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lukranit [14]
3 years ago
13

Mass m, moving at speed 2v, approaches mass 4m, moving at speed v. The two collide elastically head-on. Part A Find the subseque

nt speed of mass m.

Physics
2 answers:
pshichka [43]3 years ago
5 0

The velocity of mass m is \boxed{0.4v} and velocity of mass 4m is \boxed{1.4v} after elastic collision.

Further explanation:

An elastic collision is a collision where both law of conservation of momentum and law of conservation of energy followed.

Given:

Mass of first body is m.

Initial speed of first body is 2v.

Mass of second body is 4m.

Initial speed of second body is v.

Concept:

To obtain the final velocity of both the body for an elastic collision, equation of conservation given as:

1.

Equation of conservation of momentum:

\boxed{m_1u_1+m_2u_2=m_1v_1+m_2v_2}

Here, m_1 is the mass of first body, u_1 is the initial speed of first body, v_1 is the final speed of first body, m_2 is the mass of second body, u_2 is the initial speed of second body and v_2 is the final speed of second body.

Substitute m for m_1, 2v for u_1, 4m for m_2 and v for u_2 in above equation and simplify.

6v=v_1+4v_2  

Rearrange the above equation for value v_1 :

v_1=6v-4v_2                                                             …… (I)

2.

Equation of conservation of Kinetic energy:

\boxed{\dfrac{1}{2}m_1u_1^2+\dfrac{1}{2}m_2u_2^2=\dfrac{1}{2}m_1v_1^2+\dfrac{1}{2}m_2v_2^2}

Here, m_1 is the mass of first body, u_1 is the initial speed of first body, v_1 is the final speed of first body, m_2 is the mass of second body, u_2 is the initial speed of second body and v_2 is the final speed of second body.

Substitute m for m_1, 2v for u_1, 4m for m_2 and v for u_2 in above equation and simplify.

5v_2^2-12vv_2+7v^2=0  

Solving the above quadratic equation, we get

v_2=1.4v

Put the value of v_2 in equation (I).

v_1=0.4v

Thus, the velocity of mass m is \boxed{0.4v} and velocity of mass 4m is \boxed{1.4v} after elastic collision.

Learn more:

1. Volume of gas after expansion: brainly.com/question/9979757

2. Principle of conservation of momentum: brainly.com/question/9484203

3. Average translational kinetic energy: brainly.com/question/9078768

Answer Details:

Grade: Middle School

Subject: Physics

Chapter: Energy and conservation

Keywords:

Mass m, speed 2v, mass 4m, speed v, two collide elastically, conservation, momentum, energy, 1.4v, 0.4v, first, second, initial and final.

meriva3 years ago
4 0
Thank you for posting your question here at brainly. A mass of m moves with 2V towards in the opposite direction of a mass, 4m moving at a speed of V, the speed of m was 2/5V and the mass of 4m was 7.5V. I hope it helps.
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