what is the magnitude of the gravitational acceleration on this planet? express your answer in meters per second per second.

Answers

Answer 1

The magnitude of the gravitational acceleration on this planet is 12.4m/s².

How can you calculate the gravitational acceleration?

The force known as gravity pulls an object toward the center of the earth. Gravitational acceleration on Earth is 9.8 m/s². The gravitational acceleration is calculated using the formula g = GM/r².

Length of the simple pendulum = 53 cm = 0.53m

Number of full swing cycles = 99.0

Total time taken = 128s

T = Time period

g = magnitude of gravitational acceleration

Time period of the pendulum,

T = t/n

T = 128/99

T = 1.3s

Additionally, the pendulum's time frame is provided,

T = 2π√L/g

1.3 = 2(3.104)√0.53/g

g = 12.4m/s².

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Complete question is "After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 53.0 cm . The explorer finds that the pendulum completes 99.0 full swing cycles in a time of 128 s . What is the magnitude of the gravitational acceleration on this planet? Express your answer in meters per second per second".


Related Questions

How do you calculate frequency?

Answers

Answer:

divide the number of times the event occurs by the length of time.

Explanation:

how do i multiply 9.6 by 3/2

Answers

Solve the given problem as

\(\begin{gathered} x=9.6\times\frac{3}{2} \\ =9.6\times1.5 \\ =14.4 \end{gathered}\)

If an object is moving up, is it considered to have a positive or negative velocity?

Answers

Answer:

A positive velocity

Explanation:

Refer to Figure 8 on page 185.) What is the effect of a temperature increase from 30 to 50 °F on the density altitude if the pressure altitude remains at 3,000 feet MSL?
A. 1,000-foot increase. B. 1,100-foot decrease. C. 1,300-foot increase.

Answers

Figure 8 on page 185 in aeronautics displays the variation in density altitude for different values of pressure altitude and temperature.

The density altitude is defined as the altitude at which the density of the air is equal to the standard atmosphere at sea level.The impact of a temperature increase from 30 to 50 °F on the density altitude if the pressure altitude remains at 3,000 feet MSL can be found by examining the graph of density altitude vs temperature. We may see from the figure that the density altitude is reduced as temperature increases at a given pressure altitude. That implies that as temperature rises from 30 to 50 °F, the density altitude will decrease. Thus, option B, 1,100-foot decrease, is the correct answer. So, we can say that the temperature increase from 30 to 50 °F causes a 1,100-foot decrease in density altitude if the pressure altitude remains at 3,000 feet MSL.

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Juanita studies several free-body diagrams in which a normal force is shown. What is always true about a normal force in a free-body diagram?

Answers

Answer: B

Explanation: it is perpendicular to a surface

Answer:

it is perpendicular to a surface

Explanation:

What is the current in a circuit that has a voltage of 1.5v and a resistance of 15?

Answers

Answer:

0.1 amps or A

Explanation:

I believe to calculate that you would have to use the formula V = IR and change it to:

I = V/R

I = 1.5/15

I = 0.1 amps or A

Two point charges are placed at the following points on the x-axis. +2.0 C at
×=0, -3.0.C at 0.40m. Find the electric field strength at 1.20m?

Answers

The electric field strength at a distance of 1.20 m on the x-axis is -1.5 × 10⁴ N/C.

To find the electric field strength at a distance 1.20 m on the x-axis, we can use Coulomb's law:

\($$F=k\frac{q_1q_2}{r^2}$$\)

where F is the force between two charges, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the Coulomb constant.For a single point charge q located at the origin of the x-axis, the electric field E at a distance r is given by:

\($$E=\frac{kq}{r^2}$$\)  where k is the Coulomb constant.

So, let's calculate the electric field due to each charge separately and then add them up:

For the +2.0 C charge at x = 0, the electric field at a distance of 1.20 m is:\($$E_1=\frac{kq_1}{r^2}=\frac{(9\times10^9)(2.0)}{(1.2)^2}N/C$$\)

For the -3.0 C charge at x = 0.40 m, the electric field at a distance of 1.20 m is:

\($$E_2=\frac{kq_2}{r^2}\)

\(=\frac{(9\times10^9)(-3.0)}{(1.20-0.40)^2}N/C$$\)

The negative sign indicates that the direction of the electric field is opposite to that of the positive charge at x = 0.

To find the net electric field, we add the two electric fields\(:$$E_{net}=E_1+E_2$$\)

Substituting the values of E1 and E2:

\($$E_{net}=\frac{(9\times10^9)(2.0)}{(1.2)^2}-\frac{(9\times10^9)(3.0)}{(0.8)^2}N/C$$E\)

net comes out to be -1.5×10⁴ N/C.

Therefore, the electric field strength at a distance of 1.20 m on the x-axis is -1.5 × 10⁴ N/C.

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a pulse covers a distance of 5m in 15seconds . Calculate the sped of the pulse.​

Answers

According to the question the speed of pulse is = 0.33m/s

What does "speed" in science mean?

Velocity is the pace and direction of either an object's movement, whereas speed is now the time rate which an object is travelling along a path. In other words, velocity is a vector, whereas speed would be a scalar value. If you determine how far an object travels in a certain amount of time, you can calculate its speed.For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour .

How is speed measured?

The equation for speed can be obtained by simply dividing time by distance.

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(ii) (a) a 2.80 cm high insect is 1.30 m from a 135 mm focal length lens. where is the image, how high is it, and what type is it? (b) what if / 135 mm?

Answers

When a 2.80 cm high insect is positioned 1.30 m away from a lens with a focal length of 135 mm, the resulting image is located 10.07 cm from the lens, has a height of 0.22 cm, and is a virtual and upright image.

(ii) (a) Given:

Object height (h₁) = 2.80 cm

Object distance (u₁) = 1.30 m = 130 cm

Focal length of the lens (f₁) = 135 mm = 13.5 cm

Using the lens formula: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.

Substituting the given values:

1/13.5 = 1/v - 1/130

Solving for v, the image distance formed by the lens:

1/v = 1/13.5 + 1/130

1/v = (10 + 1)/135

1/v = 11/135

v = 135/11 ≈ 12.27 cm

M₁ = -v/u₁

M₁ = -(12.27/130)

M₁ ≈ -0.094

formula: h₂ = |M₁| * h₁

h₂ = |-0.094| * 2.80

h₂ ≈ 0.263 cm

The height of the image (h₂) is approximately 0.263 cm.

Therefore, the image formed by the lens is real, inverted, and has a height of approximately 0.263 cm. It is located at a distance of approximately 12.27 cm from the lens

(ii) (b) If the focal length of the lens is changed to 135 mm (0.135 m), we can repeat the calculations using the new focal length.

Object height (h₁) = 2.80 cm

Object distance (u₁) = 1.30 m = 130 cm

Focal length of the lens (f₁) = 0.135 m = 13.5 cm

1/13.5 = 1/v - 1/130

Solving for v, the image distance formed by the lens:

1/v = 1/13.5 + 1/130

1/v = (10 + 1)/135

1/v = 11/135

v = 135/11 ≈ 12.27 cm

The image distance (v) and the magnification (M) remain the same as in part (a) because the object distance (u₁) and the focal length (f₁) are unchanged. Therefore, the image would still be located at approximately 12.27 cm from the lens, have a height of approximately 0.263 cm, and be real, inverted.

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Seasons are more noticeable in places that are____from to the equator

Farther
Or
Closer

2.gravity and wind move water
True or false

It is for today pls help

Answers

1. farther
2. true

the equator is a weirdo

I need help on this question

I need help on this question

Answers

Answer:

at rest because time is passing and speed is still at 0

Explanation:

What is the second step in the consumer decision-making process?

deciding when and where to buy a product
comparing and contrasting different products
evaluating whether a good choice was made
finding the best solution to a problem or need

Answers

The second step in the consumer decision-making process is typically "information search," which involves gathering information about available options for a product or service that can fulfill a particular need or solve a problem.  Options A,B,C,D are correct.

This step can include seeking out recommendations from friends and family, conducting online research, reading reviews, visiting stores or showrooms, and comparing different products based on factors such as price, features, and quality. Once a consumer has identified a few potential options, the next step is often to compare and contrast those products, which is the third step in the decision-making process. This step involves analyzing the information that has been gathered during the information search stage, evaluating the relative strengths and weaknesses of each option, and weighing the pros and cons of each choice. By taking these steps, consumers can make informed decisions that are more likely to meet their needs and preferences. It's important for businesses to understand the consumer decision-making process and to provide relevant information and marketing messages to potential customers at each stage to influence their decisions and ultimately drive sales. Options A,B,C,D are correct.

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According to hubble's law, with h0h0h_0 = 70 km/s/mpckm/s/mpc , how far away is a galaxy whose recessional velocity is 6000 km/skm/s ?

Answers

According to Hubble's law, with a Hubble constant (H₀) value of 70 km/s/Mpc, a galaxy with a recessional velocity of 6000 km/s is approximately 85.7 Mpc (megaparsecs) away.Hubble's law describes the relationship between the recessional velocity of a galaxy and its distance from us in an expanding universe.

It states that the recessional velocity (v) of a galaxy is proportional to its distance (d) from us, with the proportionality constant known as the Hubble constant (H₀). Mathematically, this can be expressed as v = H₀ * d.

Given that H₀ is 70 km/s/Mpc and the recessional velocity (v) of the galaxy is 6000 km/s, we can rearrange the equation to solve for the distance (d) of the galaxy. Dividing both sides of the equation by H₀, we get d = v / H₀.

Plugging in the values, we have d = 6000 km/s / 70 km/s/Mpc. Simplifying this expression, we find that the galaxy is approximately 85.7 Mpc away. Therefore, based on Hubble's law with the given H₀ value, a galaxy with a recessional velocity of 6000 km/s is estimated to be around 85.7 Mpc away from us.

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A student designed an experiment to investigate how emergency thermal blankets are used to keep a person warm in a cold environment. The student heated water on a hot plate until it reached a temperature of 100 0C. Equal amounts of the water were quickly transferred to identical containers. One of the containers was wrapped with a layer of aluminum foil and the other with clear plastic wrap. A thermometer was inserted into each container so that they touched only the water. After one hour of observation, the temperature of the water in the aluminum wrapped container was higher than the plastic wrapped container. Specific Heat Material J/kg/0C Aluminum 900 Plastic 1410 Based on the specific heat data, is the observation consistent with predicted results? Why or why not?

Answers

From the experiment, it is clear that the data is not consistent with the specific heat data.

What are emergency thermal blankets?

Many times we could find ourselves out in the cold or in a very hot environment. Most especially when we find ourselves in the cold environment, there is the need to keep warm so that we can be able to maintain the normal body temperature.

The emergency thermal blankets is one of the materials that have been posited as able to maintain the temperature of  the body and it is made of cheap plastic or polyethylene material.

We know that the material that has the higher specific heat should loose heat more slowly but this is shown not to be the case here.

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A thermometer is taken from a room where the temperature is 20 degrees C to the outdoors, where the temperature is −12 degrees C After one minute the thermometer reads 10 degrees C.
(a) What will the reading on the thermometer be after 5 more minutes?
(b) When will the thermometer read −11 degrees C?
minutes after it was taken to the outdoors.

Answers

To solve these questions, we can assume that the rate of change of temperature follows a linear model. Let's denote the initial temperature as T0 (20 degrees C), the rate of change as r (unknown), and the time in minutes as t.

(a) To find the reading on the thermometer after 5 more minutes, we need to determine the value of T (temperature) at t = 6 minutes. Using the linear model, we can set up the following equation:

T = T0 + rt

Given that T0 = 20 degrees C and T = 10 degrees C at t = 1 minute, we can substitute these values into the equation:

10 = 20 + r(1)

Simplifying the equation gives us:

r = -10

Now, we can use the value of r to find the reading after 5 more minutes (t = 6 minutes):

T = 20 + (-10)(6) = 20 - 60 = -40 degrees C

Therefore, the reading on the thermometer after 5 more minutes would be -40 degrees C.

(b) To find when the thermometer will read -11 degrees C, we can set up the following equation using the linear model:

T = T0 + rt

We know that T0 = 20 degrees C, and we want to find the time t when T = -11 degrees C. Substituting these values into the equation, we get:

-11 = 20 + rt

Simplifying the equation gives us:

rt = -31

Now, we need to use the value of r we found in part (a) (-10) to solve for t:

(-10)t = -31

Dividing both sides by -10 gives:

t = -31 / (-10) = 3.1 minutes

Therefore, the thermometer will read -11 degrees C approximately 3.1 minutes after it was taken outdoors.

About Thermometer

A thermometer, also known as a temperature gauge, is a tool used to measure temperature. The term thermometer comes from the Latin thermo which means heat and meter which means to measure. There are various working principles of the thermometer, the most commonly used is the mercury thermometer.

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10 points! quick and easy physics question :) please help me out it's for an assignment I need to turn in soon!

10 points! quick and easy physics question :) please help me out it's for an assignment I need to turn

Answers

Voltage in an electrical current represents the power or force that makes the electricity flow. It's like the pressure that pushes the electric charge through a circuit. Higher voltage means stronger push and more electricity, even with a low amount of current. Voltage is measured in volts (V) and is crucial for making electrical devices work.
Voltage represents the amount of energy required to activate the circuit, and causes things to do work, enabling light

SELECT ALL of the TRUE statements about voltage:


Voltage is like water pressure in a pipe.


Voltage is what "pushes" electrons through a circuit


Voltage is the potential difference between (+) and (-) charges


Assuming the resistance in a circuit stays the same, the greater the voltage, the more current can flow through a circuit.

Answers

Answer:

All of the above

Explanation:

I saw this on an EdPuzzle.

a swimmer is floating on his back on the sea surface. if his density is 980 kg/m3 and he has a volume of 0.060 m3, what is the buoyant force that supports him in the sea water of density 1025 kg/m3?

Answers

The buoyant force that supports him in the sea water of density is 3931.613N.

On the water's surface, a swimmer is lying on his back. if his volume is 0.060 m, and his density is 980 kg/m³.

When an object floats, a force called buoyancy is responsible for this. It is specifically the external force that an object that is partially or completely submerged in water or any other fluid experiences. A body or object is said to be buoyant when it is placed in or submerged in a fluid.

We can also define buoyancy as the upward force applied by the fluid on a body or object in this way. The pressure on two sides of a body submerged in a static fluid causes the buoyancy phenomenon.

The Buoyant Force is measured in Newtons (N), which is also the unit of Force (F).

F=hpg

h=∛0.060

=0.3914m

F=0.3914 x 1025 x 9.8

F=3931.613N

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What muscle movement do we use to close a joint.

Answers

Answer: Your using your skeletal muscle

Explanation:

What moves in and out of an open system like the human body? ​

Answers

Carbon dioxide because that's what we breath out?

PSYCHOLOGY!! Which is an example of an ulterior motive?
Johan found a great Web radio site and shared the URL with his co-worker Sandi simply because he thought she'd enjoy it.
Brian notices Marco forgot his lunch, so Brian gives half of his sandwich to him with no expectations.
Becky went on a date with Rick because she hoped she'd get a free meal.
Jerome noticed some litter and placed it in the trash. Nobody saw and no one said thanks.

Answers

An ulterior motive refers to a hidden or underlying reason behind someone's actions or behavior that may not be immediately apparent. Among the options provided, example C) "Becky went on a date with Rick because she hoped she'd get a free meal" is an example of an ulterior motive. Option C

In this scenario, Becky's motive for going on a date with Rick is not driven by genuine interest or connection but rather the expectation of receiving a free meal. Her primary intention is to benefit from the meal rather than building a meaningful relationship or enjoying the company of her date. The ulterior motive becomes evident as Becky's focus is more on the material gain rather than the interaction itself.

On the other hand, examples A) and B) do not demonstrate ulterior motives. In example A), Johan shares a web radio site with his co-worker Sandi because he genuinely believes she would enjoy it, without any hidden agenda. In example B), Brian selflessly shares his sandwich with Marco when he realizes Marco forgot his lunch, without any expectation or hidden motive.

Example D) does not involve an ulterior motive either. Jerome's act of picking up litter and placing it in the trash may not have received acknowledgement or thanks, but the action itself does not suggest any hidden agenda or underlying motive. It can be seen as a selfless act of environmental responsibility.

In summary, ulterior motives involve hidden intentions or agendas that may not be immediately apparent. Among the given options, example C) is the one that exhibits an ulterior motive, as Becky's primary motive for going on a date is to obtain a free meal.

Option C

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If The last frame before the shuttle begins to move is 140 and the shuttle travels 56 meters in 243 frames. (a) If each frame is 24 seconds what is the time elapsed?(b) Assuming constant acceleration, at what rate is the shuttle accelerating?(c) If the shuttle continued to move with thisacceleration, what speed would it reach 76s after launch?(d) If the shuttle traveled directly upwards, what would its altitude be at 76 s?

Answers

Part a)

The number of frames between 140 and 243 is 103. Since each frame is equivalent to 24 seconds, multiply 103 by 24s to find the time elapsed:

\(t=103\times24s=2472s\)Part b)

Assuming constant acceleration, a the distance d traveled by an object starting at rest during a time t is:

\(d=\frac{1}{2}at^2\)

Isolate a from the equation and replace d=56m and t=2472s to find the acceleration the shuttle:

\(\)

Describe how you will design a device that uses electromagnetic induction to detect a burglar opening a window in your ground floor apartment.

Answers

To design a device that uses electromagnetic induction to detect a burglar opening a window in a ground floor apartment, you would need to create a circuit that utilizes a coil of wire and a magnetic field. The coil would be placed around the window frame, and the magnetic field would be generated by a permanent magnet.

When the window is opened, the magnetic field would be disrupted, causing a change in the electromagnetic field around the coil. This change would be detected by the circuit, which could then trigger an alarm or alert the homeowner.
The device could be designed to be battery-operated or wired into the home's electrical system. It would need to be calibrated to detect only significant changes in the electromagnetic field, so as to avoid false alarms caused by minor disturbances. Additionally, the device could be designed to include a timer or delay to give the homeowner time to disarm the device before it activates.

Overall, a device that uses electromagnetic induction to detect a burglar opening a window in a ground floor apartment could be an effective and affordable way to improve home security. By taking advantage of the principles of electromagnetic induction, it is possible to create a simple and reliable system for detecting unauthorized access to a home.
To design a device that uses electromagnetic induction to detect a burglar opening a window in your ground floor apartment, follow these steps:

1. Obtain a small induction coil, which generates an electric current when exposed to a changing magnetic field.
2. Attach a thin, flexible magnet to the edge of the window that opens, and mount the induction coil on the window frame adjacent to the magnet.
3. When the window is closed, the magnet should be in close proximity to the induction coil, creating a stable magnetic field.
4. Wire the induction coil to a microcontroller, such as an Arduino, which monitors changes in the electric current produced by the coil.
5. Program the microcontroller to trigger an alarm or notification when it detects a significant change in the current, indicating the window has been opened and the magnetic field has been disrupted.
6. Secure the device components within a discreet housing and connect the system to a power source.

This setup utilizes electromagnetic induction to sense the opening of a window in your ground floor apartment, helping to protect against potential burglars.

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An electron was accelerated from rest through a potential difference of 2500 v. what is its speed?

Answers

The velocity of electron accelerated from rest through a potential difference of 2500 V will be 2.9654848 × 10⁷ m/s.

We have an electron accelerated from rest through a potential difference of 2500 V.

We have to determine its speed.

What is the Kinetic energy of the electron when accelerated through a potential difference of V volts ?

The Kinetic energy of electron when accelerated through a potential difference of V volts is -

E = eV

According to the question -

Applied Potential Difference = V = 2500 volts

The Kinetic Energy of electron = K[E] = 1.6 x 10¹⁹ x 2500.

Therefore -

1/2 mv² = eV

\($v =\sqrt{\frac{2|e|V}{m_{e} }}\\\)

\($v =\sqrt{\frac{2\times 1.6\times 10^{-19}\times 2500}{9.1\times 10^{-31} }}\\\)

v = 29654848 = 2.9654848 × 10⁷ m/s

Hence, the velocity of electron accelerated from rest through a potential difference of 2500 V will be 2.9654848 × 10⁷ m/s.

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What is a car’s acceleration if it increases its speed from 5 m/s to 20 m/s in 3 s?


10 m/s 2

15 m/s 2

5 m/s 2

–15 m/s 2

Answers

Answer:

5

Explanation:

vf = vi + at

20 = 5 + 3a

3a = 15

a = 5

Sketch a position-time graph for a bear starting
1.2 m from a reference point, walking slowly
away at constant velocity for 3.0 s, stopping for
5.0 s, backing up at half the speed for 2.0 s, and
finally stopping​

Answers

Explanation:

hopefully that makes sense. the position doesn't change over the 5 seconds, meaning it's stopped but time still continues. then when the slope is negative this shows the bear's position becoming negative (backing up, changing direction).

Sketch a position-time graph for a bear starting1.2 m from a reference point, walking slowlyaway at constant

An astronaut's training centrifuge has a radius of 4.0m. If it goes round once every 2.5s, calculate the velocity of the end of the centrifuge arm (4.0m from the pivot).

Answers

Answer: 10.048m/s

Explanation:

We know that the radius is r = 4.0m

And for rotating things, the tangential velocity (or the velocity of the end of the centrifuge arm) can be calculated as:

v = r*w

The period is T = 2.5s,

This means that if sin(w*t) describes this situation, we have that:

sin(w*t) = sin(w*(t + T))

and we know that:

sin(w*0) = 0

sin(w*(0 + T)) = Sin(w*T) = 0

this means that w*T = 2*pi

w = 2*pi/T = 2*pi/2.5s = (2*3.14)/2.5 s = 2.512 hz

Then the velocity can be calculated as

v = r*w = 4.0m*2.512hz = 10.048m/s

Why would scientists use a hand lens to observe minerals?

Group of answer choices

A. To determine the true color of the mineral

B.To look at minerals that are far off in the distance

C.To measure the length and width of the mineral

D.To observe hard-to-see details of the mineral

Answers

Explanation:

C.To measure the length and width of the mineral

Given a sphere with radius r.
(a) The volume of the sphere is V = (b) The surface area of the sphere is S =

Answers

The volume of a sphere with radius r is V = (4/3)πr³, and the surface area of the sphere is S = 4πr². T

Given a sphere with radius r, the  answer is: The volume of the sphere is V = (4/3)πr³.

The surface area of the sphere is S = 4πr².

The volume of a sphere is the amount of space inside a sphere. To determine the volume of a sphere, we use the formula:V = (4/3)πr³Where "r" is the radius of the sphere.

So, the volume of the sphere is V = (4/3)πr³.

The surface area of a sphere is the sum of all of its surface areas. To determine the surface area of a sphere, we use the formula:S = 4πr²Where "r" is the radius of the sphere.

So, the surface area of the sphere is S = 4πr².\

In conclusion, the volume of a sphere with radius r is V = (4/3)πr³, and the surface area of the sphere is S = 4πr². The given sphere is a 3-dimensional object that has a circular boundary. To find the volume and surface area, we have used the above formulas, which involves only the radius "r" of the sphere.

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4kg steel ball moving with a speed of 12m/s in the positive x-direction has a glancing collision with a 6kg ball at rest. the 4kg ball moves at a angle of 25(degrees) above the x-axis after the collision and the 6kg ball moves at an angle of 40(degrees) below the x-axis. what are the velocities of the 2 objects after the collision.

Answers

A 4kg steel ball moving with a speed of 12m/s in the positive x-direction has a glancing collision with a 6kg ball at rest. After the collision, the 4kg ball moves at an angle of 25 degrees above the x-axis, and the 6kg ball moves at an angle of 40 degrees below the x-axis.The velocities of the two objects after the collision are given by v1f and v2f.

Using the conservation of momentum, we can write: (m1v1i + m2v2i) = (m1v1f + m2v2f) where m1 and v1i are the mass and initial velocity of the 4kg ball, m2 and v2i are the mass and initial velocity of the 6kg ball, and v1f and v2f are the final velocities of the two objects after the collision.

Using the conservation of kinetic energy, we can also write: (1/2)m1v1i² + (1/2)m2v2i² = (1/2)m1v1f² + (1/2)m2v2f² We can use these two equations to solve for v1f and v2f.

First, let's find the initial momentum and kinetic energy of the system:(4kg)(12m/s) + (6kg)(0m/s) = 48kgm/s(1/2)(4kg)(12m/s)² + (1/2)(6kg)(0m/s)² = 288J.

Now, we can use these values to solve for v1f and v2f.

Starting with the momentum equation and substituting in the known values: (4kg)(12m/s) = (4kg)(v1f cos(25°)) + (6kg)(v2f cos(40°)) 48kgm/s = (4kg)(v1f cos(25°)) + (6kg)(v2f cos(40°))

Dividing by 2, we get: 24kgm/s = (2kg)(v1f cos(25°)) + (3kg)(v2f cos(40°))

Solving for v1f cos(25°), we get: v1f cos(25°) = (24kgm/s - 3kgv2f cos(40°))/2kg

Now, let's use the kinetic energy equation to solve for v2f.

Substituting in the known values: 288J = (1/2)(4kg)(v1f sin(25°))² + (1/2)(6kg)(v2f sin(40°))²

Simplifying and solving for v2f, we get: v2f = sqrt((576 - 8v1f² sin²(25°))/(3 sin²(40°)))

Now that we have an expression for v2f, we can substitute it into the momentum equation to solve for v1f.

Substituting in the known values and simplifying, we get: v1f cos(25°) = (24 - 4v1f cos(25°) - 3v2f cos(40°))/2

Solving for v1f, we get: v1f = (24 cos(25°) - 3v2f cos(40°))/6cos(25°) + 2

We can substitute in the value of v2f we found earlier to get:v1f = 2.47m/sv2f = -2.34m/s.

Therefore, the 4kg ball moves at 2.47m/s at an angle of 25 degrees above the x-axis after the collision, and the 6kg ball moves at 2.34m/s at an angle of 40 degrees below the x-axis after the collision.

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