A 5 kg red toy car is moving right at 10 ms^-1 when it collides with another 10 kg green car moving left at 10 ms^-1. What is the velocity of the red car after the collision?

1 Answer
ali ergin
May 31, 2017

"Animation is the answer to your problem, check it out."

Explanation:

enter image source here

  • In the solution, the collision is supposed to be completely flexible and central.
  • Remember that velocity and momentum is the quantities of the vector.
  • You should pay attention to the speed signs of moving objects in different directions
  • The red ball seen at the animation symbolizes the red toy car.
  • We solve the momentum problems by using momentum conservation and laws of kinetic energy conservation.
  • I'll give you two methods.

1)

v_r'=(2*Sigma P_b)/((m_r+m_b))-v_r

v_b'=(2*Sigma P_b)/((m_r+m_b))-v_b

"where ;"

m_r:"mass of the red toy car"
m_b:"mass of the blue toy car"
v_r':"red toy car's velocity after collision"
v_r:"red toy car's velocity before collision"
v_b':"blue toy car's velocity after collision"
v_b:"blue toy car's velocity before collision"
P_b:"total momentum before collision"

"Let us calculate total momentum before collision."

Sigma P_b=m_r*v_r+m_b*v_b
Sigma P_b=5*10-10*10
Sigma P_b=50-100
Sigma P_b=-50 kg*m*s^(-1)

v_r'=(2*(-50))/((5+10))-10

v_r'=(-100)/(15)-10=(-250)/15

v_r'=-16.67" " m*s^(-1)

v_b'=(2*(-50))/((15))-(-10)

v_b'=((-100))/((15))+10

v_b'=(-100+150)/15=50/15

v_b'=3.33" "m*s^(-1)

2)

  • Let's write momentum conservation equation.

m_r*v_r+m_b*v_b=m_r*v_r'+m_b*v_b'

5*10-10*10=5*v_r'+10*v_b'

50-100=5*v_r'+10*v_b'

-cancel(50)=cancel(5)*v_r'+cancel(10)*v_b'

-10=v_r'+2v_b'" (1)"

  • With algebraic operations using the momentum conservation equation and the kinetic energy conservation equation, you can find the following equation.

v_r+v_r'=v_b+v_b'" (proof can be done.) (2)"

10+v_r'=-10+v_b'

color(blue)(v_b^'=20+v_r')

"we can use the equation (1)"

-10=v_r'+2(color(blue)(20+v_r'))

-10=v_r'+40+2v_r'

-50=3v_r^'

v_r^'=-50/3=-16.67 " "m*s^(-1)

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