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
A long, straight, horizontal wire carries a left-to-right current of 40 A. If the wire is placed in a uniform magnetic field of
Drupady [299]

Answer:

4.5\times 10^{-5} T

Explanation:

We are given that

Current in wire=40 A

Magnetic field=B_1=3.5\times 10^{-5} T( vertically downward)

We have to find the resultant magnitude of the magnetic field 29 cm above the wire and 29 cm below the wire.

According to Bio-Savart law, the magnetic field exerted by the wire at distance R is given by

B_{wire}=B_2=\frac{\mu_0I}{2\pi R}

We have R=29 cm=\frac{29}{100}=0.29 m

1 m=100 cm

Substitute the values in the given formula

B_2=\frac{4\pi\times 10^{-7}\times 40}{2\times \pi\times 0.29}=\frac{2\times 40\times 10^{-7}}{0.29}=2.76\times 10^{-5} T

The resultant magnetic field is given by

B=\sqrt{B^2_1+B^2_2}

Substitute the values then we get

B=\sqrt{(3.5\times 10^{-5})^2+(2.76\times 10^{-5})^2}

B=4.5\times 10^{-5} T

The resultant magnitude of magnetic field is same above and below the wire as it is at same distance.

The resultant magnitude of the magnetic field 29 cm below the wire=4.5\times 10^{-5} T

Hence, the resultant magnitude of the magnetic field 29 cm above  the wire=4.5\times 10^{-5} T

7 0
3 years ago
A block and tackle is used to lift an automobile engine that weighs 1800 N. The person exerts a force of 300 N to lift the engin
Sidana [21]

Answer:

1800/300 = 6ropes

Explanation:

The engine weighs 1800N and the person exerts a force of 300N, so for him to lift the engine and exerting a force of 300N all through we divide the weight of the engine by the force exerted to know how many ropes are used. Which makes it 6 thereby each rope uses 300N to lift the engine.

8 0
3 years ago
A top is a toy that is made to spin on its pointed end by pulling on a string wrapped around the body of the top. The string has
AlladinOne [14]

Given Information:

Angular displacement = θ = 51 cm = 0.51  m

Radius = 1.8 cm = 0.018 m

Initial angular velocity = ω₁ = 0 m/s

Angular acceleration = α = 10 rad/s ²

Required Information:

Final angular velocity = ω₂ = ?

Answer:

Final angular velocity = ω₂ = 21.6 rad/s

Explanation:

We know from the equations of kinematics,

ω₂² = ω₁² + 2αθ

Where ω₁ is the initial angular velocity that is zero since the toy was initially at rest, α is angular acceleration and θ is angular displacement.

ω₂² = (0)² + 2αθ

ω₂² = 2αθ

ω₂ = √(2αθ)

We know that the relation between angular displacement and arc length is given by

s = rθ

θ = s/r

θ = 0.51/0.018

θ = 23.33 radians

finally, final angular velocity is

ω₂ = √(2αθ)

ω₂ = √(2*10*23.33)

ω₂ = 21.6 rad/s

Therefore, the top will be rotating at 21.6 rad/s when the string is completely unwound.

3 0
3 years ago
NVMMMMMMMMMMMMMMMMMMMM
sp2606 [1]
Huh??????????????????????????
8 0
3 years ago
1 Apply Look around you to an object in motion. Describe the motion by discussing its position and direction of motion in relati
luda_lava [24]
Most of the problem depends on which object you observe. For the speed, take the absolute value of the derivative of the polynomial interpolation of position verses time.
5 0
3 years ago
Other questions:
  • The number of electrons in one coulmb charge is ?
    10·1 answer
  • What are two ways you can increase the magnetic field of an electromagnetic?
    6·1 answer
  • A ball is thrown upward with a speed of 40 m/s. Approximately how much time does it take the ball to travel from the release loc
    10·1 answer
  • During an Olympic bobsled run, the Jamaican team makes a turn of radius 8.80 m at a speed of 105 km/h. What is the ratio of thei
    5·1 answer
  • Which of the following is a force or motion that
    6·1 answer
  • If youre walking from point a to b, the magnitude of your displacement will always be equal or less than or greater than your di
    8·1 answer
  • An object with a mass of 2.0 kg accelerates at 2.0 m/s^2 when an unknown force is applied to it. What is the amount of the force
    11·1 answer
  • What’s the answer ?????
    5·1 answer
  • Which famous astronomer discovered jupiter’s largest moons?.
    15·1 answer
  • Suppose an astronaut has landed on Planet * Fully equipped, the astronaut has a
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!