Block 1, of mass m1, moves across a frictionless surface with speed ui. It collides elastically with block 2, of mass m2, which is at rest (vi=0). (Figure 1)After the collision, block 1 moves with speed uf, while block 2 moves with speed vf. Assume that m1>m2, so that after the collision, the two objects move off in the direction of the first object before the collision. What is the final speed vf of block 2?
Answers
The conservation of the momentum allows to find the velocity of the second body after the elastic collision is:
[tex]v_f = \frac{2u_o}{1- \frac{m_2}{m_1} }[/tex]
the momentum is defined by the product of the mass and the velocity of the body.
p = mv
The bold letters indicate vectors, p is the moment, m the mass and v the velocity of the body.
If the system is isolated, the forces during the collision are internal and the it is conserved. Let's find the momentum is two instants.
Initial instant. Before crash.
p₀ = m₁ u₀ + 0
Final moment. After crash.
[tex]p_f = m_1 u_f + m_2 v_f[/tex]
The momentum is preserved.
p₀ = [tex]p_f[/tex]
[tex]m_1 u_o = m_1 u_f + m_2 v_f[/tex]
Since the collision is elastic, the kinetic energy is conserved.
K₀ = [tex]K_f[/tex]
½ m₁ u₀² = ½ m₁ [tex]u_f^2[/tex] + ½ m₂ [tex]v_f^2[/tex]
Let's write our system of equations.
[tex]m_1 u_o = m_1 u_f + m_2 v_f \\m_1 u_o^2 = m_1 u_f^2 + m_2 v_f^2[/tex]
Let's solve
[tex]u_f = u_o - \frac{m_2}{m_2} \ v_f \\u_f^2 = u_o^2 - \frac{m_2}{m_1} \ v_f^2[/tex]
[tex]( u_o - \frac{m_2}{m_1} v_f)^2 = u_o - \frac{m_2}{m_1} \ v_f^2 \\u_o^2 - 2 \frac{m_2}{m_1} \ u_o v_f + (\frac{m_2}{m_1} )^2 v_f^2 = u_o^2 - \frac{m_2 }{m_1} \ v_f^2[/tex]
[tex]2 \frac{m_2}{m_1} \ u_o = \frac{m_2}{m_1} v_f \ ( 1 - \frac{m_2}{m_1}) \\v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]
In conclusion, using the conservation of momentum, we can find the velocity of the second body after the elastic collision is:
[tex]v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]
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Related Questions
Mercury’s natural state is where the atoms are close to each other but are still free to pass by each other. In which state(s) could mercury naturally exist?
Answers
Answer:
Mercury's natural state is where the atoms are close to each other but are still free to pass by each other. In which state(s) could mercury naturally exist?
Liquid is the answer
Explanation:
A SMART car can accelerate from rest to a speed of 28 m/s in 20s. What distance does it travel in this time?
Answers
A car accelerates from rest to a speed of v. Later, on a highway it accelerates from v to 2v. Which takes more energy, going from 0 to v, or from v to 2v?
Answers
Answer:
I believe 0 to V sorry if im wrong
Explanation:
What is the potential energy of a 2 kg bowling ball resting at the top of a 5 m high hill? Show all of your work and include the correct units to receive full credit.
Answers
Answer:
[tex]\boxed {\boxed {\sf 98 \ J}}[/tex]
Explanation:
We are asked to find the potential energy of a bowling ball.
Potential energy is the energy an object possesses due to its position. It is calculated using the following formula.
[tex]E_p= mgh[/tex]
In this formula, m is the mass, g is the acceleration due to gravity, and h is the height.
The bowling ball has a mass of 2 kilograms. The hill is 5 meters high. Assuming this situation is occurring on Earth, the acceleration due to gravity is 9.8 meters per second squared.
m= 2 kg g= 9.8 m/s²h= 5 mSubstitute the values into the formula.
[tex]E_p= (2 \ kg )(9.8 \ m/s^2)(5 \ m)[/tex]
Multiply the numbers together.
[tex]E_p=19.6 \ kg*m/s^2(5 \ m)[/tex]
[tex]E_p=98 \ kg*m^2/s^2[/tex]
Convert the units. 1 kilogram meter squared per second squared is equal to 1 Joule. Our answer of 98 kg*m²/s² is equal to 98 Joules.
[tex]E_p= 98 \ J[/tex]
The bowling ball has 98 Joules of potential energy.
Please help...
Will give the brainliest !!!
Please answer correctly
Answers
5) a) An alpha particle consists of 4 nucleons. Two of these are protons and two are neutrons. An alpha particle carries a charge of +2 (due to the particles having 2 protons).
b) A beta minus particle is a fast moving electron that's emitted from the nucleus. It's created when neutrons in the nucleus decays to form a proton & the beta particle.
c) A 3rd type of ionising radiation has no mass. It's called gamma radiation (gamma rays / X - rays). This type of radiation is a type of wave with a very short / low wavelength. (shortest wavelength among others)
d) Gamma radiation is a part of the electromagnetic spectrum.
_______
Hope it helps ⚜
A stomp rocket takes 3.1 seconds to reach its maximum height.
What was its maximum height?
Answers
Answer:
height where rocket goes
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[tex]\purple{\rule{45pt}{7pt}}\blue{\rule{45pt}{999999pt}}[/tex]
whaT HAPPENS WHEN a net force act's
on a moving object
Answers
Explanation: I just know
A vinyl "record" with a diameter of 0.3 m is spinning at a rate of 1 m/s.
a) What would the centripetal acceleration be for a piece of gum (0.005kg) stuck to the outside edge of the record?
b) How much centripetal force will the gum have to overcome to remain "stuck" to the vinyl?
Answers
This question involves the concepts of centripetal force and centripetal acceleration.
a) The centripetal acceleration for the piece of gum stuck to the outside edge of the record will be "6.67 m/s²".
b) The gum will have to overcome "0.033 N" centripetal force to remain stuck to the vinyl.
a)
The centripetal acceleration of the gum can be found using the following formula:
[tex]a_c=\frac{v^2}{r}[/tex]
where,
[tex]a_c[/tex] = centripetal acceleration = ?
v = linear speed of record = 1 m/s
r = radius of the record = [tex]\frac{diameter}{2}=\frac{0.3\ m}{2}=0.15\ m[/tex]
Therefore,
[tex]a_c=\frac{(1\ m/s)^2}{0.15\ m}\\\\a_c = 6.67\ m/s^2[/tex]
b)
Now, the centripetal force can be given as follows:
[tex]F_c=ma_c\\F_c=(0.005\ kg)(6.67\ m/s^2)\\F_c=0.033\ N[/tex]
Learn more about centripetal force here:
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The attached picture shows the centripetal force.
Alex drops a soccer ball and a table tennis ball from the top of a ladder. He wants to compare the velocities of the balls just before they hit the ground.
Which formula should Alex use to calculate the velocity of each ball,
assuming they are in free fall?
A) v=Gt
B) g=vt
C) t=vg
D) v=G/t
Answers
Answer:
d is the correct answer
Explanation:i did this math
a runner joys 12km north than turs and runs 16km east in three hours.
a. what is his displacement
b. calculate his average speed
c. calculate his average including the direction
Answers
Explanation:
a.displacement is vector quantity there fore
we combine the two direction
[tex] {c}^{2} = \sqrt{ {a}^{2} + {b}^{2} } [/tex]
[tex] {c}^{2 } = \sqrt{ {12}^{2} + {16}^{2} } [/tex]
[tex] {c}^{2} = \sqrt{400 } [/tex]
[tex]c = 20[/tex]
displacement is 20km to wards north
b:average speed
[tex]v = s \div t[/tex]
20/3=6.67
c: please type correctly
In your response be very specific and break down each item on the list, then state if they would be classified the same or differently.
Consider the definition for each as you respond.
• atoms
• elements
• compounds
• molecules
• matter
Answers
1. Atoms are the smallest particle of a chemical element that can exist.
2. Elements are pure substances and they are only made of one type of atom. Elements are found in the periodic table (can be metals, non metals, gases, liquids).
3. Compounds are made up of two or more types of atoms chemically bonded together.
4. Molecules are made up of two or more types of atoms not chemically bonded together.
5. Matter is really any substance that has mass and takes up volume.
A cyclist pedals up to the top of a hill.
a) What kind of energy is being used to do work against gravity?
b) State the type of energy the cyclist has when he stops at the top of the hill.
c) When the cyclist moves downhill without pedaling, what type of energy does he gain?
Answers
Explanation:
A) kinetic energy
B) potential energy
C) Mechanical energy
a) The motorcyclist rises utilising chemical energy's "mechanical energy" (kinetic and potential energy). b) The cyclist's highest "gravitational potential energy" is transformed into motion downhill. c) When the rider moves downhill, potential energy becomes "kinetic energy." "Kinetic energy" is most vital.
a) "Mechanical energy" is used by the cyclist to ride up the slope. Kinetic and potential energy from an object's motion and position make up mechanical energy. As they pedal, cyclists transform chemical energy from their bodies into mechanical energy. This mechanical energy overcomes gravity as the cyclist climbs. As the cyclist climbs, potential energy accumulates, which is translated into kinetic energy as they descend.
b) At the summit of the slope, the biker has "gravitational potential energy." An object's gravitational potential energy depends on its position in a gravitational field. The biker has gained potential energy by climbing against gravity. At the crest of the hill, the cyclist's kinetic energy is lowest while potential energy is highest. The cyclist's potential energy is ready to be turned into kinetic energy as they descend.
c) Without pedalling, the rider gains "kinetic energy." The cyclist's speed increases as they descend, converting potential energy into kinetic energy. The cyclist's potential energy is turned into kinetic energy by gravity. As the rider descends, their potential energy diminishes but their kinetic energy increases, speeding up their bike. The biker converts potential energy into kinetic energy as he descends, and most of it is converted back at the bottom.
In conclusion, the cyclist climbs the incline using "mechanical energy" from chemical energy. They descend using "gravitational potential energy" at the top. Potential energy becomes "kinetic energy" when the rider descends without pedalling, speeding up the bike. Potential-to-kinetic energy conversion helps the cyclist climb the slope.
To know more about kinetic energy
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Three of the forces in nature attract particles together, with varying strengths, to build the universe. Which is the only one that energizes the universe by making nuclear fusion possible
Answers
Answer:
The photon or quantum of light
Explanation:
what is rotational dynamics
Answers
Rotational dynamics is the study of forces and motions about an axis of rotation.
Explanation:Formulas such as Kinematic Equations and Newton's laws can be expressed in rotating coordinate frames such as: Newton's 2nd Law Fnet=m x a translates into Torque = I x α Where I is Moment of Inertia (the rotational analogous term to mass)
Answer:
Rotational dynamics is the study of forces and motions about an axis of rotation.
Explanation:
Formulas such as Kinematic Equations and Newton's laws can be expressed in rotating coordinate frames such as:
Newton's 2nd Law Fnet=m x a translates into Torque =I x α Where I is Moment of Inertia (the rotational analogous term to mass)
and α is angular acceleration.
consider two vectors A and B Where A-B and |A+B|=|A-2B| vector B is directed in the positive x_direction and A makes an angle of 60°above the positive x_axis find magnitude of the two vectors
Answers
Answer:
It should be mentioned that an efficient way to work this vector addition problem is with the cosine law for general triangles (and since
a
,
b
and
r
from an isosecles triangle, the angles are easy to figure). However, in the interest of reinforcing the usual systematic approach to vector addition, we note that the angle
b
makes with the +x axis is 30
0
+105
0
=135
0
(a) The x component of
r
x
=(10.0m)cos30
0
+(10.0m)cos135
0
=1.59m
(b) the y component of
r
is r
y
=(10.0m)sin135
0
= 12.1 m.
(c) the magnitude of
r
is r = ∣
r
∣=
(1.59m)
2
+(12.1m)
2
=12.2m
(d) The angle between
r
and the +x direction is tan
−1
[(12.1m)/(1.59m)]=82.5
0
Explanation:
The mass of the hammer is 0.454 kg. Calculate the weight of the hammer.
Answers
Explanation:
weight =0.454 × 9.8=4.4492N
Answer:
4.45 n sorry if I am wrong
what we have learned about the different cultures of Native Americans
Answers
Native Americans worldview is deep and intense and infused with spiritual meaning. Everything in their culture ties into their belief system and their love for their land and people.
Which of these is a unique use of beta particles?
A. CT scanners
B. Tracing chemicals in the environment C. Killing bacteria
D. Smoke detectors
Answers
Answer:
The answer is A, CT scanners.
if there is a gravitational force between all objects, why do we not feel or observe it?
Answers
Answer:
We do. It's just way too small compared to the force between the objects we're observing and the earth. It's like looking inside a room with an elephant and a grain of rice. The rice is there, it's just too small compared to the room and the elephant inside for you to notice it. Or, if you ever traveled on a plane, you can easily see the towns, or the roads, but not the single people walking the street.
Part B
Based on the information in the article, how could plants be used in the future to help counteract some human
emissions?
Answers
Answer:
Having more plants performing photosynthesis could help reduce the amount of carbon dioxide in the atmosphere.
Explanation:
sample answer
The plants can be used in the future to help counteract some human
emissions they absorb carbon dioxide from the air and release oxygen.
What is photosynthesis?It is a process carried out by photosynthetic autotrophic organisms, such as plants, algae and some prokaryotes. These organisms capture sunlight, convert it into chemical energy, which will be used to produce organic compounds, based on water and carbon dioxide.
Trees, like other plants, in the process called photosynthesis, absorb carbon dioxide from the air and release oxygen. They also make the air wetter and cooler. In this way, plants contribute to the good quality of the air we breathe.
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Plzzzz help meeeeee plzzz
Answers
hun I wish I can help you but I have the same problem here!! sorry
What are some simple machines that decrease mechanical advantage used to do? increase work decrease work multiply distance to increase speed.
Answers
Answer:
Wheel and axleForce multipliersLeverInclined planePulleyScrewWedgeExplanation:
Simple machines are devices with no, or very few, moving parts that make work easier. Many of today's complex tools are just combinations or more complicated forms of the six simple machines, according to the University of Colorado at Boulder. For instance, we might attach a long handle to a shaft to make a windlass, or use a block and tackle to pull a load up a ramp. While these machines may seem simple, they continue to provide us with the means to do many things that we could never do without them.
Have a great day! :D
Some machines decrease mechanical advantage and are utilized to multiply distance to decrease speed.
What is the mechanical advantage?Mechanical advantage can be described as a measure of the ratio of output force to input force in a system. Mechanical advantage is used to analyze the forces in simple machines such as levers and pulleys.
Mechanical Advantage= output force (load) /input force(effort)
The mechanical advantage will increase as the slope of the inclined plane decreases but the load has to move with more distance. Under the mechanical advantage, the distance the load will move will be a fraction of the distance through applied force.
Thus, the mechanical advantage is decreased by some simple Machines decrease and are used to multiply distance to decrease speed.
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Can anyone help out with this question?
I'll mark as brainliest
Thankyou.
Answers
Answer:
p=I×B
Explanation:
If a current 'I' flows through a given element in your circuit, losing voltage 'V' in the process, then the power 'P' dissipated by that circuit element is the product of that current and voltage.
Managers use information systems to help them make decisions that will improve their businesses. What three levels of information do managers need to make these decisions? Provide one example of how information systems can provide this data.
Answers
The main categories of information systems include management-level system, operational-level system, and strategic-level system.
Information system simply means the integrated set of components that are vital for the collection, storage, and processing of data to make organizational decisions.
Information systems can be used at operational level in order to provide data that can support operational activities by keeping track of the transactions of the company.
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Sound is repeated near hills. Give reason
Answers
Explanation:
Sound is repeated near hills due to reverberation. The sound effect is prolonged is an empty room because , in a furnished room, reverberation occurs less than in a room with no furniture.
Answer:
sound that occurs in nature, such as those of animal, trees, people, the wind, the rain, etc. are the natural sounds. it is heard near the hill because of the echo and the reverberation of the sound
A car accelerates from 20m/s to 30m/s in 10 sec. Find the cars acceleration using v=u+at
Answers
Answer:
1
Explanation:
because when we use v=u+at we derived v-u÷t
how do astronomers determine the origin of a meteorite that reaches earth?
Answers
Researchers begin their study by identifying the rock type and then dating the meteorite
Explanation:
.
Does the mass of an object always equal the sum of its parts?
yes
no
Answers
Usain Bolt has a mass of 94.1 kg and he had a KE of 7,250 J when running the one hundred meter dash. Calculate how fast he was running
Answers
Answer:
[tex]\displaystyle v = 12.4134 \ m/s[/tex]
General Formulas and Concepts:
Energy
Kinetic Energy Formula: [tex]\displaystyle KE = \frac{1}{2}mv^2[/tex]
m is mass (in kg)v is velocity (in m/s)Explanation:
Step 1: Define
Identify variables.
KE = 7250 J
m= 94.1 kg
Step 2: Solve for v
Substitute in variables [Kinetic Energy Formula]: [tex]\displaystyle 7250 = \frac{1}{2}(94.1)v^2[/tex]Isolate v term: [tex]\displaystyle 154.091 = v^2[/tex]Isolate v: [tex]\displaystyle v = 12.4134[/tex]Topic: AP Physics 1 - Algebra Based
Unit: Energy
give to examples of electrical energy being transformed into light?
Answers
Answer:
A lightbulb is connected to an outlet that has a source of electricity. The electrical energy is converted into light energy to allow the bulb to glow.
Explanation: Lightning is a discharge of static electricity. The lightning bolt lights up the sky.