Suppose that 2.5 moles of an ideal gas are in a chamber in equilibrium at temperature 310 K and volume 0.5 m3. 1) What is the pressure in the chamberi?

Answer: 624.98 mL

Explanation:

According to the Ideal Gas Law:

[tex]\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}[/tex] (1)

Where:

[tex]P_{1}=2.4 atm[/tex] is the pressure of the bubble under the surface

[tex]V_{1}=250 mL[/tex] is the volume of the bubble under the surface

[tex]T_{1}=15\°C + 273.15=288.15 K[/tex] is the temperature of the bubble under the surface

[tex]P_{2}=1 atm[/tex] is the pressure of the bubble at the surface

[tex]V_{2}[/tex] is the volume of the bubble at the surface

[tex]T_{2}=27\°C + 273.15=300.15 K[/tex] is the temperature of the bubble at the surface

So, we have to find [tex]V_{2}[/tex]:

[tex]V_{2}=\frac{P_{1}V_{1}T_{2}}{T_{1}P_{2}}[/tex] (2)

[tex]V_{2}=\frac{(2.4 atm)(250 mL)(300.15 K)}{(288.15 K)(1 atm)}[/tex] (3)

Finally:

[tex]V_{2}=624.98 mL[/tex]  This is the volume of the bubble when it reaches the surface

The volume of the bubble when it reaches the surface is about 625 mL

The basic formula of pressure that needs to be recalled is:

Pressure = Force / Cross-sectional Area

or symbolized:

[tex]\large {\boxed {P = F \div A} }[/tex]

P = Pressure (Pa)

F = Force (N)

A = Cross-sectional Area (m²)

Let us now tackle the problem !

In this problem , we will use Ideal Gas Law as follows:

Given:

Initial Volume = V₁ = 250 mL

Initial Pressure = P₁ = 2.4 atm

Initial Temperature = T₁ = 15 + 273 = 288 K

Final Pressure = P₂ = 1.0 atm

Final Temperature = T₂ = 27 + 273 = 300 K

Unknown:

Final Volume = V₂ = ?

Solution:

[tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]

[tex]\frac{2.4(250)}{288} = \frac{1.0V_2}{300}[/tex]

[tex]\frac{600}{288} = \frac{1.0V_2}{300}[/tex]

[tex]\frac{25}{12} = \frac{V_2}{300}[/tex]

[tex]V_2 = \frac{25}{12} \times 300[/tex]

[tex]V_2 = 625 \texttt{ mL}[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Pressure

Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant , Liquid , Pressure

Answer:

CONCAVE

Explanation:

Convex lenses bend light rays so they come together at focus. Concave lenses spread light rays apart so they do not come together at a focus.

hope this answer help u!!

Answer:

Concave lens

Explanation:

Concave lenses are thicker at ends and thinner at middle. When parallel rays of light pass through the concave lens, they are refracted and spread out so that they appear to come from a common point known as principle focus. Due to this reason, Concave lens also called as diverging lens.

1. With this statement, the author is referring to the fact that the vehicles are one of the largest polluters of the air. In order to reduce the pollution, the vehicles that are used will need to be changed, and with it the pollution will decrease significantly. The reduction of the pollution will come because the vehicles on hydrogen will not cause any pollution, so the enormous amounts of carbon dioxide released from the combustion of the engines will be thing of the past.

2. There are several challenges with this type of vehicles in order for them to replace the fossil fuel driven ones. The big price is one of the factors, as the majority of the people can not afford these cars. Another problem is that these vehicles are not as fast as the fossil fuel driven ones, and lot of people enjoy fast driving, despite it not being safe. There are millions of vehicles out there on the roads, and changing all of them with hydrogen vehicles will take a lot of time, as lot of those vehicles are new ones, so the people will not be willing to just throw them away and leave them rot in their garages. In order for the change of the driving park to be accomplished, the prices should go down, the people to be more serious about the environment and its protection, and patience as several decades will probably be needed for a change like this to be competed.

3. The fuel celled cars are a viable answer to decrease the pollution, as they are not causing any pollution, but instead will stop the process of large emissions of carbon dioxide from the fossil fueled cars. While this method is a good one, it should not be the only, as on its own it can not have the desirable effect, but instead all the major polluters should be included in the process. The industry and the production of energy are one of the major polluters as well, so they will need to follow the example, as if they not, the problem will stay, considering that the industry is constantly growing and the demand for energy is constantly growing too.

Answer:

t = 025 s

Explanation:

We know

weight, W =  4 pounds

spring constant, k = 2 lb/ft

Positive damping, β = 1

Therefore mass,  m =  W / g

                             m = 4 / 32

                                  = 1 / 8 slug

From Newtons 2nd law

[tex]\frac{d^{2}x}{dt^{2}}=-kx-\beta .\frac{dx}{dt}[/tex]

where x(t) is the displacement from the mean or equilibrium position. The equation can be written as

[tex]\frac{d^{2}x}{dt^{2}}+\frac{\beta }{m}.\frac{dx}{dt}+\frac{k}{m}x=0[/tex]

Substituting the values, the DE becomes

[tex]\frac{d^{2}x}{dt^{2}}+8\frac{dx}{dt}+16x=0[/tex]

Now the equation is

[tex]m^{2}+8m+16=0[/tex]

and on solving the roots are

[tex]m_{1}[/tex] = [tex]m_{2}[/tex] = -4

Therefore the general solution is [tex]x(t)=e^{-4t}\left ( c_{1}+c_{2}t \right )[/tex]

Now for initial condition x(0) = -1 ft

                                        x'(0)= 8 ft/s

Now we can find the equation of motion becomes,

[tex]x(t)=e^{-4t}\left ( -1+4t \right )[/tex]

Therefore, the mass passes through the equilibrium when

x(t) = 0

[tex]e^{-4t}\left ( -1+4t \right )[/tex] = 0

-1+4t = 0

t = [tex]\frac{1}{4}[/tex]

  = 0.25 s

Answer:

Strong nuclear force

Explanation:

Strong nuclear force (which is the strongest of the forces of the universe) is responsible for the attractive force between quarks to form nucleons (protons and neutrons). It is the reason why the protons (that are positive in charge) do not fly apart due to electromagnetic repulsion in the nucleus of an atom.

Answer:

[tex]p_2 = 1.76 atm[/tex]

Explanation:

given data:

v_1 = 2.37 L

v_2 = 1.68 L

p_1 =1.15 atm

p_2 = ?

t_1 = 280 K

t_2 = 304 K

from Gas Law Equation

, WE HAVE

[tex]\frac{p_1 v_1}{t_1} =\frac{p_2 v_2}{t_2}[/tex]

Putting the values

[tex]\frac{1.15*2.37}{280}  =\frac{p_2 *1.68}{304}[/tex]

[tex]9.733*10^{-3} = \frac{p_2 *1.68}{304}[/tex]

[tex]9.733*10^{-3}*304 = p_2*1.68[/tex]

[tex]\frac{9.733*10^{-3}*304}{1.68} =p_2[/tex]

[tex]p_2= 1.76 atm[/tex]

a) we can answer the first part of this by recognizing the player rises 0.76m, reaches the apex of motion, and then falls back to the ground we can ask how

long it takes to fall 0.13 m from rest: dist = 1/2 gt^2 or t=sqrt[2d/g] t=0.175

s this is the time to fall from the top; it would take the same time to travel

upward the final 0.13 m, so the total time spent in the upper 0.15 m is 2x0.175

= 0.35s

b) there are a couple of ways of finding thetime it takes to travel the bottom 0.13m first way: we can use d=1/2gt^2 twice

to solve this problem the time it takes to fall the final 0.13 m is: time it

takes to fall 0.76 m - time it takes to fall 0.63 m t = sqrt[2d/g] = 0.399 s to

fall 0.76 m, and this equation yields it takes 0.359 s to fall 0.63 m, so it

takes 0.04 s to fall the final 0.13 m. The total time spent in the lower 0.13 m

is then twice this, or 0.08s

Answer:

Part a)

[tex]T = 0.35 s[/tex]

Part b)

[tex]T' = 0.041 s[/tex]

So for top 15 cm the time interval is sufficiently larger than the time interval of last 15 cm

Explanation:

Part a)

Maximum height reached is

H = 76 cm

now the velocity of the player at starting position is given as

[tex]v_f^2 - v_i^2 = 2ad[/tex]

[tex]0 - v^2 = 2(-9.81)(0.76)[/tex]

[tex]v = 3.86 m/s[/tex]

time taken by it in top 15 cm position is given as

[tex]y = \frac{1}{2}gt^2[/tex]

[tex]0.15 = \frac{1}{2}(9.81)t^2[/tex]

[tex]t = 0.175 s[/tex]

so total time in that position is double because in that position first it will go up and then go down

[tex]T = 0.35 s[/tex]

Part b)

Now for bottom position of 15 cm first we will find the time to reach (76 - 15)cm have

[tex]H = \frac{1}{2}gt^2[/tex]

[tex](0.76 - 0.15) = \frac{1}{2}(9.81)t^2[/tex]

[tex]t_1 = 0.352 s[/tex]

now for total time to drop

[tex]t_2 = \sqrt{\frac{2H}{g}}[/tex]

[tex]t_2 = 0.394 s[/tex]

so time interval of last 15 cm is given as

[tex]t' = 0.394 - 0.352[/tex]

[tex]T' = 0.041 s[/tex]

So for top 15 cm the time interval is sufficiently larger than the time interval of last 15 cm

Answer:

28.5 deg

Explanation:

The resistance of a nichrome wire at 0.0 ∘c if its resistance is 120.00 ω at 11.5 ∘c is 28.5 deg.

R = R0[1+ alpha(T-T0)]

R(28.5)=0.2000[1-0.005(28.5-0)]

The resistance of a nichrome is 28.5 deg.

The resistance of a nichrome wire at 0.0 ∘c if its resistance is 120.00 ω at 11.5 ∘c is 28.5 deg.

R = R0[1+ alpha(T-T0)]

R(28.5) = 0.2000[1-0.005(28.5-0)]

Nichrome is continuously silvery-grey in shade, is corrosion-resistant, has an excessive melting thing of approximately 1, four hundred °C (2,550 °F), and has an electrical resistivity of around 112 microOhm-cm, that's around 66 times better resistivity than copper of one.678 microOhm-cm.

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Answer:

Answer to the question:

Explanation:

The value of the internal resistance of an ideal voltmeter is infinite.

The value of the internal resistance of an ideal ammeter is zero.

Final answer:

The ideal internal resistance for a voltmeter is very high to avoid affecting the circuit during voltage measurements, while for an ammeter it should be very low to avoid affecting current measurements. Incorrect use of meters can lead to inaccurate readings and potential damage.

Explanation:

Ideal Internal Resistance of Meters:

When it comes to the ideal internal resistance of a voltmeter, it should be as high as possible. This is because a voltmeter is used in parallel with a component to measure its voltage. If the voltmeter has a high internal resistance, it will minimize the current flowing through the voltmeter, thereby causing minimal change in the overall circuit operation. For example, a digital voltmeter can have an internal resistance in the megaohms (MΩ), which is ideal for not affecting the circuit.

On the other hand, the ideal internal resistance of an ammeter is very low. An ammeter is connected in series with a circuit to measure the current flowing through it. Thus, to prevent it from significantly altering the voltage drop across the circuit or the current itself, an ammeter should have minimal resistance. Digital ammeters can have much lower internal resistance compared to analog meters, making them less intrusive in circuit measurements.

If a meter with the wrong internal resistance is used, it could cause incorrect readings and potentially damage the meter or the circuit. For instance, using a meter in ammeter mode to measure voltage can short circuit the meter, as an ammeter's low resistance is not meant to handle the high potential differences associated with voltage measurements.

The IKAROS spacecraft, propelled by the force of light from the sun, would have its speed increased by 30 m/s after 3 months of flight under the assumption that this is the only force acting on the 290 kg spacecraft.

The increase in speed of the IKAROS spacecraft can be calculated using the formula force = mass x acceleration. The force exerted by the sunlight is given as 1.12 mN or 0.00112 N. The mass of the spacecraft is given as 290 kg. So, the acceleration can be calculated as force/mass which is (0.00112 N)/(290 kg) = 3.86 x 10⁻⁶ m/s². This acceleration is continuous, so over time it imparts a speed increase to the spacecraft.

The time over which the acceleration is acting is 3 months or 3 x 30 x 24 x 60 x 60 seconds = 7.776 x 10⁶ s. Using the formula speed = acceleration x time, the increase in speed can be calculated as (3.86 x 10⁻⁶ m/s²) x (7.776 x 10⁶ s) = 30 m/s. So, the speed of the spacecraft would increase by 30 m/s after 3 months of flight assuming this force is the only one acting on it.

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The speed of the spacecraft would increase by 100800 m/s after 3.0 months of flight.

To calculate the increase in speed of the spacecraft after 3.0 months of flight, we can use the equation:

F = m * a

Where F is the force, m is the mass, and a is the acceleration. Rearranging the equation, we get:

a = F / m

Plugging in the force value of 1.12 mN and the mass of the spacecraft which is 290 kg, we can calculate the acceleration:

a = 1.12 mN / (290 kg)

Next, we need to convert the time of 3.0 months into seconds. Since there are 30 days in each month, and each day has 24 hours and 60 minutes, we can calculate:

3.0 months = 3.0 * 30 days * 24 hours * 60 minutes * 60 seconds

After converting the time into seconds, we can use the equation:

v = u + at

Where v is the final velocity, u is the initial velocity (assumed to be 0 since the spacecraft is starting from rest), a is the acceleration, and t is the time. Rearranging the equation, we get:

v = at

Plugging in the calculated acceleration and the converted time, we can calculate the final velocity:

v = (1.12 mN / (290 kg)) * (3.0 * 30 days * 24 hours * 60 minutes * 60 seconds)

Simplifying the calculation, we get:

v = 100800 m/s

Therefore, the speed of the spacecraft would increase by 100800 m/s after 3.0 months of flight, assuming the force from the solar sails is the only force acting on the spacecraft.

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Answer:

D) 0.33 m/s² to the right

Explanation:

Apply Newton's second law.  Take right to be positive and left to be negative.

∑F = ma

20 N − 5 N = (45 kg) a

a = 0.33 m/s²

The couch accelerates at 0.33 m/s² to the right.

Answer: acceleration = 0.33m/s² to the right.

Explanation: when two forces act in opposite direction along same axis thier resultant direction is always with that force of higher magnitude in this case 20N

Resultant force F = -5N + 20N = 15N to the right.

But

F = Mass * acceleration

acceleration = F/ mass

= 15N/45kg

= 0.33N/kg

Which is also 0.33m/s² to the right.

Answer:

The speed on boat in still water is  [tex]56 \frac{km}{h}[/tex]  and the rate of the current is   [tex]10 \frac{km}{h}[/tex]

Explanation:

Since speed , [tex]v= \frac{Distance\, traveled(D)}{Time\, taken(t)}[/tex]

Therefore speed of motor boat while traveling upstream is

[tex]v_{upstream}=\frac{92}{2}\frac{km}{h}=46\frac{km}{h}[/tex]

and  speed of motor boat while traveling downstream is

[tex]v_{downstream}=\frac{132}{2}\frac{km}{h}=66\frac{km}{h}[/tex]

Let speed of boat in still water be [tex]v_b[/tex] and rate of current be [tex]v_w[/tex]

Therefore [tex]v_{upstream}=v_b-v_w=46\frac{km}{h}[/tex]   ----(A)

and  [tex]v_{downstream}=v_b+v_w=66\frac{km}{h}[/tex]     ------(B)

Adding equation (A) and (B)  we get

[tex]2v_b= (46+66) \frac{km}{h}=112 \frac{km}{h}[/tex]

=>[tex]v_b= 56 \frac{km}{h}[/tex]   ------(C)

Substituting the value of  [tex]v_b[/tex] in equation (A) we get

[tex]v_w= 10 \frac{km}{h}[/tex]

Thus the speed on boat in still water is  [tex]56 \frac{km}{h}[/tex]  and the rate of the current is   [tex]10 \frac{km}{h}[/tex]

Answer:

s = 23.72 m

v = 21.56 m/s²  

Explanation:

given

time to reach the ground (t) = 2.2 second

we know that

a) s = u t + 0.5 g t²

   u = 0 m/s

   g = 9.8 m/s²

   s = 0 + 0.5 × 9.8 × 2.2²

  s = 23.72 m

b) impact velocity

      v = √(2gh)

      v = √(2× 9.8 × 23.72)    

      v =  √464.912

      v = 21.56 m/s²  

Answer:

A. d ≈ 23.72 m.

B. v ≈ 21.56 m/s.

Explanation:

d = height

v = final velocity

v0 = Initial velocity

g = gravity

t = time

A. 

Given that the time is 2.2 seconds and the initial velocity is 0, we can replace the values in to the formula.

d = v0 * t + 0.5 * g * t^2

d = 0 * 2.2 + 0.5 * 9.8 * 2.2^2

d = 0 + 23.716

d ≈ 23.72 m.

B.

​

​Sincec the initial speed is 0 m/s,

v^2 = 2 * g * d

v = sqrt(2 * g * d)

v = sqrt(2 * 9.8 * 23.72)

v = sqrt(464.912)

v ≈ 21.56 m/s

Answer: 1.024 N

Explanation:

Step 1:

Using Coulomb's law: F=kQ1Q2/d^2

We can rearrange the terms to get :

kQ1Q2=Fxr^2

Substituting: kQ1Q2=0.0224N x (1.63m)^2

Thus kQ1Q2=0.0595

We know that this value will not change when the balls are brought closer together.

Step 2:

Change from cm to m : 1cm=0.01m

24cm=0.24 m

Substitute into the new distance and the calculated value for kQ1Q2 into the coulomb law formula to calculate the new force

F=kQ1Q2/d^2=0.059/(0.24)^2

F=1.024N

Final answer:

The force between the ping-pong balls will be approximately 1.665 N when they are brought closer to a separation of 24.0 cm.

Explanation:

The force between two charged objects can be calculated using Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

In this case, the initial force between the ping-pong balls is 0.0224 N when they are separated by 1.63 m. To find the force when they are brought closer to a separation of 24.0 cm, we can use the fact that the force is inversely proportional to the square of the distance.

We can set up a proportion:

(0.0224 N) / (1.63 m)²= (x) / (0.24 m)²

Solving for x, we find that the force will be approximately 1.665 N.

Answer:

Explanation:

A) mass of displaced water = loss of mass in water = 63 - .0975 = 62.9025 kg

B) her volume = volume of displaced water

= mass of displaced water / density of water = 62.9025 / 1000 m³.

= 62.9025 x 10⁻³ m³

C) her average density = her mass / her volume = 63 / 62.9025 x 10⁻³

= 1.00155 x 10³ kg / m³

D) lung capacity = 1.75 L = 1.75 x 10⁻³ m³

buoyant force created by air in the lungs = 1.75 x 10⁻³ ( 1000- 1.29 ) =  1.74 kg

As it is more than 0.0975 kg , the apparent weight  in water so woman will float in water .

A. Mass of Water Displaced: ≈ 62.99 kg

B. Volume of Woman: ≈ 0.06299 m³

C. Average Density: ≈ 1000 kg/m³

D. Yes, she can float with lungs filled with air.

We can solve this problem using the concepts of buoyancy and density. Here's how to find the answers:

A. Mass of Water Displaced:

1. Buoyant Force: The difference between her mass in air and apparent mass underwater represents the buoyant force exerted by the water.

2. Buoyant Force = Weight in Air - Apparent Weight = (63 kg * 9.81 m/s²) - (0.0975 kg * 9.81 m/s²) (We can multiply mass by gravitational acceleration to convert it to weight, but for this problem, it cancels out)

3. Buoyant Force ≈ 618.27 N (Newtons)

Since buoyant force equals the weight of the water displaced, the mass of water displaced is:

Mass of Displaced Water = Buoyant Force / Gravitational Acceleration

Mass of Displaced Water ≈ 618.27 N / 9.81 m/s² ≈ 62.99 kg (rounded to two decimal places)

B. Volume of Woman:

1. Density of Water: We can assume the density of water to be 1000 kg/m³ (a standard value).

2. Volume of Displaced Water = Mass of Displaced Water / Density of Water

3. Volume ≈ 62.99 kg / 1000 kg/m³ ≈ 0.06299 m³ (rounded to five decimal places)

C. Average Density of Woman:

1. Woman's Volume (from part B): 0.06299 m³

2. Woman's Mass: 63 kg

3. Density = Mass / Volume

4. Average Density ≈ 63 kg / 0.06299 m³ ≈ 1000 kg/m³ (rounded to three decimal places)

D. Ability to Float:

1. Density of Air: 1.29 kg/m³

2. Volume of Air in Lungs: 1.75 L = 0.00175 m³ (convert liters to cubic meters)

3. When lungs are filled with air, her effective volume increases by the volume of air in her lungs.

4. Effective Volume with Air: 0.06299 m³ (woman's volume) + 0.00175 m³ (air in lungs) ≈ 0.06474 m³

5. When considering air in her lungs, her effective density becomes:

Effective Density = Mass / Effective Volume

Effective Density ≈ 63 kg / 0.06474 m³ ≈ 973.3 kg/m³ (rounded to one decimal place)

Since her effective density (with air in lungs) is lower than the density of water (1000 kg/m³), she would be able to float with her lungs filled with air.

Answers:

A. Mass of Water Displaced: ≈ 62.99 kg

B. Volume of Woman: ≈ 0.06299 m³

C. Average Density: ≈ 1000 kg/m³

D. Yes, she can float with lungs filled with air.

Answer:

u = 4.6 m/s

h = 8.01 m

Explanation:

Given:

Mass of the tennis ball, m = 44.0 g

Mass of the basket ball, M = 594 g

Height of fall, h = 1.08m

Now,

we have

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

where, s = distance = h

a = acceleration

u = final speed before the collision

u' = initial speed

since it is free fall case

thus,

a = g = acceleration due to gravity

u' = 0

thus we have

[tex]u^2-0^2 = 2\times9.8\tiimes1.08[/tex]

or

[tex]u = \sqrt{21.168}[/tex]

or

u = 4.6 m/s

b) Now after the bounce, the ball moves with the same velocity

thus, v = v₂

thus,

final speed ([tex]v_f[/tex]) = v = 4.6 m/s

Then conservation of energy says  

[tex]\frac{1}{2}mu_1^2+\frac{1}{2}Mu_2^2 = \frac{1}{2}mv_1^2+\frac{1}{2}Mv_2^2[/tex]  

also

applying the concept of conservation of momentum

we have

mu₁ + Mu₂ = mv₁ + Mv₂

u₁ =velocity of the tennis ball before collision = -4.6 m/s  

u₂ = velocity of the basketball before collision= 4.6 m/s  

v₁ =  velocity of the tennis ball after collision  

v₂ = velocity of the basketball  after collision

substituting the values in the equation, we get

Now,

solving both the equations simultaneously we get

[tex]v = (\frac{2M}{m+M})u_1+(\frac{m-M}{m+M})u_2[/tex]

substituting the values in the above equation we get

[tex]v = (\frac{2\times594}{44+594})(-4.6)+(\frac{44-594}{44+594})4.6[/tex]

or

[tex]v = -8.565-3.965[/tex]

or

[tex]v = -12.53m/s[/tex]

here negative sign depicts the motion of the ball in the upward direction

now the kinetic energy of the tennis ball

[tex]K.E = \frac{1}{2}mv^2[/tex]

or

[tex]K.E = \frac{1}{2}44\times 10^{-3}kg\times 12.53^2[/tex]

or

K.E = 3.45 J

also at the height the K.E will be the potential energy of the tennis ball

thus,

3.45 J = mgh

or

3.45 = 44 × 10⁻³ × 9.8 × h

h = 8.01 m

The magnitude of the downward velocity with which the basketball reaches the ground is 4.51 m/s. The height to which the tennis ball rebounds after an elastic collision with the basketball can be found by solving for the velocity of the tennis ball after the collision and using the equation h = (v2')² / (2g).

To find the magnitude of the downward velocity with which the basketball reaches the ground, we can use the equation v = gt, where g is the acceleration due to gravity. Since both the basketball and tennis ball are released from rest and fall through the same distance, they will reach the ground at the same time. Therefore, the time it takes for the basketball to reach the ground is the same as the time it takes for the tennis ball to fall and bounce back up:

t = sqrt(2h/g)

where h is the distance the balls fall. We can substitute the given values into the equation to find the time:

t = sqrt(2 * 1.08m / 9.8m/s²) = 0.46 s

Therefore, the magnitude of the downward velocity with which the basketball reaches the ground is given by v = gt:

v = 9.8m/s² * 0.46s = 4.51 m/s

For part (b), to find the height to which the tennis ball rebounds after an elastic collision with the basketball, we can use the conservation of momentum and the conservation of kinetic energy. Since the collision is elastic, the total momentum and the total kinetic energy of the two balls before the collision are equal to the total momentum and total kinetic energy after the collision:

m1v1 + m2v2 = m1v1' + m2v2'

1/2m1v1² + 1/2m2v2² = 1/2m1v1'² + 1/2m2v2'²

We can substitute the given values into the equations and solve for v2', the velocity of the tennis ball after the collision:

0.044kg * 0m/s + 0.594kg * 4.51m/s = 0.044kg * v1' + 0.594kg * v2'

1/2 * 0.044kg * 0m/s² + 1/2 * 0.594kg * (4.51m/s)² = 1/2 * 0.044kg * v1'² + 1/2 * 0.594kg * v2'²

From these equations, we can solve for v2', the velocity of the tennis ball after the collision. The height to which the tennis ball rebounds can be found using the equation:

h = (v2')² / (2g)

We can substitute the calculated value of v2' into the equation to find the height:

h = (v2')² / (2 * 9.8m/s²)

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Answer:

15.8 cm

Explanation:

In 20.8 seconds, the number of vibrations = 42

In 1 second, the number of vibrations = 42 / 20.8 = 2.019

Frequency is defined as the number of vibrations in one second.

f = 2.019 Hz

Crest travel 371 cm in 11.6 s

v = 3.71 / 11.6 = 0.319 m / s

Use

v = f x λ

λ = v / f = 0.319 / 2.019 = 0.158 m = 15.8 cm

Answer:

Determining planetary laws of motion

Explanation

Kepler worked for Tycho Brahe who was recording planetary motion for 20 years. After Brahe's demise Kepler inherited those records of planetary motion. After analyzing those records he put forth the three laws of planetary motion.

Law of Orbits: Every planet in our solar system move in elliptical orbit with sun at one focus It is also called the law of Ellipses

Law of Areas: The imaginary line drawn between the planet and sun will sweep out equal areas in equal period

Law of periods: The square of the time period of the planet is directly proportional to the cube of the semi major axis of the orbit. It is also called the law of Harmonies

Johannes Kepler is known for determining the planetary laws of motion in astronomy. Therefore option 2 is correct.

"determining planetary laws of motion," is the correct answer. Johannes Kepler was a German astronomer and mathematician who made significant contributions to our understanding of the motion of planets.

His three laws of planetary motion, known as Kepler's laws, revolutionized the field of astronomy and laid the foundation for Isaac Newton's later work on universal gravitation.

Kepler's first law, known as the law of ellipses, states that planets orbit the Sun in elliptical paths, with the Sun at one of the foci of the ellipse. This challenged the prevailing notion that planetary orbits were perfect circles.

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Final answer:

Using the principle of buoyancy and Archimedes' principle, we can determine the volume of the rock from the change in tension when submerged in water. Then, we use the volume of the rock to calculate the density of the unknown liquid where the tension is 11.4 N.

Explanation:

The problem described involves the principle of buoyancy and Archimedes' principle in particular, which states that the upward buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

When the rock is submerged in water and the tension in the string is 51.9 N, this is the weight of the rock in the air. When the rock is immersed in water and the tension becomes 31.6 N, the apparent weight is reduced due to the buoyant force of water. The difference in tension (51.9 N - 31.6 N = 20.3 N) is the weight of the water displaced, which can be converted into mass (20.3 N / 9.8 m/s2 = 2.07 kg). Knowing that the density of water is 1,000 kg/m3, we can calculate the volume of water displaced and thus the volume of the rock. When the rock is submerged in the unknown liquid and the tension is 11.4 N, a similar calculation for the buoyant force allows us to determine the density of the unknown liquid based on the known volume of the rock.

To solve for the density of the unknown liquid, we first need to determine the volume of the rock using the reduced tension in water (Archimedes' principle). Then we use the reduced tension in the unknown liquid to calculate the density of the unknown liquid. As we're given tensions rather than masses, we translate tension into weight (force) and use the equation for buoyant force (buoyant force = weight in air - apparent weight in fluid) to find the volume displaced. Since the rock displaces an equal volume of fluid, we can find the density of the unknown liquid using the buoyant force equation with the known volume of the rock.

Answer:

560 m

Explanation:

"A projectile is fired at time t = 0.0 s from point 0 at the edge of a cliff, with initial velocity components of v₀ₓ = 30 m/s and v₀ᵧ = 100 m/s.  The projectile rises, and then falls into the sea at point P. The time of flight of the projectile is 25 s.  Assume air resistance is negligible.  What is the height of the cliff?"

Use constant acceleration equation in the y direction.

y = y₀ + v₀ t + ½ gt²

0 = h + (100 m/s) (25 s) + ½ (-9.8 m/s²) (25 s)²

h = 560 m

The height of the cliff is 560 m.

1) 9.4 m/s

First of all, we can calculate the work done by the horizontal force, given by

W = Fd

where

F = 34.6 N is the magnitude of the force

d = 12.9 m is the displacement of the cart

Solving ,

W = (34.6 N)(12.9 m) = 446.3 J

According to the work-energy theorem, this is also equal to the kinetic energy gained by the cart:

[tex]W=K_f - K_i[/tex]

Since the cart was initially at rest, [tex]K_i = 0[/tex], so

[tex]W=K_f = \frac{1}{2}mv^2[/tex] (1)

where

m is the of the cart

v is the final speed

The mass of the cart can be found starting from its weight, [tex]F_g = 99.5 N[/tex]:

[tex]m=\frac{F_g}{g}=\frac{99.5 N}{9.8 m/s^2}=10.2 kg[/tex]

So solving eq.(1) for v, we find the final speed of the cart:

[tex]v=\sqrt{\frac{2W}{m}}=\sqrt{\frac{2(446.3 J)}{10.2 kg}}=9.4 m/s[/tex]

2) [tex]2.51\cdot 10^7 J[/tex]

The work done on the train is given by

W = Fd

where

F is the magnitude of the force

d is the displacement of the train

In this problem,

[tex]F=4.28 \cdot 10^5 N[/tex]

[tex]d=586 m[/tex]

So the work done is

[tex]W=(4.28\cdot 10^5 N)(586 m)=2.51\cdot 10^7 J[/tex]

3)  [tex]2.51\cdot 10^7 J[/tex]

According to the work-energy theorem, the change in kinetic energy of the train is equal to the work done on it:

[tex]W=\Delta K = K_f - K_i[/tex]

where

W is the work done

[tex]\Delta K[/tex] is the change in kinetic energy

Therefore, the change in kinetic energy is

[tex]\Delta K = W = 2.51\cdot 10^7 J[/tex]

4) 37.2 m/s

According to the work-energy theorem,

[tex]W=\Delta K = K_f - K_i[/tex]

where

[tex]K_f[/tex] is the final kinetic energy of the train

[tex]K_i = 0[/tex] is the initial kinetic energy of the train, which is zero since the train started from rest

Re-writing the equation,

[tex]W=K_f = \frac{1}{2}mv^2[/tex]

where

m = 36300 kg is the mass of the train

v is the final speed of the train

Solving for v, we find

[tex]v=\sqrt{\frac{2W}{m}}=\sqrt{\frac{2(2.51\cdot 10^7 J)}{36300 kg}}=37.2 m/s[/tex]

Answer: Ions are formed when atoms from group 1/3/2/17 gains or loses a small number of electrons.

Explanation: Let's take Na(Sodium) and Cl(chlorine), their atomic number are consecutively 11 and 17. Sodium's closest noble element is Neon(10) and Cl's is Argon(18). Now all atoms want to gain stability like the noble gases, they want their outer shell to be filled so that they don't have to wander around with other atoms. So to have stability Na will lose one of its electrons and Cl will take in one. Thus they consecutively will become plus charged and minus charged as the balance between their proton and electron numbers are gone

An ion is formed when a neutral atom gains or loses an electron.

A neutral atom has the same number of protons (+) and electrons (-).

If it gains another electron, it has too many negative charges, so it's a negative ion.

If it loses an electron, it has too many positive charges, so it's a positive ion.

=================================

What if it gains or loses a proton ?

That's a great question.  I'm glad you asked.

Under normal circumstances, this hardly ever happens.  But if it did ...

- If it somehow lost a proton from its nucleus, first of all, it would change the number of protons in the nucleus, so the atom would immediately become an atom of a different element.

- If it didn't lose an electron at the same time, then it would have too many electrons for the number of protons in the nucleus, so it would be a negative ion of the new element.

-  If it somehow added a proton to its nucleus, it would change the number of protons in the nucleus, so the atom would  become an atom of a different element.  If it didn't add another  electron at the same time, then it would have too few electrons for the number of protons in the nucleus, so it would be a  positive ion of the new element.

Answer:

91.5 m/s

Explanation:

m = mass of clay = 12 g = 0.012 kg

M = mass of wooden block = 100 g = 0.1 kg

d = distance traveled by the combination before coming to rest = 7.5 m

μ = Coefficient of friction = 0.65

V = speed of the combination of clay and lock just after collision

V' = final speed of the combination after coming to rest = 0 m/s

acceleration caused due to friction is given as

a = - μ g

a = - (0.65) (9.8)

a = - 6.37 m/s²

Using the kinematics equation

V'² = V² + 2 a d

0² = V² + 2(- 6.37) (7.5)

V = 9.8 m/s²

v = speed of clay just before collision

Using conservation of momentum

m v = (m + M) V

(0.012) v = (0.012 + 0.100) (9.8)

v = 91.5 m/s

To find the speed of the clay immediately before the impact, we can use the principle of conservation of momentum and the equation for friction. By solving the two equations simultaneously, we can determine the speed.

To find the speed of the clay immediately before the impact, we can use the principle of conservation of momentum. Since there is no external force acting on the clay-block system in the horizontal direction, the total momentum before the impact is equal to the total momentum after the impact.

Before the impact, the clay has a mass of 12 g and a velocity of v. The wooden block has a mass of 100 g and is initially at rest. After the impact, the clay and block stick together and move with a common velocity.

Using the conservation of momentum:

(mass of clay) × (velocity of clay before impact) + (mass of block) × (velocity of block before impact) = (mass of clay and block) × (velocity of clay and block after impact)

(0.012 kg) × v + (0.100 kg) × 0 = (0.112 kg) × v'

Then substituting the given distance the block slides before coming to rest and the coefficient of friction into the equation:

μ × (force of friction) × (distance) = (0.112 kg) × (final velocity after impact)² / 2

By substituting the given values and solving the two equations simultaneously, we can find the speed of the clay immediately before the impact.

Therefore, the speed of the clay immediately before the impact is approximately 2.89 m/s.

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Final answer:

The magnitude of the magnetic field at the origin when t = 0.15 μs can be found using the formula for the magnetic field produced by a moving charge.

Explanation:

The magnitude of the magnetic field at the origin when t = 0.15 μs can be found using the formula for the magnetic field produced by a moving charge:

B = (μ₀Iv)/(2πr)

Where B is the magnetic field, μ₀ is the permeability of free space, I is the current, v is the velocity of the charge, and r is the distance from the charge to the point where we want to find the magnetic field. In this case, the charge is moving parallel to the x-axis, so the current can be calculated using the formula:

I = (Qv)/L

Where Q is the charge and L is the length of the moving charge. Plugging in the values and solving the equations will give the magnitude of the magnetic field at x = 4 m when t = 0.15 μs.

To find the energy in joules equivalent to one jelly doughnut, multiply the Calorie value by 4.184. The number of stairs required to perform the same work as the energy in one jelly doughnut is calculated by dividing the work done to move up the stairs by the work done to move one stair height. To account for the body's efficiency in converting energy, divide the number of stairs calculated in part (b) by the efficiency.

(a) To find the number of joules of energy equivalent to one jelly doughnut, we need to convert the Calorie value to joules. One Calorie (capital C) is equal to 1000 calories (lowercase c), which is equal to 4.184 joules. Therefore, one jelly doughnut contains 625 calories × 4.184 joules/calorie = 2615 joules.

(b) The work done by climbing stairs is equal to the product of the force applied and the distance moved. The force can be calculated using the weight of the woman, which is equal to her mass multiplied by the acceleration due to gravity (66 kg × 9.8 m/s2). Dividing the work done to move up the stairs by the work done to move one stair height (15 cm) gives the number of stairs that the woman must climb. This is equal to 1764 joules ÷ (66 kg × 9.8 m/s2 × 0.15 m) = 181 stairs.

(c) Since the human body is only 26% efficient in converting chemical energy to mechanical energy, we need to divide the work calculated in part (b) by the efficiency to account for this loss. Therefore, the number of stairs the woman must climb to work off her breakfast is 181 stairs ÷ 0.26 = 696 stairs.

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The equation is T = KPV

Using the initial information you have, solve for K:

300 = K(4)(4)

Simplify:

300 = K(16)

Divide both sides by 16

K = 300/16

K = 18.75

Now if pressure increases by 7%, the new pressure would be 4 x 1.07 = 4.28

Volume increases by 0.07, so the new volume would be 4 + 0.07 = 4.07

Now solve for t:

T = 18.75(4.28)(4.07)

T = 326.6175

Now subtract the new temperature from the original one:

326.6175 - 300 = 26.6175 increase ( Round answer as needed).

Answer:

100 rad/s

Explanation:

Angular speed = linear speed / radius

ω = v / r

ω = (5.0 m/s) / (0.050 m)

ω = 100 rad/s

The angular speed of the pulley when the string has a linear speed of 5.0 m/s is found using the formula v = rω. So the angular speed is 100 rad/s.

To find the angular speed of the pulley when the string has a linear speed of 5.0 m/s, we can use the relationship between linear speed (v), angular speed (ω), and radius (r) of the pulley. This relationship is given by the formula v = rω, where v is the linear speed, r is the radius of the pulley, and ω is the angular speed we want to find. Given that the radius r is 5.0 cm (which we need to convert to meters by dividing by 100, so r = 0.05 m), and v is 5.0 m/s, we rearrange the formula to solve for ω:

ω = v / r

ω = (5.0 m/s) / 0.05 m

ω = 100 rad/s

Therefore, the angular speed of the pulley is 100 radians per second (rad/s).

Answer: composition, its size and shape.

Explanation:

All objects have a frequency that characterizes them, which is called natural frequency. This means that if a disturbance or vibration is emitted near the object, it will begin to vibrate due to its natural frequency.

It should be noted that there are objects that have more than one natural frequency, and this depends on the composition of the object, its elasticity, its shape and size.

The natural frequency of an object refers to the frequency at which it naturally tends to vibrate or oscillate when disturbed.

The specific factors that determine the natural frequency of an object are:

1. Mass: The mass of an object plays a significant role in determining its natural frequency.

2. Stiffness: The stiffness or rigidity of an object is another important factor in determining its natural frequency.

3. Geometry: The shape and size of an object also influence its natural frequency.

These factors interact with each other to determine the natural frequency of an object. Generally, objects with higher mass and/or higher stiffness will have lower natural frequencies, while objects with lower mass and/or lower stiffness will have higher natural frequencies.

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Answer: Because its period of rotation is 243.01 days (retrograde)

Explanation:

In comparison, Earth rotates once in about 24 hours with respect to the Sun, but once every 23 hours, 56 minutes, and 4 seconds with respect to other, distant, stars. Earth's rotation is slowing slightly with time, so in the past a day was shorter.

Venus's weak magnetic field can be attributed to its slow retrograde rotation period, lack of a convective liquid metal core, and lack of significant tectonic activity. These conditions are all contrary to those that generally contribute to generating a strong magnetic field.

The weak magnetic field of Venus could be linked to its retrograde rotation period and lack of a convective liquid metal core. Unlike planets with strong magnetic fields, Venus has a retrograde rotation period of 243 days, compared to Earth's 24-hour rotation period. The rotation period plays a key role in generating a planet's magnetic field. A faster rotation aids the creation of a dynamo effect, generating a stronger magnetic field.

Furthermore, the composition of Venus' core could also contribute to its weak magnetic field. A planet's magnetic field is typically caused by the movement of liquid metal within its core, which serves as a good conductor of electricity. It seems that Venus lacks this convective liquid metal core, thereby lacking the necessary conditions for a strong magnetic field.

Additionally, Venus may lack tectonic activity that is known to influence the generation of a magnetic field. While the surface of Venus has been modified by tectonics driven by mantle convection, it does not exhibit the same kind of plate tectonics as Earth.

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