Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed . The objects collide, stick together, and move with speed 0.100 in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?

0.00
0.800
0.900
10.0
1.20
and show your work please

Question

22-10-2019
Physics

contestada

Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed . The objects collide, stick together, and move with speed 0.100 in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?

0.00
0.800
0.900
10.0
1.20
and show your work please

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Muscardinus Muscardinus · Answer 1 · 2019-10-23T09:33:51+02:00

Explanation:

Let the mass of two objects be m. Both objects move along the same line in opposite directions. Let v and u₂ are speeds of both objects before collision.

After the collision, both objects stick together and move with the speed of 0.1 V the direction of the velocity of the first mass before the collision.

Using the conservation of momentum as :

[tex]m_1u_1+m_2u_2=(m_1+m_2)v[/tex]

[tex]V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}[/tex]

[tex]V=\dfrac{m(u_1+u_2)}{(m_1+m_2)}[/tex]

[tex]0.1v=\dfrac{m(v+u_2)}{(2m)}[/tex]

On solving above equation, [tex]u_2=-0.8v[/tex]

So, the speed of the second mass before the collision is 0.8 v. The negative sign shows that the it moves in opposite direction. Hence, this is the required solution.