A 100-g bullet is fired from a rifle having a barrel 0.600 m long. Choose the origin to be at the location where the bullet begins to move. Then the force (in newtons) exerted by the expanding gas on the bullet is 15 000 1 10 000x 2 25 000x 2 , where x is in meters. (a) Determine the work done by the gas on the bullet as the bullet travels the length of the barrel. (b) What If? If the barrel is 1.00 m long, how much work is done, and (c) how does this value compare with the work calculated in part (a)?
Answers
Answer:
a) W=9000J
b) W=11,666.67 J
c) The work done by the gas with a 1 meter barrel is 2,666.67 J greater than the work done by the gas with a 0.600 m barrel. This is about 1.3 times greater.
Explanation:
(The function written in the problem isn't too clearly written, but I believe it should be like this:
A 100-g bullet is fired from a rifle having a barrel 0.600 m long. Choose the origin to be at the location where the bullet begins to move. Then the force (in newtons) exerted by the expanding gas on the bullet is [tex]15 000 + 10 000x - 25 000x^{2}[/tex] , where x is in meters. (a) Determine the work done by the gas on the bullet as the bullet travels the length of the barrel. (b) What If? If the barrel is 1.00 m long, how much work is done, and (c) how does this value compare with the work calculated in part (a)?)
a)
Since the force applied to the bullet is going to vary with the length of the barrel, we will need to make us of integration to find the work done by the gas.
So first, we start by drawing a sketch of what the problem looks like. (See attached picture). This will help us visualize the problem better.
Now, work is defined as the following integral:
[tex]W=\int\limits^a_b {F} \, dx[/tex]
The problem tells us the force exerted by the expanding gas on the bullet is:
[tex]F(x)=15,000+10,000x-25,000x^{2}[/tex]
So we go ahead and substitute this function into the integral.
[tex]W=\int\limits^{0.6}_0 {15,000+10,000x-25,000x^{2}} \, dx[/tex]
Now, before integrating that function, we can factor it so it is easier for us to integrate and to deal with the values, so we can factor a common 5,000 out, so we get:
[tex]W=5,000\int\limits^{0.6}_0 {3+2x-5x^{2}} \, dx[/tex]
and we proceed to integrate so we get:
[tex]W=5,000[3x+x^2-\frac{5}{3}x^{3}]\limits^{0.6}_0[/tex]
and evaluate the integral, so we get:
[tex]W=5,000([3(0.6)+(0.6)^2-\frac{5}{3}(0.6)^{3}]-[3(0)+(0)^2-\frac{5}{3}(0)^{3}][/tex]
Which yields:
W=9000J
b)
For part b we follow the exact same procedure but we change the limits of integration for 0 and 1 so the integral looks like this:
[tex]W=\int\limits^1_0 {15,000+10,000x-25,000x^{2}} \, dx[/tex]
and we get the following answer:
[tex]W=5,000[3x+x^2-\frac{5}{3}x^{3}]\limits^1_0[/tex]
and
[tex]W=5,000([3(1)+(1)^2-\frac{5}{3}(1)^{3}]-[3(0)+(0)^2-\frac{5}{3}(0)^{3}][/tex]
so
W=11,666.67 J
c) The difference between the two works we calculated is:
11,666.67J-9000J=2,666.67J
so the work done by the gas with a 1 meter barrel is 2,666.67 J greater than the work done by the gas with a 0.600 m barrel.
if we did the following division:
[tex]\frac{11,666.67}{9,000}=1.3[/tex]
So we can see that this is about 1.3 times greater.
Related Questions
Suppose the deer population in a region is expected to increase by 6% in the next year. If there are currently 11,650 deer living in the region, approximately how many will be living there a year from now?
Answers
Answer:
12,349 deers
Explanation:
Present population size of deer = 11,650
Expected percentage increase in population size by next year = 6%
6% of 11,650 = 6/100 x 11,650
= 699
Adding this to the present population: 11,650 + 699 = 12,349.
Hence, the total number of deer expected to be living in the population a year from now (that is, next year) is 12,349 deers.
Using terms like GPE, KE, Transfer, Transfermation and Law of Conservation of Energy. Will a ball placeced at the start arrow and allowed to roll make it to the finish arrow? Why?
Answers
There is a temperature change of 3 °C in the room when 1.5 kg of water flows through the
radiator each second.
The specific heat capacity of water is 4200 J/kg°C.
i.
Calculate the amount of energy given to the room by the 1.5 kg of water as it passes
through the radiator.
Show your working and write down the unit.
Answers
Answer:
18900J
Explanation:
energy = Temperature change * Mass * Specific Heat Capacity
3*1.5*4200=18900
=18900J
Answer:
Explanation:
Q = mcT
where,
Q is heat(energy)
m is mass
c is specific heat capacity
T is change in temperature
so,
Q= 1.5kg x 4200 J/kg.C x 3C
Q = 18900J of energy
How much mass is required to exert a force of 25 Newtons, accelerating at 5 m/s2?
help pleaseee!
Answers
Answer:
5
explanation:
25 divided by 5
Answer:
25/5= 5
Explanation:
A car is traveling in a straight line path at a maximum speed of 7.00 m/s. The driver of the vehicle applies the brakes bringing the car to a stop after traveling 10.0 m. What is the magnitude of the car's acceleration to the nearest hundredths place?
Answers
Answer:
[tex]a=-2.45\ m/s^2[/tex]
Explanation:
An object is traveling at constant acceleration if its changes in speed are constant at the same intervals of time.
The acceleration can be calculated as follows:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
Where vo is the initial speed, vf the final speed and t is the time.
The acceleration and the distance x are related through the following equation:
[tex]v_f^2=v_o^2+2.a.x[/tex]
The car has an initial speed of vo=7 m/s when the driver stops the car (vf=0) after traveling x=10 m.
The acceleration can be calculated by solving the last equation for a:
[tex]\displaystyle a=\frac{v_f^2-v_o^2}{2x}[/tex]
[tex]\displaystyle a=\frac{0-7^2}{2*10}[/tex]
[tex]\displaystyle a=\frac{-49}{20}[/tex]
[tex]\boxed{a=-2.45\ m/s^2}[/tex]
An object starts at position 12 on a horizontal line with a reference point of 0. What is the position of the object if it moves 14 units to the left?
–26
–2
2
26
Answers
Answer:
Answer is negative -2 think about this is basically a sbrtaction problem the number starts at 12 and then it moves 14 to left which means backwards so 12-14=-2 so thats were u get -2 as your answer.
Explanation:
wanted to help people plus I am doing the quiz right now.
No matter where the light bulb is located on the central axis, what is always true about the size of the image?
Answers
Answer:
there is no image
Explanation:
A student did 24 J of work on a chair. She applied a force of 12 N and moved the chair 2 m. What question do you need to ask to determine the amount of power used?
Answers
Answer:
Explanation:
Power is expressed as P = Force * Distance/time
From the formula given, the following parameters is needed to calculate power
1) Work done
2) force
3) Distance
4) Time
From the question, the given data is incomplete. We are supposed to be given the time taken to moved the chair over the distance. with the time we can easily calculate the power used up by the student.
please help i need an answer ASAP :C
the French Broad, The Mississippi, and the Amazon are examples of ____
-turbidity
-streams
-springs
-rivers
Answers
The starting velocity was 0 m/s, and the final velocity
was -15.35 m/s. Based on this, what was the average
velocity of the rock? In general, to find the average of
any 2 things, you add them together and divide by how
many things there are.
Answers
Answer:
The average velocity is -7.675 m/s
Explanation:
Given;
initial velocity, u = 0 m/s
final velocity, v = -15.35 m/s
Based on the follow up state " In general, to find the average of any 2 things, you add them together and divide by how many things there are", the average velocity will be calculate as ;
Sum of the velocities = 0 m/s + (-15.35 m/s) = -15.35 m/s
Number of velocites = 2
AVERAGE VELOCITY = (-15.35 m/s) / (2)
AVERAGE VELOCITY = -7.675 m/s
While standing at the edge of the roof of a building, you throw a stone upward with an initial speed of 6.25 m/s. The stone subsequently falls to the ground, which is 13.3 m below the point where the stone leaves your hand. At what speed does the stone impact the ground? How much time is the stone in the air? Ignore air resistance and take g = 9.8 m/s2.
Answers
Answer:
1.) 17.3 m/s
2.) 1.8 s
Explanation:
Given that While standing at the edge of the roof of a building, you throw a stone upward with an initial speed of 6.25 m/s.
The maximum height will be calculated by using third equation of motion
At maximum height, V = 0
V^2 = U^2 - 2gH
0 = 6.25^2 - 2 × 9.8 × H
39.06 = 19.6H
H = 39.06 / 19.6
H = 1.993m
The stone subsequently falls to the ground, which is 13.3 m below the point where the stone leaves your hand. At what speed does the stone impact the ground?
Using the same formula again.
Where the height = 13.3 + 1.993
Height = 15.29m
Substitutes the height into the third equation of motion
V^2 = U^2 + 2gH
U = 0
V^2 = 0 + 2 × 9.8 × 15.29
V^2 = 299.74
V = sqrt ( 299.74 )
V = 17.3 m/s
How much time is the stone in the air? Ignore air resistance and take g = 9.8 m/s2.
Using the second equation of motion formula
H = Ut + 1/2gt^2
U = 0
15.29 = 1/2 × 9.8 × t^2
15.29 = 4.9t^2
t^2 = 15.29 / 4.9
t^2 = 3.120
t = sqrt ( 3.120 )
t = 1.766 s
Therefore, the stone is on air for 1.8s approximately.
HELP HELP HELP NOW PLEASEEEEEEE
how could you increase the kinetic energy of a wagon without increasing its mass?
Answers
Answer:
use newtons gravity of law by launching a watermelon in frot of the wagon
Explanation:
6.
How long would it take a 125 W electric motor to do 825 j of work?
Answers
Answer:
According to formula of power N = A/t Given by : N = 125 W and A = 825 J.
Here, N --- power ; A --- work ; t --- time.
Now, we can find the time t = A/N = 6.6 s
Explanation:
You stand on a pier watching water waves and see 10.9 waves pass by in a time of 28 seconds. What is the frequency of the water waves?
Answers
Answer:
0.4Hz
Explanation:
Given parameters:
Number of waves = 10.9waves
Time taken = 28s
Unknown:
Frequency of water waves = ?
Solution:
The frequency of a wave is the number of waves that passes through a point per unit of time.
Frequency = [tex]\frac{number of waves }{time}[/tex]
Insert parameters and solve;
Frequency = [tex]\frac{10.9}{28}[/tex] = 0.4Hz
A student observes an 8.0-kilogram shopping cart accelerate uniformly across a parking lot. It reaches a speed of 4.0 meters per second in 0.5 seconds. What is the magnitude of the force that causes the shopping cart to accelerate?
Answers
Answer:
F = 64 N
Explanation:
Given that,
Mass of the shopping cart, m = 8 kg
Initial speed of the shopping cart, u = 0
Final speed of the shopping cart, v = 4 m/s
Time, t = 0.5 s
We need to find the magnitude of the force that causes the shopping cart to accelerate. The force is given by the formula as follows :
[tex]F=ma\\\\F=\dfrac{m(v-u)}{t}\\\\F=\dfrac{8\times (4-0)}{0.5}\\\\F=64\ N[/tex]
So, the magnitude of force is 64 N.
Can somebody plz answer this grade6 science question? Only answer in
1-2 sentences!
(WILL MARK BRAINLIEST)
Answers
Answer:
Alkali metals are reactive, soft metals with low densities. Noble gases are all unreactive non-metals
Explanation:
Set the cannon height to 14 m and the initial speed to 20 m/s. Show how to calculate the location of the target. Verify your prediction using the simulation.
Answers
Answer:
Explanation:
The location of the target can be determined by calculating the horizontal distance according to the projectile formula
R = U*√2H/g
U is the initial speed = 20m/s
H is the maximum height = 14m
g is the acceleration due to gravity = 9.81m/s²
Substitute
R = 20*√2(14)/9.81
R = 20√28/9.81
R = 20√2.85
R = 20(1.689)
R = 33.79m
Hence the location of the target is at 33.79m
Use the excerpt from an online article to answer the question. "While the big bang theory is the most popular modern theory of how the universe formed, it is incomplete." Which question does the big bang theory leave unanswered? (1 point) When did the universe form? What is the temperature of deep space? What is the future of the universe? How did galaxies and stars form?
Answers
Which question does the big bang theory leave unanswered?
Accordingly with THE HOT BIG BANG COSMOLOGY from Andrew R. Liddle, University of Sussex, David H. Lyth, Lancaster University. Some problems are not explained by the big bang theory as the existence of multiverse or single universe as well as what laws of physics were responsible for the collapse of the big bang.
When did the universe form?
the age of the universe is the time elapsed between the Big Bang until the present moment. A few years ago, the WMAP probe collected data that led astronomers to conclude that the probe's data accepted the determination of the age of the Universe at 13.787 ± 0.020 billion years.
What is the temperature of deep space?
It depends on what part of the space we are talking about. In general, it works like this: the closer to the stars, the higher the temperature. Another factor is the presence of matter: heat can be retained by it. As the space becomes empty, the temperature drops. In the total vacuum (no matter), the temperature drops to minus 272 ºC, 1 degree above absolute zero.
How did galaxies and stars form?
Typically, most stars were formed from large molecular clouds. When somewhere in the cloud there is a certain density of massive molecules, they tend to collapse and the central density then tends to increase rapidly, while the density on the outside remains almost constant.
The most accepted theory for the formation of galaxies is that the structures we observe today are formed as a consequence of the growth of primordial fluctuations due to gravitational instability. The primordial fluctuations caused that the gases were attracted to areas of denser material, supercumulus, galactic clusters, galaxies, stellar cumulus and stars are formed hierarchically. One consequence of this model is that the location of galaxies indicates areas of high density in the primordial Universe. Thus, the distribution of galaxies is closely related to the physics of the early Universe.
Recent data provides evidence that the first galaxies formed much earlier than astronomers predicted, only 600 million years after the Big Bang. This leaves little time for the primordial small instabilities to have grown large enough for protogalaxies to form galaxies.
Answer:
Your answer is: What is the future of the universe
Explanation:
a motor with an efficiency of 75 percent must supply 240J of useful work. what amount of work must be supplied to the motor
Answers
Answer:
e=75%=0.75 work output = usful work=240j
Explanation:
Explain the relationship between temperature, density, and states of
matter
Answers
Answer:
Higher temperature makes an object less dense 2. Density governs the state of matter for the object, hence as water becomes less and less dense, it becomes gas (water vapour) 3. Higher temperature makes an object has more pressure, hotter gas has higher pressure.
Explanation:
Relation Between Density and Temperature Temperature is the measure of heat. Density is the measure of how closely any given entity is packed or it is the ratio of the mass of the entity to its volume.
I hope this works
What happens to the tension in the string as the weight of the block increases? Explain your answer
Answers
Answer:
the weight becomes thicker and harder to carry as the weight plottens,
Explanation:
i did this
What controllable risk factors for heart disease did Brenda’s father have?
Answers
Controllable risk factors that Brenda'a father may have had include dietary choices, amount of exercise, sleep schedule, among other things.
The controllable risk factors for heart disease that Brenda’s father has include stress, smoking, high blood pressure, etc.
Blood pressure is a risk factor for heart disease. High blood pressure increases the risk of heart disease.
Another risk factor is smoking. It is advisable for people not to smoke in order to avoid having diseases. If one smokes, there's a higher chance that the person will have heart disease.
In conclusion, it's also important for one to rest very well and not stress himself or herself.
Read related link on:
https://brainly.com/question/22909359
An object of mass 10 kg is released from rest above the surface of a planet such that the object’s speed as a function of time is shown by the graph above. The force due to gravity exerted on the object is most nearly
Answers
Answer:
100NExplanation:
Hey there!!!, there are no attached files/graphs to this question, but we can find our way and solve for the gravitational force acting on the mass
Step one:
given data
mass= 10kg
acceleration due to gravity= 9.81m/s^2
Step two:
The expression for the gravitation force is given as
Gravitational force F=mass * acceleration due to gravity
Fg=ma
substituting we have
Fg=10*9.81
Fg=98.1N
The force due to gravity exerted on the object is most nearly 100N
Alisa needs to make some hot tea for her ill mother. She uses some ice-cold water from the freezer and heats it up in the kettle. As she hears the teapot whistling, she asks herself, “How is the motion of the ice water’s particles changing as the hot tea is being made?”
Answers
1. chemistry the study of matter and energy and how they interact 2. physics the systematic study and analysis of facts 3. science a process to test a proposed solution to a problem 4. scientific method the study of the structure, properties, and interactions of materials and the changes they undergo
Answers
Answer:
1. Chemistry- the study of the structure, properties, and interactions of materials and the changes they undergo.
2. Physics- the study of matter and energy and how they interact.
3. Science- the systematic study and analysis of facts.
4. Scientific method- a process to test a proposed solution to a problem.
Explanation:
1. Chemistry is a branch of science that deals with the study of the structures, properties, and interactions of various materials with other materials. It also includes the study of such changes that may occur during such interactions.
2. Physics is also one branch of science that deals with the study of matter and energy. Contrary to chemistry, this scientific branch deals with the interaction of matter and energy, their motion, and behavior especially related to space and time.
3. Science is the systemic study and analysis of facts. It is the understanding of the natural and scientific world, dealing with the elements of how and why things work.
4. Scientific method is the method or process by which tests are made to ascertain problems and find a solution for such. It is the method of getting knowledge and solutions, the experimentation to get to a conclusive result.
Calculate the acceleration of a 300,000-kg jumbo jet just before takeoff when the thrust on the aircraft is
120,000n
I
Answers
Answer:
0.4 m/s²
Explanation:
Use Newton's second law.
∑F = ma
120,000 N = (300,000 kg) a
a = 0.4 m/s²
What is true about the electric and magnetif fields as the electromagnetic wave moves?
a The angle between them is constantly increasing
b the angle between them is decreasing
c They are parallel
d They are perpendicular (90º)
Answers
Answer:
d They are perpendicular (90º)
Explanation:
When electric and magnetic fields moves they are perpendicular to one another.
Electromagnetic fields are composed of both electric and magnetic fields. In motion, the two fields moves perpendicular to one another. These waves are mostly generated through natural activities. They are called transverse waves and moves perpendicular to the particles. Examples are light waves, radio waves, etc.What are some immediate effects that alcohol have on people?
Answers
Answer:
Depending on how much is taken and the physical condition of the individual, alcohol can cause:
-Slurred speech.
-Drowsiness.
-Vomiting.
-Diarrhea.
-Upset stomach.
-Headaches.
-Breathing difficulties.
-Distorted vision and hearing.
Explanation:
•slurred speech
•distorted vision and hearing
At what point does the rollercoaster have the most GPE? A,C B,A C,E D,B E,D
Answers
Answer:
b
Explanation:
A cart is loaded with a brick and pulled up a ramp. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart on top of the ramp?
Answers
Answer:
Potential energy = 13.23 J
Explanation:
Given that,
The mass of the loaded cart, m = 3 kg
Its height of the seat top is 0.45 m
We need to find the potential energy of the loaded cart on top of the ramp. We know that, the potential energy of an object is due to its height. It can be given by the formula as follows :
[tex]E=mgh\\\\E=3\ kg\times 9.8\ m/s^2\times 0.45\ m\\\\E=13.23\ J[/tex]
So, the required potential energy is 13.23 J.
