Respuesta :
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.
The velocity of mass [tex]m[/tex] is [tex]\boxed{0.4v}[/tex] and velocity of mass [tex]4m[/tex] is [tex]\boxed{1.4v}[/tex] 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 [tex]m[/tex].
Initial speed of first body is [tex]2v[/tex].
Mass of second body is [tex]4m[/tex].
Initial speed of second body is [tex]v[/tex].
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:
[tex]\boxed{m_1u_1+m_2u_2=m_1v_1+m_2v_2}[/tex]
Here, [tex]m_1[/tex] is the mass of first body, [tex]u_1[/tex] is the initial speed of first body, [tex]v_1[/tex] is the final speed of first body, [tex]m_2[/tex] is the mass of second body, [tex]u_2[/tex] is the initial speed of second body and [tex]v_2[/tex] is the final speed of second body.
Substitute [tex]m[/tex] for [tex]m_1[/tex], [tex]2v[/tex] for [tex]u_1[/tex], [tex]4m[/tex] for [tex]m_2[/tex] and [tex]v[/tex] for [tex]u_2[/tex] in above equation and simplify.
[tex]6v=v_1+4v_2[/tex]
Rearrange the above equation for value [tex]v_1[/tex] :
[tex]v_1=6v-4v_2[/tex] …… (I)
2.
Equation of conservation of Kinetic energy:
[tex]\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}[/tex]
Here, [tex]m_1[/tex] is the mass of first body, [tex]u_1[/tex] is the initial speed of first body, [tex]v_1[/tex] is the final speed of first body, [tex]m_2[/tex] is the mass of second body, [tex]u_2[/tex] is the initial speed of second body and [tex]v_2[/tex] is the final speed of second body.
Substitute [tex]m[/tex] for [tex]m_1[/tex], [tex]2v[/tex] for [tex]u_1[/tex], [tex]4m[/tex] for [tex]m_2[/tex] and [tex]v[/tex] for [tex]u_2[/tex] in above equation and simplify.
[tex]5v_2^2-12vv_2+7v^2=0[/tex]
Solving the above quadratic equation, we get
[tex]v_2=1.4v[/tex]
Put the value of [tex]v_2[/tex] in equation (I).
[tex]v_1=0.4v[/tex]
Thus, the velocity of mass [tex]m[/tex] is [tex]\boxed{0.4v}[/tex] and velocity of mass [tex]4m[/tex] is [tex]\boxed{1.4v}[/tex] after elastic collision.
Learn more:
1. Volume of gas after expansion: https://brainly.com/question/9979757
2. Principle of conservation of momentum: https://brainly.com/question/9484203
3. Average translational kinetic energy: https://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.
