The space shuttle travels at a speed of about 7.6times10^3 m/s. The blink of an astronaut's eye lasts about 110 ms. How many football fields (length=91.4 m) does the shuttle cover in the blink of an eye? The three-toed sloth is the slowest-moving land mammal. On the ground, the sloth moves at an average speed of 0.033 m/s, considerably slower than the giant tortoise have gone relative to the sloth? Do not put units in your answer.

The magnetic force on the wire has an x-component of 0 N, a y-component of 0.004056224 N in the negative y-direction, and a z-component of 0.000143712 N in the positive z-direction.

The question involves calculating the magnetic force on a current-carrying wire in a magnetic field using the right-hand rule and the formula F = I × (L × B), where F is the force, I is the current, L is the length of the wire, and B is the magnetic field. We know the current I is 0.720 A, the length L is 73.6 cm (which we will convert to meters), and the magnetic field components are By = 0.000270 T and Bz = 0.00770 T.

First, let's convert the length of the wire from centimeters to meters: L = 73.6 cm = 0.736 m.

The force on the wire in the x, y, and z directions (Fx, Fy, Fz) can be calculated using the cross product of the current direction (along the x-axis) and the magnetic field components. Since there is no x component for the magnetic field (Bx = 0), the force in the x-direction (Fx) will be zero.

Using the right-hand rule, the force in the y-direction (Fy) will be:

Fy = I × (L × Bz) = 0.720 A × (0.736 m × 0.00770 T) = 0.004056224 N, pointing in the negative y-direction (since the current is in the positive x-direction and Bz is positive).

Similarly, the force in the z-direction (Fz) is calculated as:

Fz = I × (L × By) = 0.720 A × (0.736 m × 0.000270 T) = 0.000143712 N, pointing in the positive z-direction.

Answer:

7.55 m/s, 6.56 m/s

Explanation:

v = 10 m/s, theta = 41 degree

Horizontal component of velocity = v x Cos theta = 10 x Cos 41 = 7.55 m/s

Vertical component of velocity = v x Sin theta = 10 x Sin 41 = 6.56 m/s

Final answer:

The ball's horizontal velocity is approximately 7.57 m/s, and its vertical velocity is approximately 6.46 m/s immediately after the serve.

Explanation:

The student's question about the initial horizontal and vertical velocities of a volleyball serve involves breaking down the initial velocity into its component parts using trigonometric functions. Given an initial velocity (v) of 10 m/s and an angle (θ) of 41 degrees from the horizontal, the horizontal component (vx) is calculated using cosine, and the vertical component (vy) is calculated using sine.

Using the formula:

vx = v ∙ cos(θ)

vy = v ∙ sin(θ)

For this problem:

vx = 10 m/s ∙ cos(41°)

vy = 10 m/s ∙ sin(41°)

Plugging in the values yields:

vx ≈ 7.57 m/s

vy ≈ 6.46 m/s

The ball's horizontal velocity is approximately 7.57 m/s, and its vertical velocity is approximately 6.46 m/s immediately after the serve.

Answer:

Its potential energy decreases and itselectricpotential increases.

Explanation:

The electric potential does not depend on the charge but only on the magnitude of the electric field. In particular:

- Electric potential decreases when moving in the same direction of the electric field lines

- Electric potential increases when moving in the opposite direction to the field lines

So in this case, since the electron is moving in a direction opposite to the field, the electric potential increases.

However, the electric potential energy of a charge is given by

[tex]U=qV[/tex]

where

q is the charge

V is the electric potential

Here we said that the electric potential is increasing: however, the charge q of an electron is negative. This means that the product (qV) is increasing in magnitude but it is negative, so the potential energy of the electron is decreasing.

For an electron moving in a direction opposite to the electric field its potential energy decreases and its electric potential increases.

Electric potential is the amount of work needed to move a unit charge from a point to a specific point against an electric field.it is denoted by U.

However, the electric potential energy of a charge is given by

[tex]\rm{U=qv}[/tex]

q is denoted for the charge.

V is denoted for the electric potential.

The above relation shows that the electric potential is inversely proportional to the electric potential energy.

The electric potential is independent of the charge. but it depends on the direction in which the charge is moving. If the charge moves in the direction of the electric field electric potential decreases and vice versa.

Here the electron is moving in a direction opposite to the field, the electric potential increases while electric potential energy decreases.

To learn more about the electric potential energy refers to the link.

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Answer:

The distance the block will slide before it stops is x= 3.4 m .

Explanation:

m1= 0,02 kg

V1= 400 m/s

m2= 2 kg

V2= ?

g= 9.8 m/s²

μ= 0.24

N = m2 * g = 19.6 N

Fr= μ * N

Fr= 4.704 N

due to the conservation of the amount of movement:

m1*V1 = m2*V2

V2= 4 m/s

Fr = m2*a

a= Fr/m2

a= -2.352 m/s²

matching momentum and amount of movement

Fr*t=m2*V2

t= 1.7 sec

x= V2*t - (a*t²)/2

x= 3.4 m

Answer:

The distance the block will slide before it stops is 3.3343 m

Explanation:

Given;

mass of bullet, m₁ = 20-g = 0.02 kg

speed of the bullet, u₁ =  400 m/s

mass of block, m₂ = 2-kg

coefficient of kinetic friction,  μk = 0.24

Step 1:

Determine the speed of the bullet-block system:

From the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = v(m₁ + m₂)

where;

v is the speed of the bullet-block system after collision

(0.02 x 400) + (2 x 0) = v (0.02 + 2)

8 = v (2.02)

v = 8/2.02

v = 3.9604 m/s

Step 2:

Determine the time required for the bullet-block system to stop

Apply the principle of conservation momentum of the system

[tex]v(m_1+m_2) -F_kt = v_f(m_1 +m_2)\\\\v(m_1+m_2) -N \mu_kt = v_f(m_1 +m_2)\\\\v(m_1+m_2) -g(m_1 +m_2) \mu_kt = v_f(m_1 +m_2)\\\\3.9604(2.02)-9.8(2.02)0.24t = v_f(2.02)\\\\8 - 4.751t = 2.02v_f\\\\3.9604 - 2.352t = v_f[/tex]

when the system stops, vf = 0

3.9604 -2.352t = 0

2.352t = 3.9604

t = 3.9604/2.352

t = 1.684 s

Thus, time required for the system to stop is 1.684 s

Finally, determine the distance the block will slide before it stops

From kinematic, distance is the product of speed and time

[tex]S = \int\limits {v} \, dt \\\\S = \int\limits^t_0 {(3.9604-2.352t)} \, dt\\\\ S = 3.9604t - 1.176t^2[/tex]

Now, recall that t = 1.684 s

S = 3.9604(1.684) - 1.176(1.684)²

S = 6.6693 - 3.3350

S = 3.3343 m

Thus, the distance the block will slide before it stops is 3.3343 m

Answer:

23.5 J/Kg °C

Explanation:

The amount of heat required to raise the temperature of substance of mass 1 kg by 1 degree Celcius.

c = Q / m ΔT

Here, Q / m = 282 J/kg, ΔT = 12

So, the specific heat = 282 / 12 = 23.5 J/Kg °C

The speed of the electron when it reaches point B, which is 0.395 m east of point A, is approximately 3.86×10⁵ m/s, directed towards the east.

The initial speed of the electron is provided as 4.52×10⁵ m/s. Given the electric field, we can calculate the force on the electron as F = qE, where q is the charge of the electron (-1.60 × 10⁻¹⁹ C) and E is the electric field (1.55 N/C). Hence, the force acting on the electron is F = -1.60 × 10⁻¹⁹ C * 1.55 N/C = -2.48 × 10⁻¹⁹ N.

Using F = ma, we can calculate the acceleration of the electron. Knowing the mass of the electron is 9.11 × 10⁻³¹ kg, the acceleration is a = F/m = -2.48 × 10⁻¹⁹ N / 9.11 × 10⁻³¹ kg = -2.72 × 10¹¹ m/s².

Given the distance of the movement is 0.395 m, we can use the equation v² = u² + 2as to solve for the final velocity 'v', where 'u' is the initial velocity, 'a' is the acceleration and 's' is the distance. Substituting the known values, we get v = sqrt((4.52×10⁵ m/s)² - 2 * 2.72 × 10¹¹ m/s² * 0.395 m) ≈ 3.86 x 10⁵ m/s (approximately).

So, the speed of the electron when it reaches point B is approximately 3.86 x 10⁵ m/s, directed towards the east.

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Answer:

(a) the constant of the spring is 27095.375 J/m2

(b) 0.052 m/s

(c) F=17341.04 N

Explanation:

Hello

The law of conservation of energy states that the total amount of energy in any isolated system (without interaction with any other system) remains unchanged over time.

if we assume that there is no friction, then, the kinetic energy of the train (due to movement) will be equal to the energy accumulated in the spring

Step 1

energy of the train (kinetic)

[tex]E_{k}=\frac{m*v^{2} }{2}\\  E_{k}=\frac{2.15*10^{5}kg*(0.71\frac{m}{s}) ^{2} }{2}\\E_{k}=54190.75 J\\ \\[/tex]

step 2

energy of the spring

[tex]E_{s}=\frac{Kx^{2} }{2}\\[/tex]

where K is the constant of the spring and x the length compressed.

[tex]E_{s}=\frac{Kx^{2} }{2}=54190.75 J\\\frac{Kx^{2} }{2}=54190.75 J\\\\k=\frac{2*54190.75 J}{x^{2}}\\k=\frac{2*54190.75 J}{(2.0 m)^{2} }\\ k=27095.375\frac{J}{m^{2} } \\\\[/tex]

(a) the constant of the spring is 27095.375 J/m2

(b)

[tex]x=0.640 m\\\\E_{s}=\frac{27095.375 (\frac{j}{m^{2} })*(0.640m)^{2}  }{2}\\ E_{s}=5549.1328 J\\[/tex]

equal to train energy

[tex]E_{k}=\frac{2.15*10^{5}kg*(v) ^{2} }{2}\\\frac{2.15*10^{5}kg*(v) ^{2} }{2}=5549.1328 J\\v^{2}=\frac{2*5549.1328 J}{2.15*10^{5}kg}\\v=0.052 \frac{m}{s} \\\\[/tex]

(b) 0.052 m/s

(c)

[tex]F= kx\\\\F=27095.375 \frac{J}{m^{2} }*(0.640 m)\\ F=17341.04 N\\F=17341.04[/tex]

(c) F=17341.04 N

I hope it helps

The force constant of the spring is 38.03 N/m. If the train compressed the spring 0.640 m, the train would be going at a speed of 0.418 m/s. The force the spring exerts when compressed 0.640 m is 24.34 N.

To solve these questions we use conservation of energy principles and the spring equation, F = k*x. The initial kinetic energy of the train is converted into potential energy in the spring at the point of maximum compression.

(a) What is the force constant of the spring?
Here we equate kinetic energy with potential energy by using the equations KE = 0.5 * m * v^2 and PE = 0.5 * k * x^2. We can solve for k to get k = m * v^2 / x^2, so it's (2.15 x 10^5 kg * (0.710 m/s)^2)/(2.00 m)^2 = 38.03 N/m.

(b) What speed would the train be going if it only compressed the spring 0.640 m?
Here we rearrange the previous equation for velocity, v = sqrt(k * x^2 / m) which we then place values into to calculate v = sqrt(38.03 N/m * (0.640 m)^2)/(2.15 x 10^5 kg) = 0.418 m/s.

(c) What force does the spring exert when compressed 0.640 m?
Here we refer back to Hooke's Law (F = k*x), which states that the force required to compress or extend a spring by some distance x is proportional to that distance. The spring constant (k) is the proportionality constant in this relationship. So, the force is F = (38.03 N/m * 0.640 m) = 24.34 N.

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Answer:

[tex]Q = 4.63 \times 10^6 J[/tex]

Explanation:

As we know that melting point of silver is

T = 961.8 degree C

Latent heat of fusion of silver is given as

L = 111 kJ/kg

specific heat capacity of silver is given as

[tex]s = 240 J/kg C[/tex]

now we will have

[tex]Q = ms\Delta T + mL[/tex]

[tex]\Delta T = 961.8 - 20 [/tex]

[tex]\Delta T = 941.8 degree C[/tex]

now from above equation

[tex]Q = (13.74)(240)(941.8) + (13.74)(111 \times 10^3)[/tex]

[tex]Q = 3.1 \times 10^6 + 1.53 \times 10^6[/tex]

[tex]Q = 4.63 \times 10^6 J[/tex]

Answer:L=33.93

R.E.=152.30

Explanation:

Given

mass of disk[tex]\left ( m\right )[/tex]=21kg

thickness[tex]\left ( t\right )[/tex]=0.5m

radius[tex]\left ( r\right )[/tex]=0.6m

t=0.7 sec for every complete rotation

therefore angular velocity[tex]\left ( \omega \right ) =\frac{\Delta \theta }{\Delta t}[/tex]

[tex]\left ( \omega \right )=\frac{ 2\pi }{0.7}=8.977[/tex] rad/s

Rotational angular momentum is given by

[tex]L=I\omega [/tex]

[tex]I[/tex]=[tex]\frac{mr^2}{2}[/tex]

I=3.78 [tex]kg-m^2[/tex]

[tex]L=3.78\times 8.977[/tex]

L=33.93 [tex]\hat{j}[/tex]

considering disk is rotating in z-x plane

Rotational kinetic energy=[tex]\frac{I\omega ^{2}}{2}[/tex]=152.30 J

The rotational angular momentum of the disk is 33.89 kg.m²/s directed into the page, and the rotational kinetic energy of the disk is 151.5 J.

To calculate the rotational angular momentum of the disk, we will first need to compute the moment of inertia and angular velocity. The moment of inertia is given by the formula for a solid disk, which is I = 1/2mR². Here, m is the mass of the disk (in this case, 21 kg), and R is the radius of the disk (which is 0.6 m). So, I = 0.5*21*(0.6)² = 3.78 kg.m².

Furthermore, the angular velocity (ω) can be calculated using the formula 2π/T, where T is the period, which is the time it takes for one complete rotation (0.7 s in this situation). Therefore, ω = 2π/0.7 = 8.96 rad/s.

Finally, the rotational angular momentum (L), is given by the product of the moment of inertia and angular velocity, L = I*ω. Therefore, L = 3.78 kg.m² * 8.96 rad/s = 33.89 kg.m²/s.

The direction of the rotational angular momentum is along the axis of rotation, which depends on the right-hand rule. Since it is rotating clockwise when viewed from above, the vector is directed into the page (negative z-direction).

To compute the rotational kinetic energy (KE), we use the formula KE = 1/2 I ω². Substituting the values, we get KE = 0.5*3.78 kg.m²*(8.96 rad/s)² = 151.5 J.

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The rate of cooling provided by a reversible refrigerator, working with a 10-kW compressor and thermal energy reservoirs at 250 K and 310 K, is calculated using the refrigerator's Carnot coefficient and the power of the compressor. With these specific conditions, the cooling rate is calculated to be 50 kW.

The question pertains to the functioning of a reversible refrigerator, specifically the cooling rate provided by the appliance which uses a 10-kW compressor and operates with thermal energy reservoirs at 250 K and 310 K. To determine the cooling rate, we must first understand some basics about the refrigerator's operation.

A reversible refrigerator absorbs heat Qc from a cold reservoir and discards it into a hot reservoir, while work W is done on it. This work is represented by the power exerted by the compressor. The refrigerator functions by moving a coolant through coils, which absorbs heat from the contents of the refrigerator and releases it outside.

The coefficient of performance or Carnot coefficient (KR) of the refrigerator can be computed using the formula KR = Tc / (Th - Tc) where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir, both measured in Kelvin. In this situation, KR = 250 / (310 - 250) = 5.

Since the work done W is the compressor power P, we can use the formula Qc = KR * P to find the cooling rate. Substituting the known values, Qc = 5 * 10 kW = 50 kW. Therefore, the rate of cooling provided by this refrigerator is 50 kW.

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Answer:

[tex]v' = 2.83 m/s[/tex]

Explanation:

Velocity of wave in stretched string is given by the formula

[tex]v = \sqrt{\frac{T}{\mu}}[/tex]

here we know that

T = 4 N

also we know that linear mass density is given as

[tex]\mu = 1 kg/m[/tex]

so we have

[tex]v = \sqrt{\frac{4}{1}} = 2 m/s[/tex]

now the tension in the string is double

so the velocity is given as

[tex]v' = \sqrt{\frac{8}{1}} = 2\sqrt2 m/s[/tex]

[tex]v' = 2.83 m/s[/tex]

Answer:

0.51

Explanation:

m = mass of the book = 3.5 kg

F = force applied by the broom on the book = 21 N

a = acceleration of the book

v₀ = initial speed of the book = 0 m/s

v = final speed of the book = 1.2 m/s

d = distance traveled = 0.74 m

Using the equation

v² = v₀² + 2 a d

1.2² = 0² + 2 a (0.74)

a = 0.973 m/s²

f = kinetic frictional force

Force equation for the motion of the book is given as

F - f = ma

21 - f = (3.5) (0.973)

f = 17.6 N

μ = Coefficient of kinetic friction

Kinetic frictional force is given as

f = μ mg

17.6 = μ (3.5 x 9.8)

μ = 0.51

Answer:

Speed of the airplane 10.0 s later = 12.2 m/s

Explanation:

Mass of Boeing 777 aircraft = 300,000 kg

Braking force = 445,000 N

Deceleration

            [tex]a=\frac{445000}{300000}=1.48m/s^2[/tex]

Initial velocity, u = 27 m/s

Time , t = 10 s

We have equation of motion, v =u +at

            v = 27 + (-1.48) x 10 = 27 - 14.8 = 12.2 m/s

Speed of the airplane 10.0 s later = 12.2 m/s

After applying the deceleration due to the braking force for 10 seconds, the speed of the Boeing 777 airplane reduces to 12.17 m/s.

Calculating the Final Speed of a Boeing 777 After Braking

To determine the speed of a Boeing 777 aircraft after a 10-second interval of braking, we will use the relationship between force, mass, initial velocity, and acceleration provided by Newton’s second law of motion. The braking force applied on the aircraft is 445,000 N acting opposite to the direction of motion. We can calculate the deceleration using the formula:

F = ma

Where F is the force, m is the mass, and a is the acceleration (deceleration in this case since the force is applied opposite to the direction of motion). The mass (m) of the airplane is 300,000 kg, so we can solve for 'a' as follows:

a = F / m = 445,000 N / 300,000 kg = 1.483 m/s² (deceleration)

Next, we use the kinematic equation to find the final velocity (vf) after 10 seconds:

vf = vi + at

Where vi is the initial velocity, and t is the time. We know that the initial velocity (vi) is 27.0 m/s and the time (t) is 10.0 s.

Plugging the numbers in:

vf = 27.0 m/s - (1.483 m/s² × 10.0 s) = 27.0 m/s - 14.83 m/s = 12.17 m/s

Therefore, the speed of the Boeing 777 airplane 10 seconds later is 12.17 m/s.

Answer:

it is at height of y = 0.533 m from ground

Explanation:

As per law of reflection we know that angle of incidence = angle of reflection

so here we have

[tex]tan\theta_i = tan\theta_r[/tex]

here we know that

[tex]tan\theta_i = \frac{y}{d}[/tex]

also we have

[tex]tan\theta_r = \frac{H - y}{D}[/tex]

now we have

[tex]\frac{H - y}{D} = \frac{y}{d}[/tex]

here we have

[tex]\frac{1.6 - y}{5.8} = \frac{y}{2.9}[/tex]

[tex]3y = 1.6[/tex]

[tex]y = 0.533 m[/tex]

To see the bottom of the object in the mirror, the bottom of the mirror should be at a height of half the height of the person.

To see the bottom of the object in the mirror, the person should be able to see an image of the bottom of the object reflected in the mirror.

Using the law of reflection, we can determine the height h at which the bottom of the mirror should be. The angle of incidence for the light from the bottom of the object is equal to the angle of reflection, so the height of the mirror should be equal to the height of the person's eyes, H, plus the height of the bottom of the object, h. We can calculate h using similar triangles:

h/H = d/D

where d is the distance from the object to the mirror and D is the distance from the person to the mirror. Substituting the given values, we have:

h = (d/D) * H

Substituting d = D/2, we get:

h = (D/2D) * H = H/2

Therefore, the bottom of the mirror should be at a height of half the height of the person.

Answer:

(a) 1.21 m/s

(b) 2303.33 J, 152.27 J

Explanation:

m1 = 95 kg, u1 = - 3.750 m/s, m2 = 113 kg, u2 = 5.38 m/s

(a) Let their velocity after striking is v.

By use of conservation of momentum

Momentum before collision = momentum after collision

m1 x u1 + m2 x u2 = (m1 + m2) x v

- 95 x 3.75 + 113 x 5.38 = (95 + 113) x v

v = ( - 356.25 + 607.94) / 208 = 1.21 m /s

(b) Kinetic energy before collision = 1/2 m1 x u1^2 + 1/2 m2 x u2^2

                                               = 0.5 ( 95 x 3.750 x 3.750 + 113 x 5.38 x 5.38)

                                               = 0.5 (1335.94 + 3270.7) = 2303.33 J

Kinetic energy after collision = 1/2 (m1 + m2) v^2                

                                                = 0.5 (95 + 113) x 1.21 x 1.21 = 152.27 J

Answer:

[tex]F_c = 1.4 \times 10^6 N[/tex]

Explanation:

As we know

[tex]f = 24 rpm[/tex]

so we will have

[tex]f = 24 \frac{1}{60} hz = 0.4hz[/tex]

now angular frequency is given as

[tex]\omega = 2\pi f[/tex]

[tex]\omega = 0.8\pi[/tex]

Now the inwards is given as centripetal force

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

[tex]F_c = (12000)(0.8\pi)^2(\frac{37}{2})[/tex]

[tex]F_c = 1.4 \times 10^6 N[/tex]

Final answer:

The inward force necessary to provide each blade's centripetal acceleration is approximately 4,755,076 Newtons.

Explanation:

To calculate the inward force necessary to provide each blade's centripetal acceleration, we can use the formula for centripetal force:

[tex]Fc = m \times \omega^2 \times r[/tex]

where Fc is the centripetal force, m is the mass of the blade, ω is the angular velocity, and r is the radius of the blade.

In this case, the mass of the blade is 12,000 kg, the angular velocity is 24 rpm (which can be converted to radians per second by multiplying by 2π/60), and the radius of the blade is 37 m.

Plugging these values into the formula, we get:

Fc = 12000 kg * (24 * 2π/60)^2 * 37 m

Fc ≈ 4,755,076 N

So, the inward force necessary to provide each blade's centripetal acceleration is approximately 4,755,076 Newtons.

Answer:

655128 ohm

Explanation:

C = Capacitance of the capacitor = 7.8 x 10⁻⁶ F  

V₀ = Voltage of the battery = 9 Volts  

V = Potential difference across the battery after time "t" = 4.20 Volts  

t = time interval = 3.21 sec  

T = Time constant

R = resistance  

Potential difference across the battery after time "t" is given as  

[tex]V = V_{o} (1-e^{\frac{-t}{T}})[/tex]

[tex]4.20 = 9 (1-e^{\frac{-3.21}{T}})[/tex]

T = 5.11 sec  

Time constant is given as  

T = RC  

5.11 = (7.8 x 10⁻⁶) R  

R = 655128 ohm

Answer:

55000000 years

Explanation:

Rate of North American Plate moving (Velocity) = 20 mm/yr

Degrees New York has to move = 10° west

New York's longitude = 110 km/°

Distance of New York = 110×10 = 1100 km

= 1100×10⁶ mm

[tex]\text {Time taken by the continental plate}=\frac {\text {Distance of New York}}{\text {Rate of North American Plate moving (Velocity)}}\\\Rightarrow \text {Time taken by the continental plate}=\frac{1100\times 10^6}{20}\\\Rightarrow \text {Time taken by the continental plate}=55\times 10^6\ years[/tex]

∴ Time taken by New York to move 10° west is 55000000 years

Answer:

4.89 seconds

Explanation:

The time period of a pendulum is given by

[tex]T = 2\pi \sqrt{\frac{l}{g}}[/tex]

For a second pendulum on earth, T = 2 second

[tex]2 = 2\pi \sqrt{\frac{l}{g}}[/tex]     ...... (1)

Now the time period is T when the pendulum is taken to moon and gravity at moon is 1/6 of gravity of earth

[tex]T = 2\pi \sqrt{\frac{l}{\frac{g}{6}}}[/tex]    ...... (2)

Divide equation (2) by equation (1)

[tex]\frac{T}{2} = \sqrt{6}[/tex]

T = 4.89 seconds

Answer:

97.96 [tex]\frac{rad}{s}[/tex]

Explanation:

The initial angular velocity is [tex]w_{0}[/tex] = 126 rad / s.

The constant angular deceleration is 5.00 rad / s2.

The constant angular deceleration is, by definition: dw / dt.

[tex]\frac{dw}{dt}=-5 \frac{rad}{s^{2} }[/tex]

Separating variables

[tex]dw=-5 dt[/tex]

Integration (limits for w: 0 to W0; limits for t: 0 to t)

[tex]w= w_{0}-5t[/tex]

W is by definition [tex]\frac{d\alpha }{dt}[/tex], where [tex]\alpha[/tex] is the angle.

[tex]\frac{d\alpha}{dt}=w_{0} -5t[/tex]

Separating variables

[tex]d\alpha=(w_{0} -5t )dt[/tex]

Integration (limits for [tex]\alpha[/tex]: 0 to 628; limits for t: 0 to t)

[tex]\alpha =w_{0}t-(\frac{5}{2})t^{2}[/tex]

[tex]128=126t-(\frac{5}{2})t^{2}[/tex]

Put in on the typical form of a quadratic equation:

[tex]\frac{5}{2}t^{2}-126t+628=0[/tex]

Solve by using the quadratic equation formula and discard the higher result because it lacks physical sense.

t=5.608 s

Evaluate at this time the angular velocity:

[tex]w(t=5.608)=126-5*5.608[/tex]

[tex]w(5.608)=97.96 \frac{rad}{s}[/tex]

To find the final angular speed of a rotating wheel given the initial speed, angular deceleration and the angle turned, we use an equation for angular motion. We substitute the given values and solve the equation to find the final angular speed.

To solve this question, we will be using the equation for angular motion,

ω² = ω0² + 2αθ

, where ω is the final angular speed we want to find, ω0 = 126 rad/s is the initial angular speed, α = -5.00 rad/s² is the angular deceleration, and θ = 628 rad is the angle turned through. This equation is analogous to the equation for linear motion, v² = u² + 2as, where v is final velocity, u initial velocity, a acceleration and s distance. We substitute the given values into the equation to find the final angular speed. Keep in mind, because we are dealing with deceleration, our α value is a negative.

Solve the equation: ω² - ω0² = 2αθ, which gives: ω² = (ω0² + 2αθ), ω = sqrt((ω0² + 2αθ)), ω = sqrt((126rad/s)² + 2*(-5.00 rad/s²)*628 rad). So, when you calculate the square root of the total, you will find the answer for the final angular speed.

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Answer:

EMF = 2.4 V

Explanation:

As we know by Lenz law that induced EMF is given by rate of change in magnetic flux in the coil

As we know that magnetic flux is given by

[tex]\phi = NBA[/tex]

here we know that

[tex]N = 300[/tex]

[tex]Area = 0.20 \times 0.20 = 0.04 m^2[/tex]

now we for induced EMF we have

[tex]EMF = NA\frac{dB}{dt}[/tex]

here we have

[tex]EMF = (300)(0.04)(\frac{0.90 - 0.50}{2})[/tex]

[tex]EMF = 2.4 V[/tex]

The magnitude of the induced emf in a coil, while the magnetic field is changing, can be calculated using Faraday's law. The law states that the induced emf is equal to the negative of the rate of change of the magnetic flux linked through the circuit. We use this formula to calculate the change in magnetic field, take into accounts of coil's area and number of turns then divide by the change in time.

The magnitude of the induced emf in a coil, while the magnetic field is changing, can be calculated using Faraday's law of electromagnetic induction, which states that the induced emf is equal to the negative rate of change of the magnetic fluxlinked through the circuit.

In this case, the magnetic flux, Φ, through the coil can be calculated using the formula Φ = BAN, where B is the magnetic field, A is the area of each turn (which can be calculated using the given side length) and N is the number of turns (300 in this case).

To calculate the rate of change of the magnetic flux use the formula ΔΦ/Δt, where ΔΦ is the change in magnetic flux and Δt is the change in time. In this case, the magnetic field changes from 0.50 T to 0.90 T in 2.0 s, so the change in magnetic flux is (B_final - B_initial)*A*N, and Δt is 2.0 s.

The magnitude of the induced emf (which is also the negative rate of change of the magnetic flux) is given by Faraday's law, |ε| = |ΔΦ/Δt|.?

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Answer:

0.42 m/s²

Explanation:

r = radius of the flywheel = 0.300 m

w₀ = initial angular speed = 0 rad/s

w = final angular speed = ?

θ = angular displacement = 60 deg = 1.05 rad

α = angular acceleration = 0.6 rad/s²

Using the equation

w² = w₀² + 2 α θ

w² = 0² + 2 (0.6) (1.05)

w = 1.12 rad/s

Tangential acceleration is given as

[tex]a_{t}[/tex] = r α = (0.300) (0.6) = 0.18 m/s²

Radial acceleration is given as

[tex]a_{r}[/tex] = r w² = (0.300) (1.12)² = 0.38 m/s²

Magnitude of resultant acceleration is given as

[tex]a = \sqrt{a_{t}^{2} + a_{r}^{2}}[/tex]

[tex]a = \sqrt{0.18^{2} + 0.38^{2}}[/tex]

[tex]a[/tex] = 0.42 m/s²

The magnitude of the resultant acceleration of the point on the flywheel's rim after it has turned through 60.0° is approximately 0.424 m/s².

To compute the magnitude of the resultant acceleration of a point on the flywheel's rim, we need to use the equation:

θ = ω0t + 0.5αt2

Where θ is the angle turned, ω0 is the initial angular velocity, and α is the angular acceleration.

Plugging in the given values, the equation becomes:

60.0° = 0 + 0.5 * 0.600 rad/s² * t2

Simplifying, we get:

t2 = (60.0° * 2) / 0.600 rad/s²

t2 = 0.200 rad/s²

Therefore, the magnitude of the resultant acceleration is:

a = ωt = 0.600 rad/s² * sqrt(0.200 rad/s²) ≈ 0.424 m/s²

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Answer:

105.6857 nm

Explanation:

Wave length of laser pointer = λ = 685 nm = 685×10⁻⁹ m

Distance between screen and slit = L = 5.4 m

Width of bright band = 2x = 7 cm

⇒x = 3.5 cm = 3.5×10⁻² m

The first minimum occurs at

sin θ = λ/d

θ = λ/d                 (since the angle is very small, sin θ ≈ θ)

Width of slit

d = λL/x

⇒d = 685×10⁻⁹×5.4/3.5×10⁻²

⇒d = 1056.857×10⁻⁷ m

∴ The width of the slit is 105.6857 nm

Answer:

- 0.5 m/s²

Explanation:

m = mass of the clarinet case = 3.230 kg

W = weight of the clarinet case in downward direction

a = vertical acceleration of the case

Weight of the clarinet case is given as

W = mg

W = 3.230 x 9.8

W = 31.654 N

F = Upward force applied = 30.10 N

Force equation for the motion of the case is given as

F - W = ma

30.10 - 31.654 = 3.230 a

a = - 0.5 m/s²

Final answer:

By applying Newton's second law and accounting for the forces acting on the clarinet case, it is found to experience a downward vertical acceleration of 0.489 m/s², due to the net force acting on it being in the downward direction.

Explanation:

To find the vertical acceleration of the clarinet case, first identify the forces acting on it. The force of gravity (weight) pulls it downward, which can be calculated by multiplying the mass of the case by the acceleration due to gravity (9.81 m/s²). The equation for weight is W = mg, where m is mass and g is gravity.

Substituting the given values, W = 3.230 kg * 9.81 m/s² = 31.68 N. The net force [tex]F_{net}[/tex] acting on the case is the upward force by the clarinetist subtracting the weight of the case, [tex]F_{net}[/tex] = 30.10 N - 31.68 N = -1.58 N. Applying Newton's second law, F = ma, and solving for acceleration (a), a = [tex]F_{Net/m}[/tex], we find the case's vertical acceleration as a = -1.58 N / 3.230 kg = -0.489 m/s².

Therefore, the case experiences a downward acceleration of 0.489 m/s², indicating that it is slowing in its ascent or accelerating downward.

Answer:

[tex]Distance_{vaccum}=5.19cm[/tex]

Explanation:

The speed of light in these mediums shall be lower than that in vacuum thus the total time light needs to cross both the media are calculated as under

Total time = Time taken through ice + Time taken through quartz

Time taken through ice = Thickness of ice / (speed of light in ice)

[tex]T_{ice}=\frac{2.20\times 10^{-2} \times \mu _{ice}}{V_{vaccum}}[/tex]

[tex]T_{quartz}=\frac{1.50\times 10^{-2} \times \mu _{quartz}}{V_{vaccum}}[/tex]

Thus in the same time the it would had covered a distance of

[tex]Distance_{vaccum}=Totaltime\times V_{vaccum}\\\\Distance_{vaccum}=10^{-2}[2.20\mu _{ice+1.50\mu _{quartz}}][/tex]

we have

[tex]\mu _{ice}=1.309\\\\\mu _{quartz}=1.542[/tex]

Applying values we have

[tex]Distance_{vaccum}=10^{-2}[2.20\times 1.309+1.50\times 1.542][/tex]

[tex]Distance_{vaccum}=5.19cm[/tex]

The light, after going through ice and quartz, would have traveled approximately 5.198 cm in vacuum. This is calculated considering indices of refraction for each material and their thicknesses.

The subject of this question is in the domain of Physics, specifically optics. The problem wants us to compare the distances light travels in different media to its travel in vacuum. The key to solve this matter is knowing the speed of light changes depending on the medium it passes through: it's slower in media like ice or quartz than in vacuum, due to these materials' indices of refraction.

The index of refraction for ice is approximately 1.31 and for crystalline quartz is approximately 1.544. The index of refraction (n) is the ratio of the speed of light in vacuum (c), to the speed of light in the medium (v), or n = c/v. To find out the distances light travels in vacuum for the time it takes to travel through the ice and quartz, we need to multiply the thickness of each material by their respective indices of refraction.

For the ice, it's 2.20 cm * 1.31 = 2.882 cm and for the quartz, it's 1.50 cm * 1.544 = 2.316 cm. So the total distance light would have traveled in vacuum in the same time it passes through both sheets is approximately 2.882 cm + 2.316 cm = 5.198 cm.

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Answer:

55536.6 J

Explanation:

Given:

Mass of the ice = 54g

Initial temperature = 0°C

Final Temperature = 100°C

Mass of the steam = 6.6g

Now the energy required for the transformation of the ice to vapor will involve the heat requirement in the following stages as:  

1) The energy required to melt ice = mass of ice × heat of fusion of water = 54g × 334 J/g  = 18036 J

  (because heat of fusion for water = 334 J/g)

2) The energy to heat water from 0 to 100 = mass of water × specific heat of water × change in temperature = 54g × 4.186 J/g°C × 100 °C = 22604.4 J  

lastly,

3) the energy required to vaporize 6.6g of water = mass of water × heat of vaporization of water = 6.6 × 2257 J/g = 14896.2 J  

Thus,

the total energy required to transform the ice cube to accomplish the transformation = 18036 + 22604.4 + 14896.2 = 55536.6 J.

Given:

Height of tank = 8 ft

and we need to pump fuel weighing 52 lb/ [tex]ft^{3}[/tex] to a height of 13 ft above the tank top

Solution:

Total height = 8+13 =21 ft

pumping dist = 21 - y

Area of cross-section = [tex]\pi r^{2}[/tex] =  [tex]\pi 4^{2}[/tex] =16[tex]\pi[/tex] [tex]ft^{2}[/tex]

Now,

Work done required = [tex]\int_{0}^{8} 52\times 16\pi (21 - y)dy[/tex]

                                  = [tex]832\pi \int_{0}^{8} (21 - y)dy[/tex]

                                  = 832[tex]\pi([/tex][tex][ 21y ]_{0}^{8} - [\frac{y^{2}}{2}]_{0}^{8}\\[/tex])

                                  = 113152[tex]\pi[/tex] = 355477 ft-lb

Therefore work required to pump the fuel is 355477 ft-lb

Answer:

5.44×10⁶ m

Explanation:

For a satellite with period t and orbital radius r, the velocity is:

v = 2πr/t

So the centripetal acceleration is:

a = v² / r

a = (2πr/t)² / r

a = (2π/t)² r

This is equal to the acceleration due to gravity at that elevation:

g = MG / r²

(2π/t)² r = MG / r²

M = (2π/t)² r³ / G

At the surface of the planet, the acceleration due to gravity is:

g = MG / R²

Substituting our expression for the mass of the planet M:

g = [(2π/t)² r³ / G] G / R²

g = (2π/t)² r³ / R²

R² = (2π/t)² r³ / g

R = (2π/t) √(r³ / g)

Given that t = 1.30 h = 4680 s, r = 7.90×10⁶ m, and g = 30.0 m/s²:

R = (2π / 4680 s) √((7.90×10⁶ m)³ / 30.0 m/s²)

R = 5.44×10⁶ m

Notice we didn't need to know the mass of the satellite.

Explanation:

The Coulomb's law states that the force acting on two charges is directly proportional to the product of charges and inversely proportional to the square of distance between them . Mathematically, it is given by

[tex]F=k\dfrac{q_1q_2}{r^2}[/tex]

Where

k is the electrostatic constant

q₁ and q₂ are charges

r is the distance between them.

The SI unit of electric force is Newton. It can be attractive or repulsive. The attraction or repulsion depend on charges. If both charges are positive, the force is repulsive and if both are opposite charges, the force is attractive.

Answer:

[tex]U = 1.83 \times 10^5 J[/tex]

Explanation:

Total internal energy of the gas is given by the formula

[tex]U = \frac{f}{2}nRT[/tex]

here as we know that neon gas is monoatomic gas

so we will have

[tex]f = 3[/tex]

n = 50 moles

[tex]T = 20 ^0C = 20 + 273 = 293 K[/tex]

now from above equation we will have

[tex]U = \frac{3}{2}(50)(8.31)(293)[/tex]

[tex]U = 1.83 \times 10^5 J[/tex]