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Two gliders move toward each other on a linear air track, which we assume is frictionless. Glider A has a mass of 0.50 kg, and glider B has a mass of 0.30 kg; both gliders move with an initial speed of 2.0 m/s. After they collide, glider B moves away with a final velocity whose x component is +2.0 m/s. What is the final velocity of A? Suppose glider B is initially moving to the left at 5.0 m/s when it runs into glider A, which is initially at rest. At what speed does glider A move away from the collision if glider B bounces back with a speed of 0.92 m/s?

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Answer:

-0.4 m/s

-3.552 m/s

Explanation:

[tex]m_1[/tex] = Mass of first glider = 0.5 kg

[tex]m_2[/tex] = Mass of second glider = 0.3 kg

[tex]u_1[/tex] = Initial Velocity of first glider = 2 m/s

[tex]u_2[/tex] = Initial Velocity of second glider = -2 m/s

[tex]v_1[/tex] = Final Velocity of first glider

[tex]v_2[/tex] = Final Velocity of second glider = 2 m/s

As the linear momentum of the system is conserved we have

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.5\times 2+0.3\times (-2)-0.3\times 2}{0.5}\\\Rightarrow v_1=-0.4\ m/s[/tex]

The velocity of glider A is -0.4 m/s

[tex]u_1[/tex] = 0

[tex]u_2[/tex] = -5 m/s

[tex]v_2[/tex] = 0.92 m/s

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{0.5\times 0+0.3\times (-5)-0.3\times 0.92}{0.5}\\\Rightarrow v_1=-3.552\ m/s[/tex]

The velocity of glider A is -3.552 m/s

onyebuchinnaji

The final velocity of glider A after the collision  when glider B moves away with 2 m/s is 2 m/s.

The final velocity of glider A after the collision  when glider B moves away with 0.92 m/s is -3.552 m/s.

The given parameters;

  • mass of gilder A = 0.5 kg
  • mass of glider B = 0.3 kg
  • initial velocity of both gliders, u = 2 m/s
  • final velocity of glider B = 2 m/s

The final velocity of glider A after the collision is calculated  by applying the principle of conservation of linear momentum as follows;

[tex]m_au_a + m_bu_b = m_av_a + m_bv_b\\\\(0.5\times 2) + (0.3\times 2) = 0.5v_a + (0.3\times 2)\\\\0.5\times 2 = 0.5v_a\\\\v_a = 2 \ m/s[/tex]

The given parameters for the second question;

  • initial velocity of the glider B = 5 m/s (to the left)
  • initial velocity of the glider A = 0 (at rest)
  • final velocity of the glider B = 0.92 m/s (to the right)

The final velocity of glider A after the collision is calculated  by applying the principle of conservation of linear momentum as follows;

[tex]m_au_a + m_bu_b = m_av_a + m_bv_b\\\\0.5(0) + 0.3(-5) = 0.5v_a + (0.92 \times 0.3)\\\\-1.5 = 0.5v_a + 0.276\\\\-1.5 - 0.276 = 0.5v_a\\\\-1.776 = 0.5v_a\\\\v_a = \frac{-1.776}{0.5} \\\\v_a = -3.552 \ m/s[/tex]

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