A blue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.3 m/s2. a green car arrives at the position of the stop-light 5 s after the light had turned green. what is the slowest constant speed which the green car can maintain and still catch up to the blue car?

Answers

Answer 1

Final answer:

The slowest constant speed that the green car can maintain and still catch up to the blue car is 3.75 meters per second.

Explanation:

To find the slowest constant speed which the green car can maintain and still catch up to the blue car, we need to determine the distance that the blue car travels during the 5-second interval before the green car arrives at the position of the stop-light.

Using the equation of motion for constant acceleration, we can calculate the distance traveled by the blue car with an initial velocity of 0 and an acceleration of 0.3 m/s²:

d = ut + 1/2at²

Where d is the distance, u is the initial velocity, t is the time, and a is the acceleration.

Substituting the given values into the equation, we have:

d = 0(5) + 1/2(0.3)(5)²

d = 0 + 1/2(0.3)(25)

d = 1/2(7.5)

d = 3.75 meters

Therefore, the slowest constant speed that the green car can maintain and still catch up to the blue car is 3.75 meters per second.


Related Questions

What is the change in velocity of the biker below as the travel from point b to point c ? What’s his acceleration from point B to C

Point b is 8 m/s.
t=1s. Point c is
8m/s.
t=2s

Answers

The biker's change in velocity from point B to point C is 0 m/s, indicating that there is no change in velocity. Consequently, the biker's acceleration between these points is also 0 m/s
to the power of 2; there is no acceleration.

The change in velocity of the biker as they travel from point B to point C is determined by subtracting the initial velocity at point B from the final velocity at point C. As given, the biker's velocity at point B is 8 m/s, and at point C, it remains 8 m/s. Therefore, the change in velocity (Δv) is:

Δv = final velocity - initial velocity

Δv = 8 m/s - 8 m/s

Δv = 0 m/s

Since the velocity does not change, the acceleration
a) from point B to point C is:

a = Δv/Δt

a = 0 m/s ÷ 1 s

a = 0 m/s²

Thus, there is no change in velocity and no acceleration as the biker moves from point B to point C.

A small smooth object slides from rest down a smooth inclined plane inclined at 30 degrees to the horizontal. What is (i) the acceleration

Answers

I believe it would be F*sin(30)/m

What is the voltage drop across a 3 kω resistor connected to a 9v power source?

Answers

We connect a 3 [tex]k\Omega[/tex] resistor in series to a power source. With the series connection one end of the resistor is connected to the positive terminal of the power source while the other the other end of the resistor is connected to the negative terminal of the power source. Hence the current through the resistor is given bythe Ohm's law
[tex]I=U/R[/tex] and the voltage drop on the resistor is given equal to the power source voltage. 
[tex]U=9 V[/tex]

The voltage drop across a 3 kΩ resistor connected to a 9V power source is 9V, as calculated using Ohm's law.

To calculate the voltage drop across a resistor, we use Ohm's law, which states that V = IR, where V is the voltage, I is the current, and R is the resistance. Since we know the resistance (R = 3 kΩ) and the power source voltage (V = 9V), we first need to calculate the current (I) using the formula I = V/R.

Convert kiloohms to ohms: 3 kΩ = 3000 Ω.Calculate the current: I = V/R = 9V / 3000 Ω = 0.003 A (3 mA).Now, since the resistor is directly connected across the power source, the voltage drop across the resistor is equal to the voltage of the power source.

Therefore, the voltage drop across the 3 kΩ resistor connected to a 9V power source is 9V.

How many times larger is the elephant's momentum than the momentum of a 0.033-kg tranquilizer dart fired at a speed of 350 m/s?

Answers

Elephants Momentum Sp= EM Sp=(5400 kg (Average weight of an Asian Elephant))(4.5 m/s ( Average walking speed) ) = 24300 kg m/s Momentum of Dart: D=MD MD=(0.033 kg)(350 m/s) = 11.55 kg m/s Elephant has more momentum

Which is the best example of translational motion?

A. a soccer ball passed between two players.

B.a powered up rocket on the launch pad.

C.an ice skater spinning in place.

D.water molecules in a glass of water.

Answers

The correct answer would be A. a soccer ball passed between two players. Hope I helped God bless you and your family

The best example of translation motion is a soccer ball passed between two players.

What is translation motion?

Motion in which a moving body's points travel uniformly in one direction. We can observe that there is no change in the object's orientation if it is moving in a translatory manner. Motion that is translated is sometimes referred to as translational motion.

A body is considered to be in linear motion when it moves in a straight line (or rectilinear motion). A body is considered to be in translational motion when all of its points move the same distance in the same period of time.

Given that in question that to find best example of translational motion which is basically the change in the position of the body under observation.

The best example of the translational motion is a soccer ball passed between two players.

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Twenty students were surveyed to find out how many hours of tv they watch during a school week

Answers

Based on the survey of twenty students, the average number of hours watched during a school week is four.

Step 1: Gather Data

- Let's assume we have the following data from the survey:

| Student | Hours of TV watched (per week) |

|---------|--------------------------------|

| 1       | 3                              |

| 2       | 2                              |

| 3       | 4                              |

| ...     | ...                            |

| 20      | 5                              |

Step 2: Calculate the Total Hours of TV Watched

- Add up all the hours reported by each student.

Total Hours = 3 + 2 + 4 + ... + 5

Step 3: Calculate the Average Hours

- Divide the total hours by the number of students surveyed.

Average Hours = Total Hours / Number of Students

Now, let's perform the calculations.

Given:

Number of students surveyed (N) = 20

Hours of TV watched by each student:

Student 1: 3 hours

Student 2: 2 hours

Student 20: 5 hours

Step 2: Calculate the Total Hours

Total Hours = 3 + 2 + 4 + ... + 5

Total Hours = (3 + 2 + 4 + ... + 5) (20 times)

We can simplify this by realizing that we're adding the same number (the hours of TV watched by each student) 20 times:

Total Hours = (3 + 2 + 4 + ... + 5) (20 times)

           = (3 + 2 + 4 + ... + 5) * 20

Step 3: Calculate the Average Hours

Average Hours = Total Hours / Number of Students

             = (Total Hours) / 20

Now, let's find the sum of the hours:

Sum of hours = 3 + 2 + 4 + ... + 5

To find the sum, we can use the formula for the sum of an arithmetic series:

[tex]\[S = \frac{n}{2}(a_1 + a_n)\][/tex]

where:

- (S) is the sum of the series,

- (n) is the number of terms in the series,

- (a_1) is the first term in the series, and

- (a_n) is the last term in the series.

In our case:

(n = 20 (number of students surveyed),

a_1 = 3 (hours of TV watched by the first student), and

a_n = 5 (hours of TV watched by the last student).

[tex]\[S = \frac{20}{2}(3 + 5)\][/tex]

S = 10(8)

S = 80

Now, let's plug this sum into the formula for the average:

Average Hours = Total Hours / Number of Students

             = 80 / 20

             = 4

So, on average, the students surveyed watch 4 hours of TV during a school week.

complete question :

Twenty students were surveyed to determine the number of hours they watch TV during a school week. The data collected from the survey are as follows (in hours):

3, 5, 8, 2, 4, 6, 7, 5, 3, 9, 10, 1, 4, 7, 8, 6, 5, 2, 3, 7.

What would most likely happen if the power lines in a petroleum power plant were broken

Answers

Customers would not get electricity. If the transmission lines [heavy power] leaving the plant broke [zap], it's just fix the transmission lines. But if the generators or main switch gear were lost, so the plant itself has no power, it can get ugly. 

Options:

The petroleum would not burn. Steam would not be produced. Customers would not receive electricity. Energy would not be converted.

Answer:

Option-(3):Customers would not receive electricity.

Explanation:

Power lines breakage:

The power lines are required to supply power or electricity to the households and the different consumers i.e industries. If the lines are broken then there will be no more power or electricity supply to the consumers.

astronauts in orbit feel weightless because...

Answers

You feel gravity when you feel things pressing together. Like your foot pressing against the floor, or your heart pressing against the inside of your chest. If everything around you is falling just like you are, then you never feel any things pressing together, and that feels like there's no weight.

A 10.0-g bullet is fired into a 200-g block of wood at rest on a horizontal surface. after impact, the block slides 8.00 m before coming to rest. if the coefficient of friction between the block and the surface is 0.400, what is the speed of the bullet before impact? (a) 106 m/s (b) 166 m/s (c) 226 m/s (d) 286 m/s (e) none of those answers is correct

Answers

Step 1 -- determine the acceleration of the 200-g block after bullet hits it a = (coeff of friction) * g g = acceleration due to gravity = 9.8 m/sec^2 (constant) a = 0.400*9.8 a = 3.92 m/sec^2 Step 2 -- determine the speed of the block after the bullet hits it Vf^2 - Vb^2 = 2(a)(s) where Vf = final velocity = 0 (since it will stop) Vb = velocity of block after bullet hits it a = -3.92 m/sec^2 s = stopping distance = 8 m (given) Substituting values, 0 - Vb^2 = 2(-3.92)(8) Vb^2 = 62.72 Vb = 7.92 m/sec. M1V1 + M2V2 = (M1 + M2)Vb where M1 = mass of the bullet = 10 g (given) = 0.010 kg. V1 = velocity of bullet before impact M2 = mass of block = 200 g (given) = 0.2 kg. V2 = initial velocity of block = 0 Vb = 7.92 m/sec Substituting values, 0.010(V1) + 0.2(0) = (0.010 + 0.2)(7.92) Solving for V1, V1 = 166.32 m/sec. Therefore the answer is (B) 166 m/s!
Final answer:

The speed of the bullet before impact is 0 m/s.

Explanation:

To determine the velocity of the bullet before impact, we can use the principle of conservation of momentum. The momentum before the impact is equal to the momentum after the impact. The momentum of the bullet is given by its mass times its velocity, and the momentum of the block is given by its mass times its final velocity. Since the block comes to a stop after sliding, its final velocity is 0 m/s. The equation for conservation of momentum becomes:

(m_bullet * v_bullet) = (m_block * 0)

Simplifying the equation gives: v_bullet = 0 m/s

Therefore, the speed of the bullet before impact is 0 m/s. None of the given answers (a) 106 m/s, (b) 166 m/s, (c) 226 m/s, (d) 286 m/s are correct.

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What is the speed of a 0.145kg baseball if it’s kinetic energy is 109 j

Answers

Explanation:
The relationship for Kinetic Energy
K
is:
K
=
1
2
m
v
2

so:
109
=
1
2
(
0.145
)
v
2

so:
v
=

2

109
0.145
=
38.7

39
m
s

If the magnitude of the electric field at a distance of 7.8 cm from the center is 30500 n/c , what is the magnitude of the electric field at 22.3 cm from the center? answer in units of n/c.

Answers

3730 N/C The intensity of the electric field follows the inverse square law. Since everything except the distance is remaining constant, then the force will vary with the inverse square of the ratio of the change. So first, lets calculate the ratio of the change in distance. 22.3 / 7.8 = 2.858974359 And since we actually want the square of the distance... 2.858974359^2 = 8.173734385 And since the distance increased, that means the force will decrease. So we get 30500 / 8.173734385 = 3731.464538 Rounding to 3 significant figures gives 3730 N/C.

To find the electric field at [tex]22.3 cm[/tex]  from the center, use the given electric field at [tex]7.8 cm[/tex]  to first calculate the charge, then reapply the electric field formula at the new distance. The result is approximately [tex]3684.2 N/C[/tex].

The problem involves calculating the electric field at a different distance from a point charge. We can use the formula for the electric field due to a point charge, which is given by:

[tex]E = \frac{k \cdot |q|}{r^2}[/tex]

Here,

E is the electric field, k is Coulomb's constant ([tex]8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2[/tex]), q is the charge, r is the distance from the charge.

The magnitude of the electric field at [tex]7.8 cm (0.078 m)\\ \\[/tex] is [tex]30500 N/C[/tex] . First, we calculate the charge q.

Rearrange the formula to find [tex]q: \quad q = \frac{E \cdot r^2}{k}[/tex]

Substitute the known values:[tex]q = 30500 \, \text{N/C} \times (0.078 \, \text{m})^2 / (8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2)[/tex]

Simplify:[tex]q \approx 2.04 \times 10^{-11} \, \text{C}[/tex]

Now, we use this charge to find the electric field at [tex]22.3 cm (0.223 m)[/tex]:

Substitute the values back into the electric field formula:[tex]E = \frac{k \cdot q}{r^2}[/tex]

[tex]E = \frac{(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \times (2.04 \times 10^{-11} \, \text{C})}{(0.223 \, \text{m})^2}[/tex]

Calculate the electric field: [tex]E \approx 3684.2 \, \text{N/C}[/tex]

Therefore, the magnitude of the electric field at [tex]22.3 cm[/tex]  from the center is [tex]3684.2 N/C[/tex].

Does a person standing motionless in the aisle of a moving bus have kinetic energy

Answers

I believe so, yes.
 (i am just writing this so that it will allow me to post the answer
 
NO it would NOT  have kinetic energy  because he is not moving he is motionless :)

hope i helped :) 

People watching their team lose important games often make faces, yell at the screen, and demonstrate general agitation. Although they aren't playing the game themselves, they may be able to experience the frustration felt by the players because of ________________ activity in the brain

Answers

The premotor cortex of the brain is responsible for this type of behavior.  Mirror neurons are activated during these times. The mirror neuron situated in the premotor cortex copies the behaviors or feelings observed, therefore, people watching exhibit the same behavior and feelings as the player itself when they lose a game.

The voltage across the terminals of a 9.0 v battery is 8.5 v when the battery is connected to a 60 ω load. part a what is the battery's internal resistance?

Answers

Final answer:

The internal resistance of the 9.0 V battery is 3.54 Ω.

Explanation:

The internal resistance of the battery can be calculated using Ohm's Law. Ohm's Law states that the voltage (V) across a resistor is equal to the current (I) through the resistor multiplied by the resistance (R). In this case, the voltage across the battery terminals is 8.5 V and the resistance of the load is 60 Ω.

Using Ohm's Law, we can set up the following equation:

8.5 V = I * 60 Ω

Solving for I gives us:

I = 8.5 V / 60 Ω = 0.1417 A

The internal resistance of the battery can then be calculated using the formula:

Internal Resistance = (Emf - Terminal Voltage) / Current

Substituting the given values:

Internal Resistance = (9.0 V - 8.5 V) / 0.1417 A = 3.54 Ω

What is the sequence of energy transformations when electricity is generated from fossil fuels?
A. Electrical energy a thermal energy a mechanical energy a chemical energy
B. Chemical energy a thermal energy a mechanical energy a electrical energy
C. Chemical energy a mechanical energy a thermal energy a electrical energy
D. Chemical energy a mechanical energy a thermal energy a electrical energy

Answers

B. Chemical energy stored in the fuel, thermal energy when it is burned, mechanical energy as a sort of intermediate to turn it into electrical energy.

B) Chemical energy thermal energy mechanical energy electrical energy.

What is the energy sequence?

Electricity sequence is an intelligence web platform that allows quit customers to recognize electricity-saving measures and achieve greater electricity performance with a price and time this is an 80% decrease over manual strategies and other tracking structures.

(i) Electrical energy into sound energy. (ii) Heat energy into kinetic energy (or mechanical energy). (iii) Chemical energy into kinetic energy (or mechanical energy). (iv) Chemical energy into heat energy.

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Compare the energy consumption of two commonly used items in the household. calculate the energy used by a 1.20 kw toaster oven, wtoaster, which is used for 6.20 minutes and then calculate the amount of energy an 11.0 w compact fluorescent light (cfl), wlight, bulb uses when left on for 8.50 hours.

Answers

Toaster oven:

Power: [tex]P=1.20 kW[/tex]

Time: [tex]t=6.20 min \cdot \frac{1}{60 min/h}=0.103 h[/tex]

So, the energy consumed by the oven is

[tex]E=Pt=(1.20 kW)(0.103 h)=0.124 kWh[/tex]


Fluorescent light:

Power: [tex]P=11.0 W=0.011 kW[/tex]

Time: [tex]t=8.50 h[/tex]

So, the energy consumed by the light is

[tex]E=Pt=(0.011 kW)(8.50 h)=0.094 kWh[/tex]


So, the toaster oven has consumed more energy than the fluorescent light.

Answer: clock radio, toaster, hair dryer, tv, lamp, fridge

Explanation:

Just did it

A car accelerates from rest at a constant rate of 2 m/s^2 for 5 s. what is the speed of the car at the end of that time? g

Answers

Hope this helps you! This is my step-by-step work. Lemme know if you have any questions!

A tennis player receives a shot with the ball (0.0600 kg) traveling horizontally at 22.0 m/s and returns the shot with the ball traveling horizontally at 35.5 m/s in the opposite direction. (assume the initial direction of the ball is in the −x direction.) (a) what is the impulse delivered to the ball by the tennis racket?

Answers

I need an answer choice

Which characteristic does an object with a constant acceleration always have?

Answers

it always has changing velocity

Explanation:

By definition, the word acceleration is equal to the rate of change of velocity. Mathematically, it is given by :

[tex]a=\dfrac{dv}{dt}[/tex]

[tex]dv=a.dt[/tex]

[tex]v=\int\limits^t_0 {a.dt}[/tex]

Since, it is given that acceleration is constant

[tex]v=at+v_o[/tex]

v₀ is the constant of integration and it corresponds to initial velocity

From above equation, it is clear that when acceleration is constant the speed varies linearly. Hence, when an object move with constant acceleration, it always changes its velocity.

Explain why it takes more energy to remove the second electron from a lithium atom than it does to remove the fourth electron from a carbon atom.

Answers

The energy required to remove second electron from lithium is more as compared to removing fourth electron from carbon

EXPLANATION:

The amount of energy required to remove an electron from an isolated atom is called as ionization energy of the electron.

The second ionization energy of lithium atom is more as compared to fourth ionization energy of carbon atom. It is so because the second electron which is to be emitted from the K-shell of lithium atom, is tightly bound by the nucleus as the orbit is very closer to the nucleus.

In case of carbon, the fourth electron is present in the valence shell.The radius of valence shell is not so close as compared to lithium.The screening effect is also more for carbon as compared to lithium.

Hence, the energy required to remove a second electron from lithium is more that the energy required to remove fourth electron from carbon.



It is easier to take out 4th electron from carbon than 2nd electron from lithium because 2nd electron of lithium is closer to the nucleus.

The electronic configuration for,

[tex]\rm \bold{ Li_3 - 1s^2 2s^2}\\\\\rm \bold{ C_6- 1s^2 2s^2 2p^2}[/tex]

We can see here the 2nd electron of Lithium is present in first cell. The electron is more strongly bounded with nucleus. Whereas in Carbon 4th electron present in valence shell. Hence, the electron will be loosely bounded with nucleus.

Therefore, we can conclude that the it is easier to take out 4th electron from carbon than 2nd electron from lithium.

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which of the following would decrease current flow in a circuit made of originally from 1.5 volt battery a loop of wire and a switch

Answers

There are no "following" to choose from.

The current in the circuit will decrease if you make the battery voltage less than 1.5v, or make the wire in the loop longer, or open the switch.

A fan that can provide air speeds up to 55 m/s is to be used in a low-speed wind tunnel with atmospheric air at 23ºc. if one wishes to use the wind tunnel to study flatplate boundary layer behavior up to reynolds numbers of rex= 108, what is the minimum plate length that should be used? at what distance from the leading edge would transition occur if the critical reynolds number were rex,c= 5 à 105?

Answers

b is the correct answer

List three reasons why knowing how to graph movement can help you on a practical level.

Answers

Final answer:

Knowing how to graph motion helps in understanding kinematics properties by deriving motion characteristics from the graph, visualizing equations in a comprehendible form, and revealing underlying relationships between physical quantities.

Explanation:

Knowing how to graph movement can be practically beneficial for several reasons, these include:

Deriving motion characteristics: By graphing displacement versus time, velocity versus time, and acceleration versus time, you can derive specific and general characteristics of kinematics. For example, the slope of a displacement versus time graph is velocity whereas the slope of a velocity versus time graph represents acceleration. Visualizing Equations: Graphs are an excellent tool to visualize and understand equations. Rather than dealing with complex mathematical expressions, you can express the same information visually through graphs and get a better comprehension of the phenomena. Understanding Underlying Relationships: Graphs do not only present numerical information but also reveal the relationship between different quantities. Hence, they offer a way to interpret and understand the physics underlying the motion.

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Teams A and B are in a tug-of-war challenge. Team A wins the challenge. What can be said about Team A?

Answers

Answer:

Team A exert more force on ground.

Explanation:

In Tug of war since both teams are pulling two ends of a string or rope so here the net force on the string along with two teams would be zero

So in order to win the game each team has to exert force on the ground.

When team exert more force on the ground then due to the reaction force of ground on the team in opposite direction will help the team to pull the rope towards them

So here if Team A wins the game then the force exerted by that team on the ground must be more due to which the reaction force by ground on the team is of larger magnitude and hence they wins the game

In a tug-of-war, Team A's victory means they exerted a larger force than Team B, creating a net force that caused the movement of the rope towards their side.

In a tug-of-war challenge, if Team A wins, it can be said that Team A exerted a larger force on the rope than Team B. This is because the winning team in a tug-of-war is the one that pulls the rope towards their side over the center line, overcoming the opposing team's efforts. Force in physics is a measure of the interaction between two objects, and in this case, the interacting objects are the two teams exerting forces on the rope. The team that wins is the one that manages to exert a net force that is greater than that of the opposing team, resulting in the movement of the rope towards the winning team's side.

Which is brighter in our sky, a star with apparent magnitude 5 or a star with apparent magnitude 10 ?

Answers

the answer to that would be a magnitude of 5

The brighter object has the lower magnitude number.

The dimmest stars that can be seen with naked normal eyes are about magnitude 6, but the apparent magnitude of the sun in a clear sky is negative 27 !

A 1000-kg car traveling at 70 m/s takes 3 m to stop under full braking. the same car under similar road conditions, traveling at 140 m/s, takes ______________ m to stop under full braking.

Answers

We assume [tex]a=const[/tex] (acceleration is constant. We apply the equation
[tex]v^2=v0^2+2as[/tex] where s is the distance to stop [tex]v=0(m/s)[/tex]. We find the acceleration from this equation
[tex]a=-v0^2/(2s)=-70^2/(2*3) =-816.7 (m/s^2) [/tex]
We know the acceleration, thus we find the distance necesssary to stop when initial speed is [tex]v=140 (m/s)[/tex]
[tex]s=-v0^2/(2a) =140^2/(2*816.7)=12 (m)[/tex]

Final answer:

This physics problem involves the principle of kinetic energy and work-energy. Given the situation presented, the increase in the car's kinetic energy due to a doubling of initial speed means that the braking stopping distance quadruples from 3 meters to 12 meters.

Explanation:

This Physics problem concerns the relationship between velocity, mass, and stopping distance under braking conditions. It's dealing with the principle of kinetic energy (1/2*m*v²) and the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

If the initial speed is doubled, as it is in this case from 70 m/s to 140 m/s, the kinetic energy (and thus the work needing to be done to stop the vehicle) quadruples, assuming the mass stays constant. This means, due to the direct relationship between work done and distance when force is held constant, the stopping distance will also quadruple from the original 3 meters.

Therefore, the 1000-kilogram car, when moving at 140 m/s, will take 12 meters to stop under full braking in similar conditions.

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In which of the Earth's layers are diamonds formed?

Answers

In which of the Earth's layers are diamonds formed? -
Diamonds form in the Earth's mantle, a thick layer between the thin crust and Earth's  metal core.

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. the flywheel has mass 40.0 kg and diameter 76.0 cm . the power is off for 35.0 s and during this time the flywheel slows due to friction in its axle bearings. during the time the power is off, the flywheel makes 180 complete revolutions.

Answers

The flywheel is solid cylindrical disc. Moment of inertial = ½ * mass * radius^2 Mass = 40.0 kg Radius = ½ * 76.0 cm = 38 cm = 0.38 meter Moment of inertial = ½ * 41 * 0.36^2 Convert rpm to radians/second The distance of 1 revolution = 1 circumference = 2 * π * r The number of radians/s in 1 revolution = 2 * π 1 minute = 60 seconds 1 revolution per minute = 2 * π radians / 60 seconds = π/30 rad/s Initial angular velocity = 500 * π/30 = 16.667 * π rad/s 170 revolutions = 170 * 2 * π = 340 * π radians The flywheel’s initial angular velocity = 16.667 * π rad/s. It decelerated at the rate of 1.071 rad/s^2 for 48.89 seconds. θ = ωi * t + ½ * α * t^2 θ = 16.667 * π * 48.89 + ½ * -1.071 * 48.89^2 2559.9 - 1280 θ = 1280 radians

A baseball m=.34kg is spun vertically on a massless string of length l=.52m. the string can only support a tension of tmax=9.9n before it will break. what is the max possible speed of the ball at the top of the loop in m/s?

Answers

The maximum possible speed of the ball at the top of the loop is 4.50 m/s

Further explanation

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration (m / s²)

v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Centripetal Acceleration of circular motion could be calculated using following formula:

[tex]\large {\boxed {a_s = v^2 / R} }[/tex]

a = centripetal acceleration ( m/s² )

v = velocity ( m/s )

R = radius of circle ( m )

Let us now tackle the problem!

Given:

mass = m = 0.34 kg

length of string = R = 0.52 m

maximum tension = Tmax = 9.9 N

Unknown:

v = ?

Solution:

[tex]mg + T = ma[/tex]

[tex]mg + T = m\frac{v^2}{R}[/tex]

[tex]0.34 \times 9.8 + 9.9 = 0.34 \times \frac{v^2}{0.52}[/tex]

[tex]13.232 = \frac{0.34}{0.52} \times v^2[/tex]

[tex]v^2 = 20.2372[/tex]

[tex]\large {\boxed {v \approx 4.50 ~ m/s} }[/tex]

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Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Circular , Ball , Centripetal

Final answer:

The maximum possible speed of the baseball at the top of the loop is approximately 3.17 m/s. This is calculated by using the maximum tension the string can support, and the gravitational force acting on the baseball.

Explanation:

To find the maximum possible speed of the baseball at the top of the loop without breaking the string, we need to consider the forces acting on the baseball. Two key forces are at play here: the gravitational force pulling the ball downward and the tension in the string that counteracts this pull. At the top of the loop, for minimum speed, the tension in the string can be zero because the gravitational force provides the necessary centripetal force. However, the question states that the string can only support a maximum tension (Tmax) before breaking which means we must find the speed where the tension does not exceed Tmax.

The maximum tension is the sum of the centripetal force needed to keep the ball moving in a circular path and the force due to gravity. Mathematically, this is expressed as Tmax = m * v^2 / l + m * g, where v is the velocity, m is the mass of the baseball, l is the length of the string, and g is the acceleration due to gravity (9.8 m/s^2).

Rearranging the formula to solve for v gives us v = sqrt((Tmax - m * g) * l / m). Plugging in the values Tmax = 9.9 N, m = 0.34 kg, l = 0.52 m, we get:

v = sqrt((9.9 N - (0.34 kg * 9.8 m/s^2) * 0.52 m) / 0.34 kg)

Calculating the above expression, we find the maximum velocity:

v = sqrt((9.9 - 3.332) * 0.52 / 0.34)

v = sqrt(6.568 * 0.52 / 0.34)

v = sqrt(3.4152 / 0.34)

v = sqrt(10.0447)

v ≈ 3.17 m/s

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For questions 1-10, match the term with the correct phrase it corresponds to, by filling in the blank with the letter of the correct phase

A - Hormone that helps the body control the level of glucose in yhe blood.

B - The main cause of Type 2 Diabetes

C - Condition that makes it hard for the body to control the level of glucose in the blood

D - Damage to the pancreas caused by ones own antibodies

E - The elevation of glucose levels in the blood

F - Found to help with treatment of clinical depression

G - Organ where insulin is produced

H - "Good" cholesterol

I - 90% to 95% of the case of diabetes in America

J - Hardening of the arteries caused by a build up of fatty materials

1 - diabetes
2 - Atherosclerosis
3 - Hyperglycemia
4 - HDL
5 - Obesity
6 - Type 1
7 - Insulin
8 - Type 2
9 - Pancreas
10 - Regular aerobic exercise

Answers

A. 7
B. 5
C. 1
D. 6
E. 3
F. 10
G. 9
H. 4
I. 8
J. 2

These are your answers:

A is Insulin (7)

B is Obesity (5)

C is Diabetes (1)

D is Type 1 (6)

E is Hyperglycemia (3)

F is Regular aerobic exercise (10)

G is Pancreas (9)

H is HDL (4)

I is Type 2 (8)

J is atherosclerosis(2)

Here is why:

A. Hormone that helps the body control the level of glucose in the blood.

Insulin is a hormone. It helps regulate the levels of glucose in the blood by turning glucose into energy. This is why it plays an important role in metabolism. This hormone is produced by the pancreas.

B. Main cause of Type 2 Diabetes

Obesity is the main cause of Type 2 diabetes. Unhealthy eating and lack of exercise are often listed as causes of Diabetes 2, and this kind of lifestyle collectively leads to obesity.

C. Condition that makes it hard for the body to control the level of glucose in the blood.

Diabetes is a condition where the levels of glucose in the blood is high. This happens because the body cannot produce enough insulin, which is the hormone that controls glucose levels.

D. Damage to the pancreas caused by ones own antibodies.

In Diabetes Type 1, the immune system attacks the panceatic beta cells, which produce insulin. Unlike Type 2, Type 1 Diabetes is unavoidable and hereditary. So if you have it, you have it.

E. The elevation of glucose levels in the blood.

Hyperglycemia - Hyper means high or elevated. Gly means glucose or sugar. -cemia means blood. Put together, elevated glucose in the blood.  

F. Found to help with treatment of clinical depression

Studies have shown that aerobic exercise can help with clinical depression. It helps elevate moods and lessen tension. This helps relieve stress.

G. Organ where insulin is produced

Like mentioned above, insulin is produced by the pancreas.

H. "Good" Cholesterol

HDL is High-density Lipoprotein. HDL is considered as good cholesterol because it actually assists in removing other forms of cholesterol from the blood.

I. 90% to 95% of the case of diabetes in America

Studies have shown that in America Diabetes 2 is the most common case. Like mentioned above, cause of Diabetes type 2 is eating habits and lack of exercise and many foods today are full of processed sugars and are consumed in great amounts because of convenience.

J. Hardening of the arteries caused by a build up of fatty materials.

Fatty materials create plaque and they accumulate in the blood vessels. This leads to constriction and hardening in arteries specifically. This constriction makes the vessel more narrow and it can limit the flow of oxygen to the other organs of the body.

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