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
Fantom [35]
3 years ago
10

Suppose two masses labelled m1 and m2, are speeding toward each other at time t=0s. The first mass 1 has a mass and speed has va

lues of m1=3 kg and v1,i= 2 m/s (to the right). Mass 2 has a mass and speed of m2 = 5kg with an initial speed of v2,I = 5 m/s (to the left). Then at some time t there is an elastic collision between the two masses. What is the final speed and direction of m1 and m2 after the collision.
Physics
1 answer:
Shkiper50 [21]3 years ago
7 0

Answer:

The velocity of the first mass is 19.9 m/s to the left

The velocity of the second mass is 8.14 m/s to the left

Explanation:

In an elastic collision, both momentum and kinetic energy is conserved.

\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 = \frac{1}{2}m_1v_{11}^2 + \frac{1}{2}m_2v_{22}^2\\m_1v_1 + m_2v_2 = m_1 v_{11} + m_2 v_{22}

There is a lot of elaboration to solve these two equations, but substituting the values given in the question will ease the hard work.

\frac{1}{2}(3)(2)^2 + \frac{1}{2}(5)(5)^2 = \frac{1}{2}(3)v_{11}^2 + \frac{1}{2}(5)v_{22}^2\\(3)(2) - (5)(5) = (3) v_{11} + (5) v_{22}\\6 + \frac{125}{2} = \frac{1}{2}(3)v_{11}^2 + \frac{1}{2}(5)v_{22}^2\\-19 = 3 v_{11} + 5 v_{22}\\v_{11}^2 = (\frac{-19 - 5v_{22}}{3})^2\\{\rm Plugging ~this ~into~the~kinetic~energy~equation~gives:}\\\frac{137}{2} = \frac{3}{2}(\frac{-19-5v_{22}}{3})^2 + \frac{5}{2}v_{22}\\137 = \frac{361 + 190v_{22} + 25v_{22}^2}{3} + \frac{5}{2}v_{22}

Rearranging the equations gives

137 = \frac{722 + 380v_{22} + 50v_{22}^2 + 15v_{22}}{6}\\822 = 722 + 395v_{22} + 50v_{22}^2\\50v_{22}^2 + 395v_{22} - 100 = 0\\10v_{22}^2 + 79v_{22} - 20 = 0

Solving this equation quadratically gives the velocity of the second mass:

v_{22} = -8.14~{\rm or}~0.24

There are two roots to the quadratic equation, but we intuitively know that the bigger mass with the higher initial velocity will have the same direction after the collision.

Therefore, the final speed of the second mass is 8.14 m/s to the left.

Now, it is easy to calculate the velocity of the first mass.

-19 = (3)v_{11} -(-8.14)5\\ v_{11} = -19.9

You might be interested in
Ok I have no clue for this one I’m not sure what to make out of this one please help
MatroZZZ [7]

Helium, Neon, and Xenon are all part of the same column on the Periodic Table. Such a column is referred to as a Group, because they have the same number of valence electrons in their outermost shell. Hope this helps!

5 0
3 years ago
weight of Ali is 500andN.he is standing on the ground with an area of 0.025 m^2 area .we can find pressure under his feet. what
Inessa05 [86]

Answer:

20000 Pa

Explanation:

Pressure is defined as the force per unit area.

Mathematically : P =F/A    where F is force and A is area

Force = 500 N

Area= 0.025 m²

P= 500/0.025

P= 20000 Pa

8 0
3 years ago
How much metabolic energy is required for a 68kg person to run at a speed of 15km/hr for 15min ?
irga5000 [103]
<span>What I have here is exactly the same problem, however, with the time changed to 19 mins:

metabolic energy = metabolic power*time = 1.150*19*60 = 1.311 kJ..corresponding to 1.311/4.186 = 313,2 Cal or kcal 

If we reasonably assume a metabolic eff.cy of 20%, it means we need to assume food for 1500 Cal approx.

Just plug the value t=15min to the equation and you will surely get the correct answer.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
8 0
3 years ago
Calculate the mass of an 86kg object on the moon
Vikentia [17]
If an object that is 86kg on the moon then that is the answer, 86kg.
3 0
3 years ago
How can you drop two eggs the fewest amount of times, without them breaking?
MrMuchimi

Answer:

Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that's it for that egg.

4 0
3 years ago
Other questions:
  • Consider this situation: A rope is used to lift an actor upward off the stage. Of the forces listed, identify which act upon the
    13·2 answers
  • Which transformation of energy occurs in a hydroelectric power plant?
    9·1 answer
  • The 80.0-lb boy at a is suspended from the cable that passes over the quarter circular cliff rock. determine if it is possible f
    13·1 answer
  • Molecules that contain two polar bonds are _____.
    14·2 answers
  • Which of the following is NOT a benefit of cool down activities?
    14·1 answer
  • Potential energy of an apple is 6j. the apple is 3.00m high. what is the mass of the apple?​
    13·1 answer
  • Which of the following best describes pseudoscience?
    7·2 answers
  • How many cookies does it take to reach the moon???!!
    7·1 answer
  • What is an inclined plane? How does it make our work easier?
    7·1 answer
  • Why are stars given an absolute magnitude?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!