A 2.0\, \text {kg}2.0kg2, point, 0, start text, k, g, end text cart moving right at 5.0\,\dfrac{\text m}{\text s}5.0 s m ​ 5, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction on a frictionless track collides with a 3.0\,\text {kg}3.0kg3, point, 0, start text, k, g, end text cart initially at rest. The 2.0\, \text {kg}2.0kg2, point, 0, start text, k, g, end text cart has a final speed of 1.0\,\dfrac{\text m}{\text s}1.0 s m ​ 1, point, 0, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction to the left. What is the final speed of the 3.0\,\text {kg}3.0kg3, point, 0, start text, k, g, end text cart?

.20

Step-by-step explanation:

Since there are no net external forces on the carts, momentum is conserved during the collision. Let’s define the 2.0\, \text {kg}2.0kg2, point, 0, start text, k, g, end text cart as object 111 and the 3.0\,\text {kg}3.0kg3, point, 0, start text, k, g, end text cart as object 222.

\begin{aligned}p_i &= p_f m_1 v_{1i} + m_2 v_{2i} &= (m_1 + m_2) v_{f} \end{aligned}  

p  

i

​  

m  

1

​  

v  

1i

​  

+m  

2

​  

v  

2i

​  

​  

=p  

f

​  

=(m  

1

​  

+m  

2

​  

)v  

f

​  

​  

Hint #22 / 3

Rearranging to solve for the final velocity of the carts gives:

\begin{aligned} v_f &= \dfrac{m_1 v_{1i} + m_2v_{2i}}{m_1+m_2}\\ \\ &= \dfrac{(2.0\, \text {kg})\left (5.0\,\dfrac{\text m}{\text s}\right ) + (3.0\, \text {kg})\left (-3.0\,\dfrac{\text m}{\text s}\right )}{2.0\,\text {kg}+3.0\,\text {kg}}\\ \\ &= 0.20\,\dfrac{\text m}{\text s}\end{aligned}  

v  

f

​  

​  

=  

m  

1

​  

+m  

2

​  

m  

1

​  

v  

1i

​  

+m  

2

​  

v  

2i

​  

​  

=  

2.0kg+3.0kg

(2.0kg)(5.0  

s

m

​  

)+(3.0kg)(−3.0  

s

m

​  

)

​  

=0.20  

s

m

​  

​  

Since speed is the magnitude of the velocity:

|v_{f}|=0.20\,\dfrac{\text m}{\text s}∣v  

f

​  

∣=0.20  

s

m

​  

vertical bar, v, start subscript, f, end subscript, vertical bar, equals, 0, point, 20, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction

Hint #33 / 3

The correct answer is 0.20\,\dfrac{\text m}{\text s}0.20  

s

m

​  

0, point, 20, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction.