Answer:
My aunt died and I am felling down today
Background Information: Energy can not be created or destroyed. Stored energy is called
potential energy, and the energy of motion is called kinetic energy. Due to gravity, potential
energy changes as the height of an object changes, this is called gravitational potential energy.
Objective: to determine the relationship between height and gravitational potential energy.
Problem: How does the drop height (gravitational potential energy) of a ball affect the bounce
height (kinetic energy) of the ball?
Hypothesis: If the gravitational potential energy (drop height) of a ball is increased, then the
kinetic energy (bounce height) will (increase/decrease/remain the same) because
Variables: Independent variable (known information) is
Dependent variable (unknown information) is
Constants (variables kept the same for accuracy) are
Materials: List all the materials used in this experiment.
Procedure: Follow the steps below to conduct your experiment. Be sure to record all data and
any observations during the experiment. Follow all safety rules.
1. Tape the meter stick to the side of the lab table with the 0-cm end at the bottom and the 100-cm end at the
top. Be sure that the meter stick is resting flat on the floor and is standing straight up.
2. Choose a ball type and record the ball type in the data table.
3. Use the triple beam balance to determine the mass of the ball and record the ball’s mass in the data table.
4. Calculate the gravitational potential energy (GPE) for the ball at each drop height. Record GPE in data table.
a. GPE = ball mass x drop height
5. For Trial 1, hold the ball at a height of 40 cm, drop the ball carefully and observe the bounce height. Record
the bounce height in the data table.
6. Drop the ball 4 more times from 40 cm, recording the bounce height each time, for a total of 5 drops.
7. For Trial 2, repeat steps 5 and 6 but drop the ball from a height of 50 cm. Record the 5 bounce heights in
the data table.
8. For Trial 3, drop the ball five times from 60 cm and record the 5 bounce heights in the data table.
9. For Trial 4, drop the ball five times from 70 cm and record the 5 bounce heights in the data table.
10. For Trial 5, drop the ball five times from 80 cm and record the 5 bounce heights in the data table.
11. For Trial 6, drop the ball five times from 90 cm and record the 5 bounce heights in the data table.
12. For Trial 7, drop the ball five times from 100 cm and record the 5 bounce heights in the data table.
13. Repeat steps 2 through 12 for a different type of ball.
14. Calculate the average bounce height of the 5 drops for each drop height. Record the average bounce height
in the data table. Calculate the average bounce height for all Trials.
a. To calculate average: Add the 5 bounce heights for a trial then divide the total by 5 drops. Example
for Trial 1: drop1 + drop2 + drop3 + drop4 +drop5 = total; total divided by 5 = average bounce height.
i. Sample: Trial 1: 5+6+5+5+7 = 28 28/5 = 5.6 average bounce height.
15. Plot the average bounce heights on a line graph. Place the independent variable of drop height on the x-axis
and place the dependent variable of bounce height on the y-axis. Label the line with the ball type.
16. CHALLENGE: Repeat all necessary steps for a third ball type and include this data on the graph.
17. Answer discussion questions and write your lab summary.
Data:
Ball Type: Ball Mass (g) = .
Gravitational
Potential Energy
(GPE)
Bounce Height (cm)
Drop
Height (cm)
GPE = mass x height Drop 1 Drop 2 Drop 3 Drop 4 Drop 5 Average
Bounce
Height
40
50
60
70
80
90
100
Ball Type: Ball Mass (g) = .
Gravitational
Potential Energy
(GPE)
Bounce Height (cm)
Drop
Height (cm)
GPE = mass x height Drop 1 Drop 2 Drop 3 Drop 4 Drop 5 Average
Bounce
Height
40
50
60
70
80
90
100
Discussion Questions: Answer using complete sentences.
1. Describe the relationship between drop height and the bounce height.
Was the relationship the same for both ball types that you tested?
2. Compare your gravitational potential energy to your bounce height for each trial. Describe
the relationship between GPE and bounce height.
3. Look at the results of both ball types you tested.
a. Which ball type had the most gravitational potential energy?
b. Which ball type has the most mass?
c. Describe the relationship between mass and GPE.
4. What are the variables that affect gravitational potential energy of an object?
Conclusion: Write a conclusion, using complete sentences, that states the following: if your
hypothesis was supported or negated; and what the real answer to the problem is.
Summary: Write a three paragraph summary using our standard format (1. what you were doing
and why you were doing it, 2. what you learned while doing this experiment, and 3. how what you
learned relates to your life).
Answer:
this question is very lengthy and even nit at all understandable so pls can u explain it in breif
Answer:
Explanation:
I did it and this is what i got
What is the absolute magnitude of the reduction in the variation of Y when times is introduced into the regression model? What is the relative reduction? What is the name of the latter measure?
1. The absolute magnitude of the reduction in variation of Y when time is introduced into the regression model can be calculated by subtracting the variance of Y in the original model from the variance of Y in the new model.
2. The relative reduction can be calculated by dividing the absolute magnitude by the variance of Y in the original model.
3. The latter measure is called the coefficient of determination or R-squared and represents the proportion of variance in Y that can be explained by the regression model.
When time is introduced into a regression model, it can have an impact on the variation of the dependent variable Y. The absolute magnitude of this reduction in variation can be measured by calculating the difference between the variance of Y in the original model and the variance of Y in the new model that includes time. The relative reduction in variation can be calculated by dividing the absolute magnitude of the reduction by the variance of Y in the original model.
The latter measure, which is the ratio of the reduction in variation to the variance of Y in the original model, is called the coefficient of determination or R-squared. This measure represents the proportion of the variance in Y that can be explained by the regression model, including the independent variable time. A higher R-squared value indicates that the regression model is more effective at explaining the variation in Y.
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Describe the difference between
resistance in a series and parallel circuit.
The current the resistors in series are the same but their voltage will be different. In the case of parallel resistors the voltage will be the same and current will be different.
What is resistance ?Resistance in a circuit is the hindrance to current . According to Ohm's law, resistance is the ratio of voltage to the current.
In a series circuit all the components are connected in series. Whereas in a parallel circuit the components are connected in parallel.
In a series circuit the output current from one resistance is the input current of the next resistor. Hence, current through all resistors are the same but their voltage differs.
Thus, total resistance R = R1 + R2 + R3 + …
In parallel circuits all the resistors have the same voltage but they differ in current.
then the total resistance R = 1/R1 + 1/R2 + 1/R3 + ..
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A bowling ball has a mass of 50 kg and is traveling with a velocity of 18 m/s 4 points
down the lane. How much momentum does it have?
momentum= mass × velocity
p= 50×18
momentum= 900 kg m/s
What did scientists create using scientific measurements?
Answer:
lines?
Explanation:
applied a force of 55 N to accelerate a 10 kg box at 3 m/s2 along a horizontal surface. What is the magnitude of the frictional force?
Answer:
25N
Explanation:
if you calculate it right the answer will be 25
what is mach number?
Mach number is "the ratio of the speed of a body to the speed of sound in the surrounding medium" (Oxford Languages). Put simply, it's a ratio comparing the local flow velocity to the speed of sound in the medium.
It is represented with the following formula. M is the mach number, u is the local flow velocity, and c is the speed of the sound in the medium.
\(\boxed{\displaystyle M=\frac{u}{c} }\)
where should you allow more following distance behind a motorcycle or moped?
A general rule of thumb is to maintain a following distance of at least 3-4 seconds behind a motorcycle or moped.
As a general rule, it is recommended to allow more following distance behind a motorcycle or moped than you would for a car. This is because motorcycles and mopeds have a shorter stopping distance and are more susceptible to sudden movements or changes in road conditions. It is recommended to maintain a following distance of at least 2 seconds behind a motorcycle or moped, and increase that distance if you are traveling at higher speeds or in adverse weather conditions.
When driving behind a motorcycle or moped, you should always allow more following distance than you would for a car. This is because motorcycles and mopeds can stop more quickly than cars, and providing more distance will give you enough time to react and avoid a collision. A general rule of thumb is to maintain a following distance of at least 3-4 seconds behind a motorcycle or moped. This can be increased in poor weather conditions or during heavy traffic to ensure safety.
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Calculate the maximum wavelength of light capable of dissociating the f–f bond in one molecule of fluorine if the bond energy, or bond dissociation energy, is 157 kj/mol.
The maximum wavelength of light capable of dissociating the f–f bond in one molecule of fluorine if the bond energy, or bond dissociation energy, is 157 kJ/mol is 7.625 × 10⁻⁵ meters.
Given:
Bond dissociation energy = 157 kJ/mol.
we know,
Avogadro's number = 6.023 × 10²³ mole⁻¹
Speed of light = 3 × 10⁸ms⁻¹
Planck constant = 6.626 × 10⁻³⁴ Js
To calculate the maximum wavelength of light capable of dissociating the f–f bond in one molecule of fluorine,
The energy required to break one f--f bond is calculated as,
⇒ Bond energy / Avogadro's number
= 157 × 10³/ 6.023 × 10²³
= 26.067 × 10⁻²⁰ Joules
Let the wavelength of the light required to break one f -f bond be λ.
We find the maximum wavelength by using Einstein's equation for photon energy.
Einstein's equation for photon energy is represented mathematically by the following formula:
E = hf = hc / λ
In this equation,
E is the energy.h is the Planck constant.f is photon frequency.λ is the wavelength.v is the speed of lightSubstituting the values in the formula,
⇒ 26.067 × 10⁻²⁰ = ( 6.626 × 10⁻³⁴ × 3 × 10⁸) / λ
⇒ λ = ( 6.626 × 10⁻³⁴ × 3 × 10⁸) / 26.067 × 10⁻²⁰
= 7.625 × 10⁻⁵ m
Hence, the maximum wavelength is 7.625 × 10⁻⁵ m.
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The diagram above shows a ballistic pendulum. A 10 g bullet is fired into the suspended 2 kg block of wood and
remains embedded inside it (a perfectly inelastic collision). After the impact of the bullet, the block swings up to a
maximum height h. If the initial speed of the bullet was 35 m/s:
A.) What was the momentum of the bullet before the collision?
B.) What was the kinetic energy of the bullet before the collision?
C.) What was the velocity of the bullet-block system just after the collision?
D.) What was the total kinetic energy of the bullet-block system after the collision?
E.) What is the maximum possible potential energy of the bullet-block system when it reaches its maximum height?
F.) What is the maximum possible height of the bullet-block system?
The kinetic energy of the bullet-block system is equal to the potential energy of the bullet-block system when it reaches its maximum height.
Conservation of Linear momentumAccording to the principle of conservation of linear momentum, momentum before collsion is equal to momentum after collision. Let us now answer the questions individually.
1) The momentum of the bullet before collsion = (0.001 Kg * 35 m/s) = 0.35 Kgms-1
2) The kinetic energy of the bullet before collision = 0.5 * 0.001 * (35 m/s)^2 = 0.6125 J
3) Velocity after collsion is obtained from;
(0.001 Kg * 35 m/s) + (2 kg * 0 m/s) = (0.001 Kg + 2 kg) v
v = 0.35/2.001 =
v=0.1749 m/s
4) Total kinetic energy after collison = 0.5 * (0.001 Kg + 2 kg) * (0.1749 m/s)^2
= 0.031 J
5) The maximum possible potential energy of the bullet-block system when it reaches its maximum height = Total kinetic energy after collison = 0.031 J
6) The maximum possible height of the bullet-block system is obtained from;
PE = mgh
h = 0.031 J/(0.001 Kg + 2 kg) * 9.8 ms-2
h = 0.0015 m or 0.15 cm
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If you double the current through a resistor, by what factor does the power dissipated by the resistor change?.
If you double the current through a resistor, the power dissipated by the resistor change by factor of 4.
What is electric current?The stream of positive charges which flow from the positive terminal to the negative terminal of the battery attached in a circuit.
Power dissipated through a resistor is related to current as
P =I²R
When the current is doubled, the new power will be
P' = (2I)²R
P' = 4 I²R
P' = 4P
Thus, the power change by the factor of 4.
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Consider the causal LTI system with impulse response h(t) = u(t). Prove that this system is an integrator, i.e., the output of the system is the integral of the input. X(t) 1 2 t t(2-t) 0 h(t) 1 b 1 21 Figure 1: Input function and impulse response
Using the input and impulse response given in Fig.1, find and sketch the output calculating x(t) * h(t). You can either use the integral definition of the convolution or the Reflect-and-Shift approach.
The impulse response of the LTI system is h(t) = u(t).Let's find the output for the given input and impulse response using the integral definition of the convolution, given as follows:x(t) h(t) = ∫x(τ)h(t-τ)dτWe have to consider two cases when t < 0 and t ≥ 0.
Case 1:
When t < 0x(t) h(t) = ∫x(τ)h(t-τ)dτWhen t < 0, h(t - τ) = u(t - τ) = 0 for all τ > t. Therefore, for this range of t, x(t) h(t) = 0.Case 2:
When t ≥ 0x(t) h(t) = ∫x(τ)h(t-τ)dτ= ∫x(τ)u(t-τ)dτSince u(t - τ) = 1 for τ ≤ t and u(t - τ) = 0 for τ > t, we can split the integral into two parts:x(t) h(t) = ∫x(τ)u(t-τ)dτ= ∫x(τ)u(t-τ)dτ + ∫x(τ)u(τ-t)dt= ∫x(τ)u(t-τ)dτ + ∫x(t-τ)u(τ)dτ= ∫0tu(τ)x(t-τ)dτ + ∫t∞u(τ)x(t-τ)dτ= ∫0tx(t-τ)dτAs the function x(t) is given,we can evaluate the integral:
x(t) h(t) = ∫0tx(t-τ)dτ= ∫0t(2-τ)dτ= 2t - t²/2Let's plot the graph of the output function using the given input and impulse response:Graph of the output functionAbout Impulse ResponseIn signal processing and control theory, the impulse response, or impulse response function, of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, the impulse response is the reaction of any dynamic system in response to some external change.
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Lars is balancing equations with his study group. He is unsure about one equation because each member of the study group came up with a different answer. Which is the proper way to balance the equation Ca(OH)2 + H3PO4 → Ca3(PO4)2 + H2O?
Follow my lead or ur answer is very wrong
Fluffy, a greyhound travels 15 m in 2 s while another greyhound, Tiberius, travels 20 m in 5 s. Construct a distance-time graph comparing the two dogs.
Answer:
3
Explanation:
dogs
What type of circuit have you made?
The type of circuit which have been made is the series circuit in this scenario.
What is a Series circuit?
This is a complete path which involves the whole electric current flowing through the various parts such as resistor etc..
There is only one path of current in which it does not undergo any form of split during motion.
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A _____ is a series of events and activities with no slack time. a. risk path b. foundation path c. baseline path d. critical path.
The D. critical path is a series of events and activities with no slack time.
It is a path that defines the longest duration required to complete a project. It is significant in the project management methodology as it helps the project manager establish a timeline for the project while also identifying the activities that are most critical to the project's completion. If an activity on the critical path takes longer than anticipated, the whole project will be delayed, and if an activity is completed earlier than expected, then it might not be worth it to continue the project, and the client might not be willing to pay for it.
The critical path analysis allows managers to identify and control the critical factors that can impact a project's success, enabling them to focus on the most important areas and make informed decisions about the project. So the correct answer is D. critical path, is a series of events and activities with no slack time.
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The mass of a newborn baby's brain has been found to increase by about 1.6 mg perminute. (a) How much does the brain's mass increase in one day?
ANSWER
2304 mg
EXPLANATION
The rate is given in mg per minute. To find how much the brain's mass increases in one day we have to find how many minutes are in a day.
Assuming that a day has 24 hours and 1 hour has 60 minutes:
\(24h\cdot\frac{60\min}{1h}=1440\min \)One day has 1440 minutes. Then, in one day the brain's mass increases:
\(1.6mg/\min \cdot1440\min =2304mg\)The newborn baby's brain's mass increases 2304 mg in one day.
A bullet travelling horizontally with speed of 30m/s strike a wooden plank normal it surface, passing through it with a speed of 10m/s. Find the time taken by the the bullet to pass through the wooden plank of 5cm thickness
The bullet takes 0.0025 seconds to pass through the wooden plank of 5 cm thickness when it is traveling horizontally with an initial speed of 30 m/s and a final speed of 10 m/s.
The time taken by the bullet to pass through the wooden plank can be determined using the equation of motion for constant acceleration.
Given:
Initial speed (u) = 30 m/s
Final speed (v) = 10 m/s
Distance (s) = 5 cm = 0.05 m
To find the time taken (t), we need to calculate the acceleration (a) first. We can use the equation:
v² = u² + 2as
Rearranging the equation, we have:
a = (v² - u²) / (2s)
Substituting the given values:
a = (10² - 30²) / (2 * 0.05)
Simplifying the expression:
a = (-800) / (0.1)
a = -8000 m/s²
The negative sign indicates that the acceleration is in the opposite direction of the initial velocity.
Next, we can use the equation of motion:
v = u + at
Substituting the values:
10 = 30 + (-8000) * t
Simplifying the equation:
-8000t = -20
Dividing by -8000:
t = 20 / 8000
t = 0.0025 s
Therefore, the time taken by the bullet to pass through the wooden plank of 5 cm thickness is 0.0025 seconds.
To find the time taken by the bullet to pass through the wooden plank, we need to calculate the acceleration first using the equation of motion.
By rearranging the equation and substituting the given values, we can find the acceleration.
Then, using the equation of motion again, we can solve for time.
The negative sign in the acceleration indicates that it is in the opposite direction of the initial velocity.
The resulting time is 0.0025 seconds.
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A glass of water has a temperature of 31 degrees Celsius. What state of matter is it in?
Answer:
Liquid
Explanation:
Water...
- below 0 degrees Celsius is a solid.
- above 0 degrees Celsius is a liquid.
- above 100 degrees Celsius is a gas.
if the current density in a wire is given by j=alpha*r,where alpha is a constant and r is the distance from the center of the wire, 0
Given:
The current density is,
\(J=ar\)a is a constant, and the radius of the wire is R.
To find:
The current in the wire
Explanation:
The current in the wire is,
\(\begin{gathered} I=\int JdA \\ =\int ardA \end{gathered}\)We know,
\(\begin{gathered} A=\pi r^2 \\ dA=2\pi rdr \end{gathered}\)So,
\(\begin{gathered} I=\int_0^Rar\times2\pi rdr \\ =2\pi a\int_0^Rr^2dr \\ =2\pi a\times\frac{R^3}{3} \end{gathered}\)Hence, the required current is,
\(\frac{2\pi aR^3}{3}\)What is the Force in Newtons exerted by brick with a mass of 0.5 kg and an Acceleration of 52m/s2?
a.
According to Figure 2-1, what is the displacement of the mass during interval A-D?
12 meters
18 meters
20 meters
24 meters
Well, the figure seems to report that velocity is measured in m/s²... That label should say m/s. (Unless of course this is the graph of acceleration over time, but then the answer would probably be more complicated than the given choices.)
If the graph indeed shows velocity, and the unit is just a typo, then the displacement from A to D is equal to the area under the curve.
From A to B, the area is of a triangle with height 4 m/s and base 1 s, hence the area is 1/2 • (4 m/s) • (1 s) = 2 m.
From B to C, it's a rectangle with length 3 s and height 4 m/s, hence with area (3 s) • (4 m/s) = 12 m.
From C to D, it's a trapezoid with "height" 2 s and bases 4 m/s and 2 m/s, hence with area 1/2 • (4 m/s + 2 m/s) • (2 s) = 6 m.
The total displacement is then 2 m + 12 m + 6m = 20 m.
A solid ball of mass 6 kg, rolls down a hill that is 6 meters high. What is the rotational KE at the bottom of the hill?
Newton's Second Law states
1. an object's acceleration is proportional to its mass and to the net force acting on it.
2. an object's acceleration is inversely proportional to its mass and proportional to the net force acting on it.
3. an object's acceleration is inversely proportional to its mass and to the net force acting on it.
4. force, mass, and acceleration have no relation.
The correct statement of Newton's Second Law is: An object's acceleration is inversely proportional to its mass and proportional to the net force acting on it.
What is Newton's Second Law?Newton's Second Law of Motion states that the force acting on an object is directly proportional to the mass of the object and its acceleration. In other words, the greater the force applied to an object, the greater its acceleration, and the greater the object's mass, the less it will accelerate for a given force.
This law is often expressed mathematically as F = ma, where F is the force applied to an object, m is the object's mass, and a is its acceleration.
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A moving object is in equilibrium. Which best describes the motion of the object if no forces change?
It will change directions.
It will slow down and stop.
It will maintain its state of motion.
It will speed up and then slow down.
Answer:
it is It will maintain its state of motion. because of newtons law states that any object in morion will stay in motion unless acted upon another force pushing against it
Explanation:
Answer:
It will maintain its state of motion.
Explanation:
Ple can someone help me to answer this question
The length of the uniform meter stick is 50 cm and the mass of the uniform meter stick is 50 g.
A sketch of the uniform stick and the massThe sketch of the uniform stick and the mass will be two based on the given statement.
when the uniform stick balances on knife at 10 cm from one end;-------------------------------------------------------
↓ 10cm Δ (L - 10 cm) ↓
200g M
When the knife edge is moved 5 cm further|---------------15 cm-----------------|
-----------------------------------------------------------------------
↓ 8.75 cm Δ (L - 15 cm) ↓
200g M
From the first diagram, apply principle of moment;
200(10) = M(L - 10) ------- (1)
From the second diagram, apply principle of moment;
200(8.75) = M(L - 15) ------- (2)
From equation (1); M = (2000) / (L - 10)
From equation (2); M = (1750) / (L - 15)
Solve (1) and (2);
(2000) / (L - 10) = (1750) / (L - 15)
1750(L - 10) = 2000(L - 15)
L - 10 = 2000/1750(L - 15)
L - 10 = 1.143(L - 15)
L - 10 = 1.143L - 17.14
17.14 - 10 = 1.143L - L
7.14 = 0.143L
L = 7.14/0.143
L = 50 cm
Mass of the uniform stickM = (2000) / (50 - 10)
M = 50 g
Thus, the length of the uniform meter stick is 50 cm and the mass of the uniform meter stick is 50 g.
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paula and steve are pulling their daughter jessie on a sled. steve pulls with a force of 18lb at an angle of 10degrees. paula pulls with a force of 12 lb at an angle of 15 degrees. find the magnitude of the resultant force on jessie and the sled.
According to the question the magnitude of the resultant force is approximately 22.47 lb.
What is magnitude?Magnitude is a measure of the size or intensity of something. It is most commonly used to describe the size of earthquakes, but can also be used to describe the size of other phenomena such as storms, winds, and floods. Magnitude can also refer to the size of a star or other celestial body. Magnitude is expressed as a number on a logarithmic scale, with larger numbers representing larger magnitudes.
We can use the Law of Cosines to calculate the magnitude of the resultant force. The Law of Cosines states that for a triangle with side lengths a, b, and c and angle C opposite side c, the following formula holds:
c2 = a2 + b2 - 2abcos(C)
In this case, a is 18 lb, b is 12 lb, and C is the angle between the two forces, 25 degrees. We can substitute these values into the formula and solve for c, the magnitude of the resultant force:
c2 = (18 lb)2 + (12 lb)2 - 2(18 lb)(12 lb)cos(25 degrees)
c2 = 324 + 144 - 432cos(25 degrees)
c2 = 324 + 144 - 216cos(25 degrees)
c2 = 468 - 216cos(25 degrees)
Now we can solve for c:
c = √(468 - 216cos(25 degrees))
c ≈ 22.47 lb
Therefore, the magnitude of the resultant force is approximately 22.47 lb.
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A 10 kg box falls off a building. The box is shown at 4 different positions along its
path.
For each position of the box, calculate the potential energy (PE). Then use the law of
conservation of energy to determine the kinetic energy (KE). Calculate the velocity of the box
at each point for extra credit.
Main answer-
PE=mgh
KE=E-PE
V = (2*g*h)^½
at point A
PE = 10*9.8*50=4900 J
KE = 0 J ( because the velocity of the body is 0)
V=0
at point B
PE = 10*9.8*35=3430 J
KE = 4900-3430=1470 J
V= ( 2*9.8*15)^ ½
V=17.14 m/s
at point C
PE= 10*9.8*25=2450 J
KE=4900-2450=2450 J
V= (2*9.8*25)^ ½
V=22.135 m/s
at point D
PE=10*9.8*0=0 J
KE=4900-0=4900 J
V=(2*9.8*50)^ ½
V=31.30 m/s
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Complete each statement with the word that makes it true.
The noble gases are the least
of any elements on the periodic table.
The
form acidic compounds with hydrogen.
The halogens are the most reactive among all the
.
Answer:
reactive
halogens
nonmetals
Explanation:
Noble gases are the least reactive of all elements on the periodic table. The halogens form acidic compounds with hydrogen. Halogens are most reactive among all the nonmetals.
What are halogens?Halogens are the chemical elements placed in group 7 of the modern periodic table, which contains five elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), and astatine (At).
Halogens can be described as nonmetals among which fluorine and chlorine (Cl) are gases and bromine (Br) is a liquid, and iodine (I) and astatine (At) are solids at room temperature. Halogens are generally the most reactive among the nonmetals and their reactivity decreases from F to At.
The word ‘halogen’ means “salt-forming“. Halogens exist in the form of ions or compounds because of their high reactivity.
Halogens are generally homonuclear diatomic so one molecule exists with two halogen atoms each. Halogens possess seven valence electrons because halogens have a deficiency of one electron to get a noble gas configuration. Therefore, they form negative ions, highly reactive due to high electronegative.
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a small 10.0 g bug stands at one end of a thin uniform bar that is initially at rest on a smooth horizontal table. the other end of the bar pivots about a nail driven into the table and can rotate freely, without friction. the bar has mass 70.0 g and is 120 cm in length. the bug jumps off in the horizontal direction, perpendicular to the bar, with a speed of 25.0 cm/s relative to the table.what is the angular speed of the bar just after the frisky insect leaps?
The angular speed of the bar just after the bug jumps is 0.67 rad/s.
The angular velocity of the bar just after the bug jumps can be calculated using the conservation of angular momentum. Angular momentum is the product of the moment of inertia of an object and its angular velocity.
The moment of inertia of the bar about its pivot is given by:
I = \(mr^2\)
The moment of inertia of the bar about its center of mass is given by:
I = (1/2) \(mr^2\)
The moment of inertia of the bug about its center of mass is given by:
I_bug = (1/5) \(mr^2\)
The total moment of inertia of the system (bar and bug) about the pivot is:
I_total = I_bar + I_bug
The angular velocity of the bar can be calculated using the conservation of angular momentum:
momentum = I_total * angular velocity
Rearranging and solving for angular velocity, we get:
angular velocity = momentum / I_total
The moment of inertia of the bar about its center of mass is:
\(I_bar = 1/2 * m * r^2 = (1/2) * (70.0 g) * (120 cm) * (1 cm)^2 = 11,520 cm^2\)
The moment of inertia of the bug about its center of mass is:
\(I_bug = (1/5) * (70.0 g) * (1 cm)^2 = 700 cm^2\)
The total moment of inertia of the system is:
\(I_t = I_b + I_bu = 11,520 cm^2 + 700 cm^2 = 12,220 cm^2\)
The total mass of the system is:
m = m_bar + m_bug = 70.0 g + 10.0 g = 80.0 g
The angular velocity can be calculated using the conservation of angular momentum:
angular velocity = momentum / I_total = \((80.0 g) * (12,220 cm^2) / (12,220 cm^2)\)= 0.67 rad/s
Therefore, the angular speed of the bar just after the bug jumps is 0.67 rad/s.
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