1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Daniel [21]
3 years ago
10

Two billiard balls with the same mass m move towards one another. Ball one travels in the positive x-direction with a speed of v

1i, and ball two travels in the negative x-direction with a speed of v2i. The two balls collide elastically, and both balls change direction after the collision. If the initial speeds of the balls were v1i=2.0m/s and v2i =1.0m/s, what would be the final speed and direction of ball two, v2f, in m/s?
Physics
1 answer:
Kitty [74]3 years ago
4 0

Answer:

v_{2f}=2m/s in the positive x-direction.

Explanation:

Conservation of momentum tells us that the momentum before the collision must be equal to the momentum after the collision: p_i=p_f.

Before the collision we have:

p_i=m_1v_{1i}+m_2v_{2i}=mv_{1i}+mv_{2i}=m(v_{1i}+v_{2i})

And after the collision:

p_f=m_1v_{1f}+m_2v_{2f}=mv_{1f}+mv_{2f}=m(v_{1f}+v_{2f})

Since they must be equal we have:

m(v_{1i}+v_{2i})=m(v_{1f}+v_{2f})

Which is the same as:

v_{1i}+v_{2i}=v_{1f}+v_{2f}

And can be written as:

v_{1i}-v_{1f}=v_{2f}-v_{2i}

Since the collision is elastic, kinetic energy is conserved: K_i=K_f

Before the collision we have:

K_i=\frac{m_1v_{1i}^2}{2}+\frac{m_2v_{2i}^2}{2}=\frac{mv_{1i}^2}{2}+\frac{mv_{2i}^2}{2}=\frac{m}{2}(v_{1i}^2+v_{2i}^2)

And after the collision:

K_f=\frac{m_1v_{1f}^2}{2}+\frac{m_2v_{2f}^2}{2}=\frac{mv_{1f}^2}{2}+\frac{mv_{2f}^2}{2}=\frac{m}{2}(v_{1f}^2+v_{2f}^2)

Since they must be equal we have:

\frac{m}{2}(v_{1i}^2+v_{2i}^2)=\frac{m}{2}(v_{1f}^2+v_{2f}^2)

Which is the same as:

v_{1i}^2+v_{2i}^2=v_{1f}^2+v_{2f}^2

And can be written as:

v_{1i}^2-v_{1f}^2=v_{2f}^2-v_{2i}^2

Which is the same as:

(v_{1i}-v_{1f})(v_{1i}+v_{1f})=(v_{2f}-v_{2i})(v_{2f}+v_{2i})

But since we already proved that v_{1i}-v_{1f}=v_{2f}-v_{2i}, we can cancel those terms and we have that:

v_{1i}+v_{1f}=v_{2f}+v_{2i}

So we have the system:

v_{1i}-v_{1f}=v_{2f}-v_{2i}

v_{1i}+v_{1f}=v_{2f}+v_{2i}

Adding both sides between them we obtain:

v_{1i}-v_{1f}+v_{1i}+v_{1f}=v_{2f}-v_{2i}+v_{2f}+v_{2i}

Which is:

2v_{1i}=2v_{2f}

Which means:

v_{2f}=v_{1i}=2m/s

Where we used a positive velocity since ball 1 travels in the positive x-direction at the beginning.

You might be interested in
Two equal charges with magnitude Q and Q experience a force of 12.3442 when held at a distance r. What is the force between two
Pepsi [2]

Answer:197.504 N

Explanation:

Given

Two Charges with magnitude Q experience a  force of 12.344 N

at distance r

and we know Electrostatic force is given

F=\frac{kq_1q_2}{r^2}

F=\frac{kQ\cdot Q}{r^2}

F=\frac{kQ^2}{r^2}

Now the magnitude of charge is 2Q and is at a distance of \frac{r}{2}

F'=\frac{k2Q\cdot 2Q}{\frac{r^2}{2^2}}

F'=16F

F'=197.504 N

4 0
3 years ago
This question relates to the practicality of searching for intelligent life in other solar systems by detecting their radio broa
Montano1993 [528]

Answer:

2.77287\times 10^{15}\ m

Explanation:

P = Power = 50 kW

n = Number of photons per second

h = Planck's constant = 6.626\times 10^{-34}\ m^2kg/s

\nu = Frequency = 781 kHz

r = Distance at which the photon intensity is i = 1 photon/m²

Power is given by

P=nh\nu\\\Rightarrow n=\dfrac{P}{h\nu}\\\Rightarrow n=\dfrac{50000}{6.626\times 10^{-34}\times 781000}\\\Rightarrow n=9.66201\times 10^{31}\ photons/s

Photon intensity is given by

i=\dfrac{n}{4\pi r^2}\\\Rightarrow 1=\dfrac{9.66201\times 10^{31}}{4\pi r^2}\\\Rightarrow r=\sqrt{\dfrac{9.66201\times 10^{31}}{4\pi}}\\\Rightarrow r=2.77287\times 10^{15}\ m

The distance is 2.77287\times 10^{15}\ m

3 0
3 years ago
A bulldozer does 4,500 J of work to push a mound of soil to the top of a ramp that is 15 m high. The ramp is at an
Andreas93 [3]

Answer:

170 N

Explanation:

Given in the question that, work a bulldozer can do = 4500 J

<h3>Step 1</h3>

We will use trigonometry identity to find the distance bulldozer will travel up the hill

sin(35) = opp/hypo

sin(35) = 15/hypo

hypo = 15/sin(35)

hypo = 26.15m

<h3>Step 2</h3>

Formula to use

work done = force × distance

Plug values in the above formula

4500 = force x 26.15

force = 4500/26.15

force = 172.08

force ≈ 170 N

<h3 /><h3 /><h3 />

3 0
3 years ago
Read 2 more answers
When Mendeleev organized elements in his periodic table in order of increasing mass, similar elements with similar properties we
Temka [501]
Similar elements with similar properties were in the same groups and periods for instance lithium(Li) and sodium(Na) are alkaline metals and so belong to the same group (that is group 1).Also Hydrogen(H) and Helium(He) both have only one shell or energy level and so belong to the same period.
8 0
3 years ago
If it takes a ball dropped from rest 2.261 s to fall to the ground, from what height H was it released? Express your answer in m
algol [13]

Answer:

Height, H = 25.04 meters

Explanation:

Initially the ball is at rest, u = 0

Time taken to fall to the ground, t = 2.261 s

Let H is the height from which the ball is released. It can be calculated using the second equation of motion as :

H=ut+\dfrac{1}{2}at^2

Here, a = g

H=\dfrac{1}{2}gt^2            

H=\dfrac{1}{2}\times 9.8\times (2.261)^2

H = 25.04 meters

So, the ball is released form a height of 25.04 meters. Hence, this is the required solution.

7 0
3 years ago
Other questions:
  • Tala wants to create a sound echo. She can create the echo using a pane of glass or a carpet square. Which one does she choose?
    14·1 answer
  • Difference between relaxation time and collision time?
    7·2 answers
  • A particle has velocity v⃗1 v → 1 as it accelerates from 1 to 2. What is its velocity vector v⃗2 v → 2 as it moves away from poi
    11·1 answer
  • ASAP When salt is dissolved in water, the result is a A. gas B. compound C. homogeneous mixture D. heterogeneous mixture
    8·2 answers
  • Explain whether P waves or S waves are infra sound
    15·1 answer
  • True or false a microchip lets computers process infomation very quickly
    14·1 answer
  • What is the amount of disorder in a system
    13·1 answer
  • A branch falls from a tree How fast is the branch moving after 0 28 seconds
    9·1 answer
  • 8. What are the two types of mechanical waves?
    14·1 answer
  • 4. A desk with a mass of 10 kg is pushed across a floor with an acceleration of 4 m/s?. What
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!