When Light travels at a speed of 1.97 x 10^8 m/s in crown glass. When a ray of light travels from air into crown glass at an incidence angle of 30 degrees. What is the angle of refraction?

To find the velocity of the center of mass of the hollow sphere at the bottom of the incline, we can use the principle of conservation of energy.

The total mechanical energy of the system is conserved, and it can be calculated as the sum of the gravitational potential energy and the rotational kinetic energy:

E = mgh + (1/2)Iω²

Where:

m = mass of the hollow sphere

g = acceleration due to gravity

h = height of the incline

I = moment of inertia of the hollow sphere

ω = angular velocity of the hollow sphere

Given:

m = 4.00 kg

g = 9.8 m/s²

h = 0.50 m (since the length of the incline is 50.0 cm)

r = 0.05 m (radius of the hollow sphere)

The moment of inertia of a hollow sphere rotating about its diameter is I = (2/3)mr².

Substituting the values into the equation:

E = (4.00 kg)(9.8 m/s²)(0.50 m) + (1/2)(2/3)(4.00 kg)(0.05 m)²ω²

At the bottom of the incline, the height h = 0, and the entire energy is in the form of rotational kinetic energy:

E = (1/2)(2/3)(4.00 kg)(0.05 m)²ω²

Since the hollow sphere rolls without slipping, the linear velocity v and angular velocity ω are related by v = rω.

Simplifying the equation:

E = (1/2)(2/3)(4.00 kg)(0.05 m)²(ω²)

We want to find the velocity v of the center of mass of the hollow sphere at the bottom of the incline. Since v = rω, we can solve for ω:

E = (1/2)(2/3)(4.00 kg)(0.05 m)²(v²/r²)

Simplifying further:

E = (1/2)(2/3)(4.00 kg)(0.05 m)²(v²/(0.05 m)²)

Solving for v:

v = sqrt((2E) / (2/3)m)

Substituting the values of E and m:

v = sqrt((2[(1/2)(2/3)(4.00 kg)(0.05 m)²ω²]) / (2/3)(4.00 kg))

v = sqrt(0.05 m²ω²)

Since ω = v/r, we have:

v = sqrt(0.05 m²(v/r)²)

v = 0.05 m(v/r)

Now we can substitute the given value of the incline angle θ = 30 degrees:

v = 0.05 m(v/r) = 0.05 m(sin θ / cos θ)

v = 0.05 m(tan θ)

v = 0.05 m(tan 30°)

Calculating the value:

v ≈ 0.025 m/s

Therefore, the velocity of the center of mass of the hollow sphere at the bottom of the incline is approximately 0.025 m/s.

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Answer:

P=F/A

Explanation:

P. Is pressure

F is force

A is area

Answer:

Explanation:

Velocity is the change of displacement of a body with respect to time.

Velocity = Displacement/Time

Displacement = Δv * Δt

From the graph, it can be seen that the object sliding along the horizontal has a velocity of 0m/s since it starts travelling when v = 0m/s

For the time;

Δt =t2-t1

Δt = 8-0

Δt = 8s

object's displacement = 0 * 8

Hence the object displacement is 0m

answer:

the house of representatives is an example of representatives!

explanation:

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The current of the river is 7 mph, and the speed the rower would row at in still water is 20 mph.

The speed downstream is : V + C).

distance between the cities = 18 miles,

time taken =  2/3 hour

(V + C) = 18 / (2/3) = 27 mph

The speed upstream is = V - C

distance between the cities = 18 miles

time taken upstream =  18/13 hour

(V - C) = 18 / (18/13)

= 13 mph

(V + C) = 27                           (Equation 1)

(V - C) = 13                            (Equation 2)

We add both equations:  

2V = 40

V = 20 mph

(20 + C) = 27

C = 27 - 20

C = 7 mph

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The temperature of sweat when it is first produced is two degree more than normal temperature of the body because sweat removes extra heat from the body.

Our body begins to sweat when our body temperature goes up more than two degrees from normal which is 102 degree F. When you sweat, your body temperature drops back to the safe range which is 96.6 to 100.6 degrees F.

So we can conclude that The temperature of sweat when it is first produced is two degree more than normal temperature of the body because sweat removes extra heat from the body.

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Let me try:

Normal force= 169.74N

Coefficient of kinetic friction= 0.577

Explanation

a. For a given inclined plane, normal friction is equal to the force perpendicular to the plane which is equal to

mgcos theta = 20×9.8× cos30 = 169.74N

b. The coefficient of kinetic friction for an inclined plane is given as

tan theta =tan 30 = 0.577

Answer:

Example for 1. Law of Inertia

Falling forward while getting down from a moving bus:

When a passenger gets down from a moving bus, their upper body is still in motion, and when it comes in contact with the ground which is at rest, their body topples forward due to the inertia of motion.

Example for 2. Law of Acceleration

Hitting a Ball:

A ball develops a certain amount of acceleration after being hit. The acceleration with which the ball moves is directly proportional to the force applied to it. This means that the harder you hit the ball, the faster it will move

Example for 3. Law of Interaction

Walking:

Whenever people walk, their foot exerts a force on the ground. The ground then exerts an equal force which points in the opposite direction. It is this force (force due to friction) that allows the person to move forward.

Example for 4. Work and Power

As P=F.v

Cycling:

A person riding a bicycle possesses some amount of energy. This energy is utilized by the cyclist to do work on the paddles of the bicycle by applying some force and enabling the bicycle to move forward.

Example for 5. PE to KE

An apple hanging on a tree:

It has the potential energy due to its raised position. When the apple falls from the tree. The falling apple has the kinetic energy. Thus the potential energy stored in the apple in its raised position changes into the kinetic energy when the apple is falling. This kinetic energy does work on stone as the apple strikes the stone, and it makes the stone to move into the ground.

Example for 6. Sound and Light

TV:

We see TV takes electrical energy as input and produces. light energy, sound energy.

Example for 7. Heat and Electricity

The electric heaters:

An electric heater is an electrical device that converts an electric current into heat.

Answer:

Steps to determine the specific heat capacity.

1. Place a beaker on a balance and press zero.

2. Now add the oil to the beaker and record the mass of the oil.

3. Read the starting temperature of the oil.

4. Connect a joulemeter to the immersion heater.

5. Time for thirty minutes.

6. Read the number of joules of energy that passed into the immersion heater.

7. Read the final temperature of the oil.

8. Use the following formula to calculate the specific heat capacity.

Explanation:

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Answer:

Some of the payoffs companies receive when offering child care benefits to employees;

1) Employees are proud to tell others they work for such establishments which make the establishment attractive to talents

2) Reduced attrition for work place policy

3) Increased loyalty of the employees to the companies mission

4) Workers are less likely to take work appointment in other places

5) Child care offering are some of the aspects workers consider when searching for jobs

6) Companies can enjoy tax breaks

Explanation:

The phrase "a wave that moves along the interface of two different materials, like air and water" describes a surface wave.

A surface wave is a type of wave that propagates along the boundary or interface between two different materials or mediums, such as air and water or between two layers of a solid material. Surface waves exhibit both characteristics of transverse and longitudinal waves, with particle motion occurring both perpendicular and parallel to the direction of wave propagation.

Surface waves are commonly observed in various natural phenomena, such as ocean waves, ripples on the surface of water, seismic waves, and electromagnetic waves propagating along the Earth's surface. These waves are influenced by the properties and interaction between the two materials they traverse. For example, in the case of ocean waves, the interaction between air and water causes the water particles at the surface to move in a circular motion.

Unlike electromagnetic waves, which are characterized by oscillating electric and magnetic fields and can travel through space without the need for a medium, surface waves require a material interface to propagate. They are confined to the boundary between the two materials and do not propagate through the bulk of either medium.

In summary, a surface wave is a wave that moves along the interface or boundary between two different materials, exhibiting both transverse and longitudinal motion. It is distinct from electromagnetic waves, which can travel through space, as surface waves require a material interface for propagation.

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The mass of the ice cube needed to cool your 300mL coffee from 85.0°C to 57.0°C, taken from a -17.0°C freezer, is approximately 27.9 grams.

To determine the mass of the ice cube, we must consider the energy balance between the coffee and the ice. First, calculate the energy needed to raise the ice's temperature to 0°C. This can be done using the formula Q = mcΔT, where Q is energy, m is mass, c is specific heat, and ΔT is the change in temperature.

Next, calculate the energy needed to melt the ice using Q = mLf, where Lf is the latent heat of fusion. Then, calculate the energy released by the cooling coffee using the same mcΔT formula. Finally, set the sum of the energy needed to warm and melt the ice equal to the energy released by the cooling coffee and solve for the mass (m) of the ice cube.

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The speed of the water flow through the hole in the figure is 2.97 m/s.

The speed of the water flow through the hole in the figure is calculated by applying the principle of conservation of energy as shown below.

change in kinetic energy = change in potential

ΔK.E = ΔP.E

where;

¹/₂mv² - ¹/₂mu² = mgh₁ - mgh₂

where;

¹/₂m(v² -u²) = mg(h₁ -h₂)

¹/₂(v² -u²) = g(h₁ -h₂)

¹/₂(v² -0) = g(h₁ -h₂)

v² = 2g(h₁ -h₂)

v = √(2g(h₁ -h₂))

v = √(2 x 9.8(0.5 - 0.05))

v = 2.97 m/s

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Answer:

0.303 seconds

Explanation:

We need to find the time that the cell phone takes to reach the sink. So, we will use the following equation

Where

yi is the initial position, so yi = 0.45 m

vi is the initial velocity. Since it is freefall, vi = 0 m/s

a is the acceleration due to gravity, so a = -9.8 m/s²

y is the final position, so y = 0 m

t is the variable that we need to find.

So, replacing the values, we get:

Now, we can solve for t

Therefore, you have 0.303 seconds before your cell phone is ruined.

The presence of a global layer of iridium-rich clay at the K-T boundary provides strong evidence supporting the meteor-impact hypothesis for the mass extinction event.

One of the key lines of evidence supporting the meteor-impact hypothesis for the mass extinction at the Cretaceous-Tertiary (K-T) boundary is the discovery of a distinct layer of sediment enriched in iridium. Iridium is an extremely rare element on Earth's surface but is more abundant in meteorites and asteroids. The Alvarez team, composed of Luis Alvarez, his son Walter Alvarez, and their colleagues, first proposed this hypothesis in 1980, suggesting that the impact of a large asteroid or comet caused the extinction event.

The smoking gun evidence comes from the identification of a global layer of clay that is enriched in iridium and is found precisely at the K-T boundary in geological records worldwide. This iridium anomaly was first discovered in the rocks of the Gubbio section in Italy and has since been confirmed in numerous other locations around the world. The amount of iridium found in this layer far exceeds what would be expected from natural terrestrial processes, providing strong evidence of an extraterrestrial impact.

The high concentration of iridium and the global distribution of this iridium-rich clay layer strongly support the hypothesis that a large meteor impact occurred at the K-T boundary, leading to widespread environmental devastation and the subsequent mass extinction event. The impact would have released immense energy, causing widespread fires, a global dust cloud, and long-lasting climate effects. The resulting environmental changes likely contributed to the extinction of various species, including the dinosaurs.

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→ The charge in electron charge Q(e) is equal to the charge in coulombs Q(C) times 6.24150975⋅1018:

1C = 6.24150975⋅10¹⁸e

Q(e) = Q(C) × 6.24150975 × 10¹⁸

Q(e) = 96,500 × 6.24150975 × 10¹⁸

Q(e) = 6.02305690875 × 10²³

which is round off to

→ 6.03 × 10²³ electrons

Answer:

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

force = mass × acceleration

From the question we have

mass = 6,000 kg

acceleration = 8 m/s²

We have

force = 6,000 × 8 = 48,000

We have the final answer as

Hope this helps you

The strength of gravity on Zarflax-beta-9z is 17 N/kg.

We can use the formula:

weight = mass x gravity

to determine the strength of gravity on Zarflax-beta-9z.

We know that the mass of the book is 3 kg and its weight is 51 N. So, we can rearrange the formula to solve for gravity:

gravity = weight / mass

gravity = 51 N / 3 kg

gravity = 17 N/kg

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Answer:

In a physical change a substance changes from one PHASE to another

Answer:

I believe that it's C

Explanation:

196 children and 165 adults were admitted to the amusement park on that day.

Let's assume that the number of children who entered the park was "x" and the number of adults who entered was "y". According to the problem, we know that the admission fee for children is $1.5 and for adults is $4. Using this information, we can create two equations:

1.5x + 4y = 954  (total admission fees collected on that day)
x + y = 361  (total number of people who entered the park)

Now, we need to solve these equations simultaneously to find the values of x and y. One way to do this is to use substitution. We can rearrange the second equation as x = 361 - y and substitute this value of x in the first equation:

1.5(361-y) + 4y = 954

Expanding the brackets and simplifying, we get:

541.5 + 2.5y = 954
2.5y = 412.5
y = 165

Substituting this value of y in x + y = 361, we get:

x + 165 = 361
x = 196

Therefore, 196 children and 165 adults were admitted to the amusement park on that day.

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Answer:

he density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ

Explanation:

The quantity is represented by θ is a function of time and The quantity represented by \(\theta_o\) is not a function of time. The quantity represented by \(\omega_o\) is not a function of time. The quantity is represented by ω is a function of time and It is not an explicit function of time. The time variable t in the equation represents the time elapsed.

Part A: True. The quantity represented by θ is a function of time. It represents the angular position of the particle at a given time t. As time changes, the angular position of the particle also changes.

Part B: False. The quantity represented by \(\theta_o\) is not a function of time. It represents the initial angular position of the particle, which is a constant value and does not depend on time.

Part C: False. The quantity represented by \(\omega_o\) is not a function of time. It represents the initial angular velocity of the particle, which is a constant value and does not change with time.

Part D: True. The quantity represented by ω is a function of time. It represents the angular velocity of the particle at a given time t. As time changes, the angular velocity of the particle can change due to the angular acceleration.

Part E: \(\omega^2 = \omega^2_o + 2\alpha(\theta- \theta_o)\) is not an explicit function of time. It does not involve the variable t and can be used to relate the final angular velocity ω, initial angular velocity  \(\omega_o\) , angular acceleration α, and the change in angular position \((\theta- \theta_o)\) without explicitly considering time.

Part F: The time variable t in the equation\(\omega = \omega_0 + \alpha t\) represents the time elapsed from when the angular velocity equals   \(\omega_o\)  until the angular velocity equals ω. It measures the duration during which the angular acceleration α causes the change in angular velocity from   \(\omega_o\)  to ω.

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A cart speed will often increase on a downhill slope while decreasing on an uphill section. A steeper gradient portion has a more pronounced impact on the acceleration or slowdown of a vehicle's speed.

The cart speed/velocity will progressively rise by the same amount each second. The rate of acceleration of the car increases with the slope's steepness (or the ramp's greater angle of inclination). This is so because the slope's angle determines how much gravity is felt.

Therefore, the more gravitational potential energy that can be turned into kinetic energy, the higher the ramp will be, and the more kinetic energy there is, the faster the car will move.

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The event that causes the least amount of time to go by on the game clock is a free throw.

In conclusion, the event that causes the least amount of time to go by on the game clock is a free throw.

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Explanation:

Hey there!!

Here,

Weighs = 65n

Gravity = 10n

We know that,

weighs = mass × gravity.

65 = m × 10

\(m = \frac{65}{10} \)

Therefore the mass is 6.5 kg.

Hope it helps...

(a) The area needed for a counterflow exchanger is approximately 30.59 m².

(b) If parallel flow were used, the area would be increased by a factor of approximately 1.81.

(a) The area required for a counterflow heat exchanger can be calculated using the equation:

Q = U × A × ΔT

where Q is the heat transfer rate, U is the overall heat transfer coefficient, A is the surface area, and ΔT is the temperature difference between the hot and cold fluids.

First, calculate the heat transfer rate for the carbon tetrachloride:

Q₁ = m₁ × Cp₁ × ΔT₁ = 19,000 kg/h × 0.86 kJ/kg·°C × (85 - 40) °C = 677,400 kJ/h

Next, calculate the heat transfer rate for the cooling water:

Q₂ = m₂ × Cp₂ × ΔT₂ = 13,500 kg/h × 4.18 kJ/kg·°C × (85 - 20) °C = 5,194,100 kJ/h

The overall heat transfer rate is given by Q = min(Q₁, Q₂) = 677,400 kJ/h.

Using the equation Q = U × A × ΔT, we can rearrange it to solve for A:

A = Q / (U × ΔT)

Substituting the given values, we have:

A = 677,400 kJ/h / (1,700 W/m²·°C × (85 - 40) °C) ≈ 30.59 m²

Therefore, the area needed for a counterflow exchanger is approximately 30.59 m².

(b) If parallel flow were used, the area required would be increased by a factor of:

A_parallel = A_counterflow × (1 + (1 / (Cp₂ / Cp₁)))

Cp₁ and Cp₂ are the specific heat capacities of the carbon tetrachloride and cooling water, respectively.

Using the given values:

A_parallel = 30.59 m² × (1 + (1 / (0.86 kJ/kg·°C / 4.18 kJ/kg·°C))) ≈ 55.48 m²

The area would be increased by a factor of approximately 1.81 if parallel flow were used to achieve more rapid initial cooling of the carbon tetrachloride.

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Answer:

Explanation:

The force acting on an object given it's mass and acceleration can be found by using the formula

From the question

mass = 10 kg

acceleration = 2 m/s²

We have

Force = 10 × 2

We have the final answer as

Hope this helps you