Question

A 1.0 kg cart moving right at 5.0 on a frictionless track collides with a 3.0 kg cart moving left at 2.0mThe 1.0 kg cart has a final speed of 4.0 to the left.SWhat is the final speed of the 3.0 kg cart?Consider rightward as the positive direction.Round answer to two significant digits.

Answer 1

We are given the following information

Mass of Cart 1 = m₁ = 1 kg

Mass of Cart 2 = m₂ = 3 kg

Initial velocity of Cart 1 = u₁ = 5 m/s

Initial velocity of Cart 2 = u₂ = -2 m/s

Final velocity of Cart 1 = v₁ = -4 m/s

Final velocity of Cart 2 = v₂ = ?

Please note that velocity is taken positive when moving right and negative when moving left.

Recall that the total momentum before the collision must be equal to the momentum after the collision.

Mathematically,

`\begin{gathered} p_{\text{before}}=p_{\text{after}} \\ m_1u_1+m_2u_2=m_1v_1+m_2v_2 \end{gathered}`

Substitute the given values and solve for v₂

`\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ 1\cdot_{}5_{}+3\cdot_{}(-2)_{}=1\cdot_{}(-4)_{}+3\cdot_{}v_2 \\ 5_{}-6_{}=-4_{}+3\cdot_{}v_2 \\ 5_{}-6_{}+4=3\cdot_{}v_2 \\ 3=3\cdot_{}v_2 \\ (3)/(3)=v_2 \\ 1=v_2 \\ v_2=1\: \end{gathered}`

Therefore, the final speed of the 3.0 kg cart is 1 m/s

Also, note that cart 2 will be moving right after the collision since the speed is positive.