}\\\\V_f = 4.64m/s[/tex]

From conservation of momentum principle, [tex]m_Bv_B = 0[/tex]

[tex]m_ov_o + m_Bv_B = (m_b+m_B)V_f\\\\0.006V_o = (0.006+1)*4.64\\\\V_o = 777.97m/s[/tex]

C) The force in the cable is due to the centrfugal force of the system, which is due to the motion of the system is a curved path and weight of the system

[tex]F = \frac{m_b+m_B}{L}V_f^2 + (m_b+m_B)g\\\\F = \frac{0.006+1}{2.2}*4.64^2 + (0.006+1)9.81\\\\F = 19.71N[/tex]

For more information on this visit

https://brainly.com/question/17756498

Answer:

the kinetic energy of the 2 kg mass after the 100 m is equal to 1962 J

Explanation:

mass of block A = 2 kg

mass of block B = 4 kg

distance the blocks were pushed = 100 m

NB: Blocks were pushed the same distance at the same equal time period. And the ground is without friction.

Work done in moving the 2 kg mass along the 100 m distance is,

work = force x distance moved

force exerted by the 2 kg mass = 2 x 9.81 m/s^2(acceleration due to gravity)

force = 19.62 N

therefore,

work done = 19.62 x 100 = 1962 Joules of work.

According to energy conservation principles, the kinetic energy impacted of the 2 kg mass through this distance will be equal to the work done in moving the 2 kg mass through this distance.

Therefore, the kinetic energy of the 2 kg mass after the 100 m is equal to 1962 J

Answer:

A) Fb = 671.3 N

B) The diver will sink.

Explanation:

A)

The buoyant force applied on an object by a fluid is given by the following formula:

Fb = Vρg

where,

Fb = Buoyant Force = ?

V = Volume of the water displaced by the object = 68.5 L = 0.0685 m³

ρ = Density of Water = 1000 kg/m³

g = 9.8 m/s²

Therefore,

Fb = (0.0685 m³)(1000 kg/m³)(9.8 m/s²)

Fb = 671.3 N

B)

Now, in order to find out whether the diver sinks or float, we need to find weight of the diver with gear.

W = mg = (71.8 kg)(9.8 m/s²)

W = 703.64 N

Since, W > Fb. Therefore, the downward force of weight will make the diver sink.

The diver will sink.

Answer:

either +z direction or -z direction.

Explanation:

The direction of the electric field, in an electromagnetic wave always is perpendicular to the direction of the magnetic field and the direction of propagation of the wave.

You assume a system of coordinates with the negative x axis as the west direction, and the y axis as the up direction

In this case, the wave is propagating toward the west (- x direction), and the magnetic field vector points up (+ y direction), then, it is mandatory that the electric field vector points either +z direction or -z direction.

Answer: in this question, the only charge in the cavity is Q. Inside the conducting spherical shell, the electric field is zero.

While outside the shell, the electric field is given by: k(q + Q)/r²

Where;

K= is a constant which is given as, 8.99 x 10^9 N m² / C².

Q= source charge which creates the electric field

q= is the test charge which is used to measure the strength of the electric field at a given location.

r= is the radius

Explanation: Inside the conducting spherical shell, the electric field is zero since the Electric field vanishes everywhere inside the volume of a good conductor.

Answer:

A. 2.82 eV

B. 439nm

C. 59.5 angstroms

Explanation:

A. To calculate the energy of the photon emitted you use the following formula:

[tex]E_{n1,n2}=-13.4(\frac{1}{n_2^2}-\frac{1}{n_1^2})[/tex]     (1)

n1: final state = 5

n2: initial state = 2

Where the energy is electron volts. You replace the values of n1 and n2 in the equation (1):

[tex]E_{5,2}=-13.6(\frac{1}{5^2}-\frac{1}{2^2})=2.82eV[/tex]

B. The energy of the emitted photon is given by the following formula:

[tex]E=h\frac{c}{\lambda}[/tex]   (2)

h: Planck's constant = 6.62*10^{-34} kgm^2/s

c: speed of light = 3*10^8 m/s

λ: wavelength of the photon

You first convert the energy from eV to J:

[tex]2.82eV*\frac{1J}{6.242*10^{18}eV}=4.517*10^{-19}J[/tex]

Next, you use the equation (2) and solve for λ:

[tex]\lambda=\frac{hc}{E}=\frac{(6.62*10^{-34} kg m^2/s)(3*10^8m/s)}{4.517*10^{-19}J}=4.39*10^{-7}m=439*10^{-9}m=439nm[/tex]

C. The radius of the orbit is given by:

[tex]r_n=n^2a_o[/tex]   (3)

where ao is the Bohr's radius = 2.380 Angstroms

You use the equation (3) with n=5:

[tex]r_5=5^2(2.380)=59.5[/tex]

hence, the radius of the atom in its 5-th state is 59.5 anstrongs

A) The energy E of the emitted photon in electron volts is; E = 2.856 eV

B) The wavelength in nanometers of the emitted photon is; λ = 434.4nm

C) The radius of the hydrogen atom in nanometers in its initial 5th energy level is; rₙ = 1.323 nm

A) Formula for the energy E of the emitted photons is;

E = -13.6([tex]\frac{1}{n_{2}^2} - \frac{1}{n_{1}^2}[/tex])

We are given;

n₂ = 5

n₁ = 2

Thus;

E = -13.6([tex]\frac{1}{5^2} - \frac{1}{2^2}[/tex])

E = 2.856 eV

B) The formula for the wavelength is;

λ = hc/E

where;

h is Planck's constant = 6.626 × 10⁻³⁴ m².kg/s

c is speed of light = 3 × 10⁸ m/s

E is energy of photon

λ is wavelength of the photon

Earlier we saw that E = 2.856 eV. Converting to Joules gives;

E = 4.5758 × 10⁻¹⁹ J

Thus;

λ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(4.5758 × 10⁻¹⁹)

λ = 4.344 × 10⁻⁷ m

Converting to nm gives;

λ = 434.4nm

C) Formula for the radius of the hydrogen atom is;

rₙ = n²a₀

where;

a₀ is bohr's radius = 5.292 × 10⁻¹¹ m

n = 5

Thus;

rₙ = 5² × 5.292 × 10⁻¹¹

rₙ = 1.323 × 10⁻⁹

rₙ = 1.323 nm

Read more at; https://brainly.com/question/17227537

Answer:

11.8 Joules

Explanation:

Given:-

- The height of the target ball, si = 0.860 m

- The mass of target and steel ball, m = 0.012 kg

- The target ball travels a distance ( x ) after being struck = 1.40 m

Find:-

What is the kinetic energy (in joules) of the target ball just after it is struck?

Solution:-

- We are given the initial distance of the target ball as 0.86 m above the floor which travels a distance ( x ) after being struck.

- We will employ the one dimensional kinematic equation of motion to determine the initial velocity ( vi ) of the target ball as follows:

                        [tex]vf^2 = vi^2 - 2*g*x[/tex]

Where,

                  vf: The final velocity of target ball at maximum height = 0

                  g: The gravitational acceleration constant = 9.8 m/s^2

- Plug in the required parameters and evaluate the ( vi ) as follows:

                      [tex]0^2 = vi^2 - 2*( 9.80 )*( 1.40 )\\\\vi^2 = 27.44\\\\vi = \sqrt{27.44} = 5.24 m/s[/tex]

- The kinetic energy ( Ek ) of an object with mass ( m ) and initial velocity ( vi ) is expressed as:

                       [tex]E_k = 0.5*m*(vi)^2\\\\E_k = 0.5*0.86*27.44\\\\E_k = 11.8 J[/tex]

Answer: The kinetic energy of the target ball just after it is struck is 11.8 Joules.

Answer:

Explanation:

Sensorimotor Infants "think" by acting on the world with their eyes, ears, hands, and mouth.

Preoperational. Development of language and make-believe play takes place.

Concrete Operational children think in a logical, organized fashion only when dealing with concrete information they can perceive directly.

Formal Operational.  Adolescences  can also evaluate the logic of verbal statements without referring to real-world circumstances.

Sensorimotor, preoperational, concrete operational, and formal operational are Piaget's four phases of cognitive development.

The way youngsters think, investigate, and figure things out is referred to as cognitive development.

Piaget defined four stages of cognitive development:

1. Sensorimotor. From birth through the age of 18-24 months.

2. Preoperational.From infancy (18-24 months) until toddlerhood (age 7)

3. Operational concrete. 7 to 11 years old

4. Formal operational. From adolescence to adulthood

Hence, sensorimotor, preoperational, concrete operational, and formal operational are Piaget's four phases of cognitive development.

To learn more about the cognitive development refer to:

https://brainly.com/question/14282522

#SPJ2

Answer:

(a) 0.0885 Hz

(b) 0.21 m/s

Explanation:

(a) Frequency: This can  be defined as the number of cycle completed in one seconds.

From the question,

Note: 2 crest = one cycle,

If four crest = 22.6 s,

Then two crest = (22.6/2) s

= 11.3 s.

T = 11.3 s

But,

F = 1/T

F = 1/11.3

F = 0.0885 Hz.

(b)

Using,

V = λF...................... Equation 1

Where V = speed of wave, F = Frequency of wave, λ = wave length.

Given: F = 0.0885 Hz, λ = 2.37 m.

Substitute these values into equation 1

V = 2.37(0.0885)

V = 0.21 m/s.

Answer:

C) less than 129 lb.

Explanation:

Let the elevator be slowing up with magnitude of a . That means it is accelerating downwards  with magnitude a .

If R be the reaction force

For the elevator is going downwards with acceleration a

mg - R = ma

R = mg - ma

R measures its apparent weight . Spring scale will measure his apparent weight.

So its apparent weight is less than 129 lb .

Answer:

Explanation:

The kinetic energy possessed by the block when sliding will be equal to the energy needed to compress the string.

Kinetic energy = 1/2 mv² and energy stored in the spring = 1/2 ke²

m = mass of the block (in kg) = 2.8 kg

v = speed of the block (in m/s) = 2.4 m/s

k = force constant of the spring

e = extension (in metres) = 0.056m

Since KE = energy stored in the spring

1/2 mv² = 1/2 ke²

mv² = ke²

2.8(2.4)²  = k(0.056)²

16.128 = 0.003136k

k = 16.128/0.003136

k =  5,142.86

The force constant of the spring is 5,236.36

The force that constant of the spring is 5,142.86.

The kinetic energy that should be possessed by the block at the time when sliding will be equivalent to the energy required to compress the string.

Here

Kinetic energy = 1/2 mv² and energy stored in the spring = 1/2 ke²

m = mass of the block (in kg) = 2.8 kg

v = speed of the block (in m/s) = 2.4 m/s

k = force constant of the spring

e = extension (in metres) = 0.056m

Since KE = energy stored in the spring

So,

1/2 mv² = 1/2 ke²

mv² = ke²

Now

2.8(2.4)²  = k(0.056)²

16.128 = 0.003136k

k = 16.128/0.003136

k =  5,142.86

Learn more about force here: https://brainly.com/question/3398162

Answer:

The classification of that same issue in question is characterized below.

Explanation:

The given values are:

Current, I = 50.0 A

Diameter, d = 0.10 cm

(a)...

As we know,

⇒  Magnetic force = Copper wire's weight

So,

⇒   [tex]B\times I\times L=M\times g[/tex]

On putting the estimated values, we get

⇒  [tex]B\times 50\times 1=7.037\times 10^{-3}\times 9.81[/tex]

⇒  [tex]50B=69.03297\times 10^{-3}[/tex]

⇒  [tex]B=1.38\times 10^{-3} \ T[/tex]

(b)...

As we know,

⇒  [tex]m=\delta\times L\times \frac{\pi \ d^2}{4}[/tex]

⇒      [tex]=8960\times 1\times \frac{\pi \ (0.001)^2}{4}[/tex]

⇒      [tex]=2240\times \pi \ 0.000001[/tex]

⇒      [tex]=7.037\times 10^{-3} \ kg[/tex]

Explanation:

The relationship between electric force and distance between charged objects is given by the formula as follows :

[tex]F=\dfrac{kq_1q_2}{d^2}[/tex]

k is electrostatic constant and d is distance between charges

The electric force between charges is inversely proportional to the square of distance between them.

Answer:

The thermal power emitted by the body is [tex]P_t = 286.8 \ Wm^{-2}[/tex]

The net power radiated is  [tex]P_{net} = 460 \ W[/tex]

Explanation:

From the question we are told that

   The length of the assumed hum[tex]T_{room} = 20 ^oC[/tex]an body is  L =  2.0 m

   The circumference of the assumed human body is  [tex]C = 0.8 \ m[/tex]

   The  Stefan-Boltzmann constant is  [tex]\sigma = 5.67 * 10^{-8 } \ W\cdot m^{-2} \cdot K^{-4}.[/tex]

    The temperature of skin [tex]T_{body} = 30^oC[/tex]

     The temperature of the room is  

    The emissivity is  e=0.6

The thermal power radiated by the body is mathematically represented as

           [tex]P_t = e * \sigma * T_{body}^4[/tex]

substituting value

        [tex]P_t = 0.6 * 5.67*10^{-8} * (303)^4[/tex]

        [tex]P_t = 286.8 \ Wm^{-2}[/tex]

The net power radiated by the body is mathematically evaluated as

    [tex]P_{net} = P_t * A[/tex]

Where A is the surface area of the body which is mathematically evaluated as

     [tex]A = C* L[/tex]

substituting values

      [tex]A = 0.8 * 2[/tex]

      [tex]A = 1.6 m^2[/tex]

=>    [tex]P_{net} = 286.8 * 1.6[/tex]

=>   [tex]P_{net} = 460 \ W[/tex]

Answer:

C

Explanation:

The intermolecular forces between the water molecule is less binding than that of the copper molecule. Hence the water would take a shorter time to be converted to vapour where the temperature of boiling is constant however the temperature of that of the copper molecule keeps increasing.

Answer:

Loudness: decreases

Amplitude: decreases

Pitch: stays the same

Frequency: stays the same

Explanation:

1.

An oscilloscope measures how much the microphone is vibrating, or how much electricity it is sending. This means that a louder noise will register higher on the oscilloscope. Since the size of the waves at Y is lower than at X, the loudness of the sound has decreased.

2.

Similarly to loudness, amplitude measures how far the crests of the waves are from the nodes. Since Y is closer to the center line than X, it has a lower amplitude.

3 and 4.

The pitch and frequency, for our purposes, are essentially the same thing here. They are dependent on how close together the waves on the oscilloscope are, or how quickly the microphone is vibrated. Since this stays the same throughout the entire sound, they both stay the same.

Hope this helps!

Answer:

Explanation:

During the swing , the center of mass will go down due to which disc will lose potential energy which will be converted into rotational kinetic energy

mgh = 1/2 I ω² where m is mass of the disc , h is height by which c.m goes down which will be equal to radius of disc , I is moment of inertia of disc about the nail at rim , ω is angular velocity .

mgr  = 1/2 x ( 1/2 m r²+ mr²) x ω²

gr  = 1/2 x 1/2  r² x ω² + 1/2r² x ω²

g = 1 / 4 x ω² r + 1 / 2 x ω² r

g = 3  x ω² r/ 4

ω² = 4g /3 r

= 4 x 9.8 /  3 x  .25

= 52.26

ω = 7.23  rad / s .

Answer:

Explanation:

For a convex mirror, the value of its image distance and its focal length are negative.

using the mirror formula 1/f = 1/u+1/v

f is the focal length = Radius of curvature/2 = 0.560/2

f= 0.28m

u is the object distance = 10.6m

v is the position of the image = ?

On substitution;

1/0.28 = 1/10.6 + 1/-v

3.57 = 0.094 - 1/v

3.57 - 0.094 = -1/v

3.476 = -1/v

v = -1/3.476

v = -0.2877m

B) Since the image distance is negative, this means that the image is an upright and a virtual image. All Upright images has their image distance to be negative.

C) Magnification = Image distance/object distance

Magnification  = 0.2877/10.6

Magnification = 0.0271

Before the bus starts moving, the bus and the skater are both standing still.

When the bus starts moving and pulls away from the bus-stop, the skater stays right where she is.  

The people outside on the sidewalk see her standing still, and they see the bus moving out from under her.  

The other passengers on the bus see her rolling backwards down the aisle, toward the back of the bus.

Answer:

B. At the instant when the block is at the highest point, directed at the block.

Explanation:

Motion of an object is the change in the position of the object with respect to time. On the earth, gravity has a great influence on the motion of an object (especially in a vertical direction).

When the block is projected up in the air, it moves with a varying velocity until the velocity becomes zero due to gravity. Which make the object to rest a little in the air (when velocity = gravity) and starts to fall freely.

To ensure hitting the block by the ball, it is thrown at the block when the block is at its highest point in the air. Since the block would be at rest at this instant before it start to fall at a constant acceleration under gravity.

Answer:

The angular momentum is  [tex]L = 8440.32 \ kg \cdot m^2 \cdot s^{-1}[/tex]

Explanation:

From the question we are told that

    The mass of the woman is  [tex]m = 50 \ kg[/tex]

     The angular  speed of the rim is  [tex]w = 0.80 \ rev/s = 0.8 * [\frac{2 \pi}{1} ] = 5.024 \ rad \cdot s^{-1}[/tex]

      The mass of the disk is  [tex]m_d = 110 \ kg[/tex]

       The radius of the disk is [tex]r_d = 4.0 \ m[/tex]

The moment of inertia of the disk is mathematically represented as

        [tex]I_D = \frac{1}{2} m_d r^2_d[/tex]

substituting values

          [tex]I_D = \frac{1}{2} * 110 * 4^2[/tex]

          [tex]I_D = 880 \ kg \cdot m^2[/tex]

The moment of inertia of the woman is  

          [tex]I_w = m * r_d^2[/tex]

substituting values

        [tex]I_w = 50 * 4^2[/tex]

       [tex]I_w =800\ kg[/tex]

The moment of inertia of the system (the woman + the large disk ) is  

        [tex]I_t = I_w + I_D[/tex]

substituting values  

      [tex]I_t = 880 +800[/tex]

     [tex]I_t =1680 \ kg \cdot m^2[/tex]

The angular momentum of the system is

      [tex]L = I_t w[/tex]

substituting values  

      [tex]L = 1680 * 5.024[/tex]

      [tex]L = 8440.32 \ kg \cdot m^2 \cdot s^{-1}[/tex]

Answer:

The minimum angular spread of the laser beam is 3.32 × [tex]10^{-6}[/tex] radians (or 3.32 μrad).

Explanation:

The minimum angular spread of a wave is the ratio of its narrowest diameter to its wavelength.

From Rayleigh's formula,

Angular spread = 1.22 (wavelength ÷ diameter)

                          = 1.22 (λ ÷ D)

Given that:

diameter, D = 0.18 m and wavelength, λ = 490 nm, then;

Angular spread of the laser beam = 1.22 (λ ÷ D)

                         = 1.22[tex](\frac{490*10^{-9} }{0.18})[/tex]

                         = 1.22× 2.7222 × [tex]10^{-6}[/tex]

                        = 3.3211 × [tex]10^{-6}[/tex] rad

The minimum angular spread of the laser beam is 3.32 × [tex]10^{-6}[/tex] radians.