Drying of Cassava (Tapioca) Root. Tapioca flour is used in many countries for bread and similar products. The flour is made by drying coarse granules of the cassava root containing 66 wt % moisture to 5% moisture and then grinding to produce a flour. How many kg of granules must be dried and how much water removed to produce 5000 kg/h of flour?

Answer:

(a) 34.47 cm

(b) [tex]24.09^\circ[/tex] south of west

Explanation:

Let us draw a figure representing the individual displacement vectors in the four jumps as shown in the figure attached with this solution.

Now, let us try to write the four displacement vectors in in terms of unit vectors along the horizontal and the vertical axis.

[tex]\vec{d}_1= 31\ cm\ west = -31\ cm\ \hat{i}\\\vec{d}_2= 26\ cm\ south\ of\ west = -26\cos 44^\circ\ \hat{i} -26 \sin 44^\circ\ \hat{j}=(-18.72\ \hat{i}-18.06\ \hat{i})\ cm\\\vec{d}_3= 22\ cm\ south\ of\ east = 22\cos 56^\circ\ \hat{i} -22 \sin 56^\circ\ \hat{j}=(12.30\ \hat{i}-18.23\ \hat{i})\ cm\\\vec{d}_4= 23\ cm\ north\ of\ east = 23\cos 75^\circ\ \hat{i} +23\sin \sin 75^\circ\ \hat{j}=(5.95\ \hat{i}+22.22\ \hat{i})\ cm\\[/tex]

Now, the vector sum of all these vector will give the resultant displacement vector.

[tex]\vec{D} = \vec{d}_1+\vec{d}_2+\vec{d}_3+\vec{d}_4\\\Rightarrow \vec{D} = -31\ cm\ \hat{i}+(-18.72\ \hat{i}-18.06\ \hat{i})\ cm+(12.30\ \hat{i}-18.23\ \hat{i})\ cm+(5.95\ \hat{i}+22.22\ \hat{i})\ cm\\\Rightarrow \vec{D} =(-31.47\ \hat{i}-14.07\ \hat{i})\ cm[/tex]

Part (a):

The magnitude of the resultant displacement vector is given by:

[tex]D=\sqrt{(-31.47)^2+(-14.07)^2}\ m = 34.47\ m[/tex]

Part (b):

Since the resultant displacement vector indicates that the final position of the vector lies in the third quadrant, the vector will make some positive angle in the direction south of west given by:

[tex]\theta = \tan^{-1}(\dfrac{14.07}{31.47})= 24.09^\circ[/tex]

To find the resultant displacement of the grasshopper, we can break down the vectors into their x and y components, and then sum up the components separately. After performing the calculations, we find that the magnitude of the resultant displacement is approximately 39.4 cm and the direction is approximately 38.3° south of west.

To find the resultant displacement of the grasshopper, we need to add the individual displacement vectors. We can do this by breaking down each vector into its x and y components.

For vector (1) with a magnitude of 31.0 cm due west, the x component is -31.0 cm and the y component is 0.

Similarly, for the other vectors, the x and y components are:

Now, we can sum up the x components and y components separately to find the resultant displacement.

The magnitude of the resultant displacement can be found using the formula:

resultant magnitude = sqrt((sum of x components)^2 + (sum of y components)^2)

The direction of the resultant displacement can be found using the formula:

resultant direction = atan2((sum of y components), (sum of x components))

Plugging in the values and performing the calculations, we find that the magnitude of the resultant displacement is approximately 39.4 cm and the direction of the resultant displacement is approximately 38.3° south of west.

Answer:

The ball never passes 2m high, Hmax=1.27m

Explanation:

we assume the ball doesn't bounce when it hits the ground.

We calculate the maximum height, Vf = 0.

[tex]v_{o}^{2}=2gH_{max}\\H_{max}=v_{o}^{2}/(2g)=5^{2}/(2*9.81)=1.27m[/tex]

So, the ball never passes 2m high.

Kinematics equations:

[tex]x(t)=v_{o}t-1/2*g*t^{2}\\v(t)=v_{o}-gt[/tex]

Find annexed the graphics of x(t) and v(t)

Answer:

r=2.743

Explanation:

The energy stored on a capacitor is of type potencial, therfore depends on the capacity to "store" energy. Inthe case of the capacitor, it stores charge (Q), and the equations you use to calculate it are:

[tex]E_p=\frac{Q^2}{2C}=\frac{QV}{2}=\frac{CV^2}{2}[/tex]

In this case we know V and C, therefore we use the last expression:

[tex]E_{p1}=\frac{CV_1^2}{2}[/tex]

[tex]E_{p2}=\frac{CV_2^2}{2}[/tex]

[tex]\frac{E_{p1}}{E_{p2}}=r=\frac{\frac{CV_1^2}{2}}{\frac{CV_2^2}{2}}  \\r=(\frac{V_1}{V_2})^2\\r=(\frac{21.2}{12.8})^2[/tex]

r=2.743

Answer:

Second ball

Explanation:

When a ball is thrown up with a certain velocity when the object reaches the same point from where it was thrown the velocity of the object becomes equal to the velocity with which the ball was thrown.

First ball

[tex]v_g_1^2-u^2=2as\\\Rightarrow v_g_1=\sqrt{2as+u^2}\\\Rightarrow v_g_1=\sqrt{2as+v^2}[/tex]

Second ball

[tex]v_g_2^2-u^2=2as\\\Rightarrow v_g_2=\sqrt{2as+u^2}\\\Rightarrow v_g_2=\sqrt{2as+4v^2}[/tex]

Third ball

[tex]v_g_3^2-u^2=2as\\\Rightarrow v_g_3=\sqrt{2as+0^2}\\\Rightarrow v_g_3=\sqrt{2as}[/tex]

From the equations above it can be seen that the second ball will have the highest velocity when it hits the ground.

So, [tex]v_g_3<v_g_1<v_g_2[/tex]

Answer:

Momentum of bullet

[tex]P = 2.72 kg m/s[/tex]

momentum of baseball

[tex]P = 8 kg m/s[/tex]

Explanation:

As we know that momentum is defined as the product of mass and velocity

here we know that

mass of the bullet = 8 gram

velocity of bullet = 340 m/s

momentum of the bullet is given as

[tex]P = mv[/tex]

[tex]P = (\frac{8}{1000})(340)[/tex]

[tex]P = 2.72 kg m/s[/tex]

Now we have

mass of baseball = 0.2 kg

velocity of baseball = 40 m/s[/tex]

momentum of baseball is given as

[tex]P = (0.2)(40)[/tex]

[tex]P = 8 kg m/s[/tex]

Answer:

Force between two spheres will be 14400 N

And as the both charges of opposite nature so force will be attractive

Explanation:

We have given two conducting spheres of charges [tex]q_1=-20\mu C=-20\times 10^{-6}C\ and\ q_2=50\mu C=50\times 10^{-6}C[/tex]

Distance between the spheres = 2.5 cm =0.025 m

According to coulombs law we know that force between two charges is given by [tex]F=\frac{1}{4\pi \varepsilon _0}\frac{q_1q_2}{r^2}=\frac{Kq_1q_2}{r^2}=\frac{9\times 10^9\times 20\times 10^{-6}\times 50\times 10^{-6}}{0.025^2}=14400N[/tex]  

As the both charges of opposite nature so force will be attractive

Answer:

Acceleration, [tex]a=-2.48\ m/s^2[/tex]

Explanation:

Initial speed of the skater, u = 8.4 m/s

Final speed of the skater, v = 6.5 m/s

It hits a 5.7 m wide patch of rough ice, s = 5.7 m

We need to find the acceleration on the rough ice. The third equation of motion gives the relationship between the speed and the distance covered. Mathematically, it is given by :

[tex]v^2-u^2=2as[/tex]

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

[tex]a=\dfrac{(6.5)^2-(8.4)^2}{2\times 5.7}[/tex]

[tex]a=-2.48\ m/s^2[/tex]

So, the acceleration on the rough ice [tex]-2.48\ m/s^2[/tex] and negative sign shows deceleration.

Answer:

V1=5ft3

V2=2ft3

n=1.377

Explanation:

PART A:

the volume of each state is obtained by multiplying the mass by the specific volume in each state

V=volume

v=especific volume

m=mass

V=mv

state 1

V1=m.v1

V1=4lb*1.25ft3/lb=5ft3

state 2

V2=m.v2

V2=4lb*0.5ft3/lb=   2ft3

PART B:

since the PV ^ n is constant we can equal the equations of state 1 and state 2

P1V1^n=P2V2^n

P1/P2=(V2/V1)^n

ln(P1/P2)=n . ln (V2/V1)

n=ln(P1/P2)/ ln (V2/V1)

n=ln(15/53)/ ln (2/5)

n=1.377

Final answer:

The mass of the object is 1.53 kg.

Explanation:

To find the mass of the object, we need to use Hooke's Law which states that the force exerted by a spring is directly proportional to its extension. In this case, the spring stretches 0.2 cm per newton of applied force. The deflection of 3 cm corresponds to an applied force of 15 newtons (0.2 cm per newton * 3 cm).

Using the equation F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity (9.81 m/s^2), we can find the mass:

15 newtons = m * 9.81 m/s^2

m = 15 newtons / 9.81 m/s^2 = 1.53 kg

Therefore, the mass of the object is approximately 1.53 kg.

The mass of the object is approximately 1.53 kg.

Given that the spring stretches 0.2 cm per newton of applied force. Thus, we can say that

for F = - kx.

1 N = - k (0.2 cm)

or, k = spring constant of the given spring = [tex]\frac{F}{x}[/tex] = 5 N/cm

Now, for an object producing deflection of 3 cm, we can say that:

F = - k x = 5 N/cm × 3 cm

or, F = 15 N

This concludes that the weight of the object is 15 N.

Now, W = F = mg

hence, [tex]m = \frac{F}{g}[/tex]

or, m = [tex]\frac{15 \hspace{0.6mm} N}{9.8 \hspace{0.5mm} m/s^2}[/tex]

or, m ≈ 1.53 kg

Answer:

The arrow will hit 112.07 m from the point of release.

Explanation:

The equation for the position of an object in a parabolic movement is as follows:

r = (x0 + v0 · t · cos α, y0 + v0 · t · sin α + 1/2 · g · t²)

Where:

x0 = initial horizontal position

v0 = initial velocity

α = launching angle

y0 = initial vertical position

t = time

g = acceleration due to gravity

We know that at the final time the y-component of the vector "r" (see figure") is -1.88 m. The x-component of that vector will be the horizontal distance traveled by the arrow. Using the equation of the y-component of "r", we can obtain the final time and with that time we can calculate the value of the x-component (horizontal distance).

Then:

y = y0 + v0 · t · sin α + 1/2 · g · t²

Since the origin of the frame of reference is located at the point where the arrow is released, y0 = 0. Notice that the angle α = 26° + 15° = 41° ( see figure)

-1.88 m = 33 m/s · sin 41° · t - 1/2 · 9.8 m/s² · t²    (g is downward)

0 = -4.9 m/s² · t² + 33 m/s · sin 41° · t + 1.88 m

Solving the quadratic equation:

t = 4.5 s   ( the negative value is discarded)

Now, with this time we can calculate the horizontal distance:

x = x0 + v0 · t · cos α    (x0 = 0, the same as y0)

x = 33 m/s · 4.5 s · cos 41° = 112.07 m

The object comes to 112.07 m below its original point of release the arrow hit if it is shot with a speed of 33 m/s from a height of 1.88 m above the ground.

The equation for the position of an object in a parabolic movement is as follows:

r = (x₀ + v₀  t cos α, y₀ + v₀ t sin α + 1/2 g t²)

y = y₀ + v₀ t  sin α + 1/2 g  t²

Since the origin of the frame of reference is located at the point where the arrow is released, y₀ = 0. Notice that the angle α = 26° + 15° = 41° ( see figure)

-1.88 m = 33 m/s  sin 41°  t - 1/2  9.8 m/s²  t²  

0 = -4.9 m/s² · t² + 33 m/s · sin 41° · t + 1.88 m

Solving the quadratic equation:

t = 4.5 s  

Now, with this time we can calculate the horizontal distance:

x = x₀ + v₀  t cos α

x = 33 m/s · 4.5 s · cos 41° = 112.07 m

The object comes to 112.07 m below its original point of release the arrow hit if it is shot with a speed of 33 m/s from a height of 1.88 m above the ground.

To know more about the horizontal distance:

https://brainly.com/question/10093142

#SPJ6

Answer:

a) 0°

b) 180°

c) 90°

Explanation:

Hello!

To solve this question let a be the vector whose length is 15 m and b the vector of length 20 m

So:

|a | = 15

|b | = 20

Since we are looking for the angle between the vectors we need to calculate the length of the sum of the two vectors, this is:

[tex]|a+b|^{2} = |a|^{2} + |b|^{2} + 2 |a||b|cos(\theta)[/tex]

Now we replace the value of the lengths:

[tex]|a+b|^{2} = 15^{2} + 20^{2} + 2*15*20*cos(\theta)[/tex]

[tex]|a+b|^{2} = 625 + 600*cos(\theta)[/tex] --- (1)

Now, if:

a) |a+b| = 35

First we can see that 20 + 15 = 35, so the angle must be 0, lets check this:

[tex]35^{2} = 625 + 600*cos(\theta)[/tex]

[tex]1225 = 625 + 600*cos(\theta)[/tex]

[tex]600 =  600*cos(\theta)[/tex]

[tex]1= cos(\theta)[/tex]

and :

[tex]\theta = arccos(1)[/tex]

      θ = 0

b) |a+b|=5

From eq 1 we got:

[tex]\theta = arccos(\frac{|a+b|^{2}-625}{600})[/tex]   --- (2)

[tex]\theta = arccos(\frac{|a+b|^{2}-625}{600})[/tex]

[tex]\theta = arccos(-1)[/tex]

  θ = π     or    θ = 180°

c) |a+b|=25

[tex]\theta = arccos(\frac{|25|^{2}-625}{600})[/tex]

[tex]\theta = arccos(-1)[/tex]

  θ = π/2     or    θ = 90°

Final answer:

In vector addition, an angle of 0° between two vectors gives a resultant of 35 m, an angle of 180° gives a resultant of 5 m, and the angle for a resultant of 25 m can be found using the Law of Cosines.

Explanation:

The question involves the concept of vector addition and the use of trigonometry to determine the resultant displacement when two vectors are combined at various angles. The displacement vectors have magnitudes of 15 m and 20 m, and we are interested in finding the angles that would result in resultant displacements of 35 m, 5 m, and 25 m, respectively.

For (a) a resultant displacement of 35 m, the two vectors must be added in the same direction. This implies that the angle between them is 0°.

For (b) a resultant displacement of 5 m, the two vectors must be in exactly opposite directions. Since the difference in magnitudes is 5 m, this means that the larger vector (20 m) partially cancels out the smaller vector (15 m). Hence, the angle between them is 180°.

For (c) a resultant displacement of 25 m, we can use the Law of Cosines to determine the angle:

c2 = a2 + b2 - 2ab cos(θ)

Where a = 15 m, b = 20 m, and c = 25 m. Solving this equation will give us the value of θ.

Answer:

acceleration = 4.4 m/s²

time is 3.86 s

Explanation:

given data

initial speed = 7 m/s

final speed = 24 m/s

distance = 60 m

to find out

acceleration and time when change speed change

solution

we will apply here equation of motion for acceleration

v²-u² = 2×a×s   .................1

here v is final speed and u is initial speed and s is distance and a is acceleration

put here all these value

24²-7² = 2×a×60

so

a = 4.4

acceleration = 4.4 m/s²

and

now find time by equation of motion

v = u +at

put her value

24 = 7 + 4.4 (t)

t = 3.86

so time is 3.86 s

Answer:

1) We will have excess of electrons

2) The number of electrons transferred equals [tex]1.343\times 10^{10}[/tex]

Explanation:

Part a)

Since we know that the charge transfer occurs by the transfer of electrons only as it is given that the carpet has acquired a positive charge it means that it has lost some of the electron's since electrons are negatively charged and if a neutral body looses negative charge it will become positively charged. The electron's that are lost by the carpet will be acquired by the feet of the human thus making us negatively charged.Hence we will gain electrons making us excess in electrons.

Part b)

From charge quantinization principle we have

[tex]Q=ne[/tex]

where

Q = charge of body

n = no of electrons

e = fundamental charge

Applying values in the above equation we get

[tex]2.15\times 10^{-9}C=n\times 1.6\times 10^{-19}C\\\\\therefore n=\frac{2.15\times 10^{-9}C}{1.6\times 10^{-19}C}=1.343\times 10^{10}[/tex]

Answer:

The individual positive plate capacity is 85 Ah.

(D) is correct option.

Explanation:

Given that,

Number of plates = 15

Capacity = 595 Ah

We need to calculate the individual positive plate capacity in motive power cell

We have,

15 plates means 7 will make pair of positive and negative.

So, there are 7 positive cells individually.

The capacity will be

[tex]capacity =\dfrac{power}{number\ of\ cells}[/tex]

Put the value into the formula

[tex]capacity =\dfrac{595}{7}[/tex]

[tex]capacity =85\ Ah[/tex]

Hence, The individual positive plate capacity is 85 Ah.

Answer:

SDFGHJKL

Explanation:

Answer:displacement =787.71 m

Explanation:

Given

Driver driver the car 690 ft to the east

then turn 380 ft to the north

(a)magnitude of acceleration is [tex]=\sqrt{380^2+690^2}=\sqrt{620500}[/tex]

displacement=787.71 m

(b)direction of displacement

[tex]tan\theta =\frac{380}{690}=0.5507[/tex]

[tex]\theta =28.84^{\circ}[/tex] with east direction

The magnitude of the displacement is approximately 775 ft and its direction is roughly 29 degrees north of east.

Your total displacement after driving a car 690 ft to the east and then 380 ft to the north is calculated using the Pythagorean theorem, which states that the magnitude of the hypotenuse (displacement) of a right triangle (formed by the eastwards and northwards journeys of the car) can be found by sqrt((eastwards travel)^2 + (northwards travel)^2). Applying the theorem, we obtain sqrt((690 ft)^2 + (380 ft)^2) = 775 ft approximately.

The direction of the displacement can be found using the tangent of the angle, which is the ratio of the opposite (northwards) to the adjacent side (eastwards). Applying the inverse tangent function, we get tan^-1(380/690), which gives us approximately 29 degrees. Therefore, the direction of the displacement is 29 degrees north of east.

https://brainly.com/question/33459975

#SPJ3

Answer:

it move with velocity 1571 m/s

Explanation:

given data

wavelength λ = 4.63 × [tex]10^{-7}[/tex] m

to find out

how fast is it moving

solution

we will use here de Broglie wavelength equation

that is

wavelength λ = [tex]\frac{h}{mv}[/tex]    ..........1

here h is planck constant = 6.626068 × [tex]10^{-34}[/tex]

and m is mass of electron i.e = 9.10938188 × [tex]10^{-31}[/tex]

and v is velocity

put all value we find velocity  in equation 1

wavelength λ = [tex]\frac{h}{mv}[/tex]  

v = [tex]\frac{6.626068*10^{-34}}{9.10938188*10^{-31}*4.63*10^{-7}}[/tex]

v =  1571.035464

so it move with velocity 1571 m/s

Answer:

[tex]v=1.57*10^{3}\frac{m}{s}[/tex]

Explanation:

As DeBroglie equation proved by Davisson-Germer experiment says, the wavelength of an electron is related with its velocity with the equation:

λ = [tex]\frac{h}{mv}[/tex]

where m is the mass of the electron [tex]m=9.11*10^{-31}kg[/tex], h is the Planck´s constant [tex]h=6.626*10^{-34}J.s[/tex] and v its velocity.

Solving the equation for the velocity of the electron, we have:

v = h/mλ

And replacing the values:

[tex]v=\frac{6.626*10^{-34}J.s}{(9.11*10^{-31}Kg)*(4.63*10^{-7}m)}[/tex]

[tex]v=1570.9\frac{m}{s}[/tex]

[tex]v=1.57*10^{3}\frac{m}{s}[/tex]

Answer: 0.95 ft/year

Explanation: In order to explain this question we have to convert the units so

if we have a rate equal to 0.033 mm/hr then 0.033 mm *24*365 hr/year

then 1 m=3.28 feet

8760*0.033 *10^-3m* 3.28 feet/m=1.08*10^-4 feet*8760=0.95 feet/year

Explanation:

Given that,

Weight of water = 25 kg

Temperature = 23°C

Weight of mass = 32 kg

Distance = 5 m

(a). We need to calculate the amount of work done on the water

Using formula of work done

[tex]W=mgh[/tex]

[tex]W=32\times9.8\times5[/tex]

[tex]W=1568\ J[/tex]

The amount of work done on the water is 1568 J.

(b). We need to calculate the internal-energy change of the water

Using formula of internal energy

The change in internal energy of the water equal to the amount of the  work done on the water.

[tex]\Delta U=W[/tex]

[tex]\Delta U=1568\ J[/tex]

The  change in internal energy is 1568 J.

(c). We need to calculate the final temperature of the water

Using formula of the change internal energy

[tex]\Delta U=mc_{p}\Delta T[/tex]

[tex]\Delta U=mc_{p}(T_{2}-T_{1})[/tex]

[tex]T_{2}=T_{1}+\dfrac{\Delta U}{mc_{p}}[/tex]

[tex]T_{2}=23+\dfrac{1568}{25\times4.18\times10^{3}}[/tex]

[tex]T_{2}=23.01^{\circ}\ C[/tex]

The final temperature of the water is 23.01°C.

(d). The amount of heat removed from the water to return it to it initial temperature is the change in internal energy.

The amount of heat is 1568 J.

Hence, This is the required solution.

The work done on the water is 1568 Joules, which is also the internal-energy change of the water. The final temperature of the water is 23.015°C and to return the water to its initial temperature, 1568 Joules of heat must be removed.

(a) The amount of work done on the water is calculated using the formula for gravitational potential energy which depends on the weight's height, mass and acceleration due to gravity. Therefore, work done= mass × gravity × height = 32 kg × 9.8 m·s−2 × 5 m = 1568 Joules.

(b) As per the Law of Conservation of Energy, the work done on the water is converted completely into the internal energy of the water, so the internal-energy change of the water is 1568 Joules.

(c) The final temperature of the water can be calculated using the formula q = m × c × Δt, where 'q' is heat-transfer, 'm' is mass, 'c' is specific heat capacity and 'Δt' is change in temperature. Rearranging, we find Δt = q /(m × c). Substituting the known values gives Δt = 1568 J /(25 kg × 4.18 kJ/kgC) = 0.015 °C. Adding this to the initial temperature, we find the final temperature of the water is 23.015°C.

(d) To return the water to its initial temperature, the heat equal to the increase in internal energy must be removed. Hence, the amount of heat to be removed from the water = 1568 Joules.

https://brainly.com/question/20458806

#SPJ3

Answer:

Part a)

[tex]q_1 = -1.47 \times 10^{-6} C[/tex]

Part b)

[tex]q_2 = 3.75 \times 10^{-6} C[/tex]

Explanation:

Let the charge on two spheres is q1 and q2

now the force between two charges are

[tex]F = \frac{kq_1q_2}{r^2}[/tex]

[tex]0.116 = \frac{(9\times 10^9)(q_1)(q_2)}{0.654^2}[/tex]

[tex]q_1 q_2 = 5.51 \times 10^{-12}[/tex]

now when we connect then with conducting wire then both sphere will equally divide the charge

so we will have

[tex]q = \frac{q_1-q_2}{2}[/tex]

now we have

[tex]0.0273 = \frac{(9\times 10^9)(\frac{q_1- q_2}{2})^2}{0.654^2}[/tex]

[tex]q_1 - q_2 = 2.28\times 10^{-6} C[/tex]

now we will have

Now we can solve above two equations

Part a)

negative charge on the sphere is

[tex]q_1 = -1.47 \times 10^{-6} C[/tex]

Part b)

positive charge on the sphere is

[tex]q_2 = 3.75 \times 10^{-6} C[/tex]

Answer:

21.28 m

Explanation:

height, h = 71 m

velocity of raft, v = 5.6 m/s

let the time taken by the stone to reach to raft is t.

use second equation of motion for stone

[tex]h = ut + \frac{1}{2}at^{2}[/tex]

u = 0 m/s, h = 71 m, g = 9.8 m/s^2

71 = 0 + 0.5 x 9.8 x t^2

t = 3.8 s

Horizontal distance traveled by the raft in time t

d = v x t = 5.6 x 3.8 = 21.28 m

Answer:

25

Explanation:

Answer:

R = 3170.36m   or  R = 186.5m

Explanation:

For this problem, we have either trajectory (a), assuming that the car was going south-east, or trajectory (b), assuming the car was going north-east.

In both cases, we know that S = 830m = θ * R. Finding θ, will lead us to the value of R.

For option a:

θ = 15° = 0.2618 rad

[tex]R = \frac{S}{\theta} = 3170.36m[/tex]

For option b:

θ = 270° - 15° = 4.45 rad

[tex]R = \frac{S}{\theta} = 186.5m[/tex]

Answer:

v = 0.85 m/s

Explanation:

Given that,

Mass of the ball, m = 0.01 kg

Centripetal force on the ball, F = 0.025 N

Radius of the circular path, r = 0.29 m

Let v is the speed of the ball. The centripetal force of the ball is given by :

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

[tex]v=\sqrt{\dfrac{Fr}{m}}[/tex]

[tex]v=\sqrt{\dfrac{0.025\times 0.29}{0.01}}[/tex]

v = 0.85 m/s

So, the speed of the ball is 0.85 m/s. Hence, this is the required solution.

Answer:Increase

Explanation:

Given

You are holding 2 kg mass in each outstreched hand

If the masses are dropped then Moment of inertia will decease by [tex]2mr^2[/tex]

Where m=2 kg

r=length of stretched arm

Since angular momentum is conserved therefore decrease in Moment of inertia will result in increase of angular velocity

as I[tex]\omega [/tex]=constant

I=Moment of inertia

[tex]\omega [/tex]=angular velocity

Answer:

The statue is 1.67 miles west of both the runners

Explanation:

Wherever Amy and Alejandro meet they will have covered a total distance of 5+4 = 9 mi

They will also have run the same amount of time if they started at the same moment = t

Speed of Amy = 5 mi/h

Speed of Alejandro = 7 mi/h

Distance = Speed × Time

Distance travelled by Amy = 5t

Distance travelled by Alejandro = 7t

Total distance run by Amy and Alejandro is

5t+7t = 9

[tex]\\\Rightarrow 12t=9\\\Rightarrow t=\frac{12}{9}\\\Rightarrow t=\frac{4}{3}\ hours[/tex]

Distance travelled by Amy

[tex]5\times t=5\times \frac{4}{3}=\frac{20}{3}\\ =6.67\ miles[/tex]

The distance of Amy from the statue would be

6.67 - 5 = 1.67 miles

So, the statue is 1.67 miles west of both the runners

Answer:

E = 1.655 x 10⁷ N/C towards the filament

Explanation:

Electric field due to a line charge is given by the expression

E = [tex][tex]\frac{\lambda}{2\pi\times\epsilon_0\times r}[/tex][/tex]

where λ is linear charge density of line charge , r is distance of given point from line charge and ε₀ is a constant called permittivity and whose value is

8.85 x 10⁻¹².

Putting the given values in the equation given above

E = [tex]\frac{92\times10^{-6}}{2\times3.14\times8.85\times10^{-12}\times10^{-1}}[/tex]

E = 1.655 x 10⁷ N/C

Answer:

a) 3.6 m/s

b) 1.53 m/s

c) 0.12 m

Explanation:

t = Time taken = 0.216 s

u = Initial velocity

v = Final velocity

s = Displacement = 0.54 m

a = Acceleration due to gravity = 9.81 m/s² (negative upward)

[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow 0.54=u\times 0.216+\frac{1}{2}\times -9.81\times 0.216^2\\\Rightarrow u=\frac{0.54+\frac{1}{2}\times 9.81\times 0.216^2}{0.216}\\\Rightarrow u=3.6\ m/s[/tex]

Initial speed as it leaves the ground is 3.6 m/s

[tex]v^2-u^2=2as\\\Rightarrow v=\sqrt{2as+u^2}\\\Rightarrow v=\sqrt{2\times -9.81\times 0.54+3.6^2}\\\Rightarrow v=1.53\ m/s[/tex]

Speed at the height of 0.540 m is 1.53 m/s

[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-3.6^2}{2\times -9.81}\\\Rightarrow s=0.66\ m[/tex]

The total height the armadillo leaps is 0.66 m

So, the additional height is 0.66-0.54 = 0.12 m

Answer:

The relative density of the second liquid is 7.

Explanation:

From archimede's principle we know that the force that a liquid exerts on a object equals to the weight of the liquid that the object displaces.

Let us assume that the volume of the object is 'V'

Thus for the liquid in which the block is completely submerged

The buoyant force should be equal to weight of liquid

Mathematically

[tex]F_{buoyant}=Weight\\\\\rho _{1}\times V\times g=m\times g\\\\\therefore \rho _{1}=\frac{m}{V}...............(i)[/tex]

Thus for the liquid in which the block is 1/7 submerged

The buoyant force should be equal to weight of liquid

Mathematically

[tex]F'_{buoyant}=Weight\\\\\rho _{2}\times \frac{V}{7}\times g=m\times g\\\\\therefore \rho _{2}=\frac{7m}{V}.................(ii)[/tex]

Comparing equation 'i' and 'ii' we see that

[tex]\rho_{2}=7\times \rho _{1}[/tex]

Since the first liquid is water thus [tex]\rho _{1}=1gm/cm^3[/tex]

Thus the relative density of the second liquid is 7.

Answer:

7

Explanation:

Let the density of second liquid is d.

Density of water = 1 g/cm^3

In case of equilibrium, according to the principle of flotation, the weight of the body is balanced by the buoyant force acting on the body.

Let A be the area of cross section of block and D be the density of material of block and h be the height.

For first liquid (water):

Weight of block = m x g  = A x h x D x g .... (1)

Buoyant force in water = A x h x 1 x g  ..... (2)

Equating (1) and (2) we get

A x h x D x g = A x h x 1 x g

D = 1 g/cm^3

For second liquid:

Weight of block = m x g  = A x h x D x g .... (1)

Buoyant force in second liquid = A x h/7 x d x g  ..... (2)

Equating (1) and (2) we get

A x h x D x g = A x h/7 x d x g

D = d/7

d = 7 D = 7 x 1 = 7 g/cm^3

Thus, the relative density of second liquid is 7.

Answer:

946.92 kJ

Explanation:

This process has 3 parts:

1. The first part, where the temperature of Ethyl alcohol remains constant and it changes from gas to liquid.

2. The second part, where the temperature drops from 78°C to -114°C

3. The third parts, where the temperature remains constant and it changes from liquid to solid.

The energy lost in a phase change is:

Q = m*cl

The energy lost because of the drop in temperature is:

[tex]Q = m c(T_2-T_1)[/tex]

cl is the heat of vaporization or heat of fusion, depending on the type of phase change. c is the specific heat.

So, the energy lost in each part is:

1. [tex]Q_1 = 0.651kg*879 kJ/kg =  572.23 kJ[/tex]

2. [tex]Q_2 = 0.651kg*2.43 kJ/kgK(78.0^oC - (-114^oC)) = 303.73 kJ[/tex]

3. [tex]Q_3 = 0.651kg*109kJ/kg = 70.96 kJ[/tex]

Then, the total energy removed should be:

Q = Q1 + Q2 + Q3 = 572.23 kJ + 303.73kJ + 70.96kJ = 946.92 kJ

Answer:

[tex]\frac{F}{W} = 9.37 \times 10^{-4}[/tex]

Explanation:

Radius of the pollen is given as

[tex]r = 12.0 \mu m[/tex]

Volume of the pollen is given as

[tex]V = \frac{4}{3}\pi r^3[/tex]

[tex]V = \frac{4}{3}\pi (12\mu m)^3[/tex]

[tex]V = 7.24 \times 10^{-15} m^3[/tex]

mass of the pollen is given as

[tex]m = \rho V[/tex]

[tex]m = 7.24 \times 10^{-12}[/tex]

so weight of the pollen is given as

[tex]W = mg[/tex]

[tex]W = (7.24 \times 10^{-12})(9.81)[/tex]

[tex]W = 7.1 \times 10^{-11}[/tex]

Now electric force on the pollen is given

[tex]F = qE[/tex]

[tex]F = (-0.700\times 10^{-15})(95)[/tex]

[tex]F = 6.65 \times 10^{-14} N[/tex]

now ratio of electric force and weight is given as

[tex]\frac{F}{W} = \frac{6.65 \times 10^{-14}}{7.1 \times 10^{-11}}[/tex]

[tex]\frac{F}{W} = 9.37 \times 10^{-4}[/tex]