Chapter 7, Problem 16E

(a)

To determine

The momentum of each vehicle before the collision.

Answer to Problem 16E

The momentum of the truck before collision is $8.0\times {10}^4\text{kg}\cdot \text{m}/\text{s ,south}$ and that of car is $13.5\times {10}^3\text{kg}\cdot \text{m}/\text{s ,north}$.

Explanation of Solution

Given info: The mass of the truck is $4000\text{kg}$ and its initial velocity is $20\text{m}/\text{s}$ due south. The mass of the car is $1350\text{ kg}$ and its velocity is $10\text{m}/\text{s}$ due north.

Write the expression to find the initial momentum of the truck.

$P_{\text{t}}=m_{\text{t}}{v}_{\text{t}}$

Here,

$P_t$ is the initial momentum of the truck

$m_{\text{t}}$ is the mass of the truck

$v_{\text{t}}$ is the initial velocity of the truck

Substitute $4000\text{kg}$ for $m_{\text{t}}$ and $20\text{m}/\text{s}$ for $v_{\text{t}}$ in the above equation to find $P_t$.

$\begin{array}{c}{P}_{\text{t}}=\left(4000\text{kg}\right)\left(20\text{m}/\text{s}\right)\\ =8.0\times {10}^4\text{kg}\cdot \text{m}/\text{s},\text{ south}\end{array}$

Write the expression to find the initial momentum of the car.

$P_{\text{c}}=m_{\text{c}}{v}_{\text{c}}$

Here,

$P_c$ is the initial momentum of the car

$m_{\text{c}}$ is the mass of the car

$v_{\text{c}}$ is the initial velocity of the car

Substitute $1350\text{ kg}$ for $m_{\text{c}}$ and $10\text{m}/\text{s}$ for $v_{\text{c}}$ in the above equation to find $P_c$.

$\begin{array}{c}{P}_{\text{c}}=\left(1350\text{ kg}\right)\left(10\text{m}/\text{s}\right)\\ =13.5\times {10}^3\text{kg}\cdot \text{m}/\text{s},\text{ north}\end{array}$

Conclusion:

Therefore, the momentum of the truck before collision is $8.0\times {10}^4\text{kg}\cdot \text{m}/\text{s ,south}$ and that of car is $13.5\times {10}^3\text{kg}\cdot \text{m}/\text{s ,north}$.

(b)

To determine

The total momentum of the two vehicles after they collide.

Answer to Problem 16E

The total momentum of the two vehicles after they collide is $6.65\times {10}^4\text{kg}\cdot \text{m}/\text{s ,south}$.

Explanation of Solution

The total momentum before collision must be equal to the total momentum after collision.

Write the relation to find the total momentum associated with the system before collision.

$P={\overrightarrow{P}}_{\text{t}}+{\overrightarrow{P}}_{\text{c}}$

Here,

$P$ is the total momentum of the system before collision

${\overrightarrow{P}}_t$ is the momentum of the truck before collision

${\overrightarrow{P}}_c$ is the momentum of the car before collision

Substitute $13.5\times {10}^3\text{kg}\cdot \text{m}/\text{s ,north}$ for ${\overrightarrow{P}}_{\text{c}}$ and $8.0\times {10}^4\text{kg}\cdot \text{m}/\text{s ,south}$ for ${\overrightarrow{P}}_t$ in the above equation to find $P$.

$\begin{array}{c}P=13.5\times {10}^3\text{kg}\cdot \text{m}/\text{s ,north}-8.0\times {10}^4\text{kg}\cdot \text{m}/\text{s ,south}\\ =6.65\times {10}^4\text{kg}\cdot \text{m}/\text{s ,north}\end{array}$

According to the principle of conservation of momentum total momentum after collision will be equal to total momentum before collision but will be opposite in direction.

Conclusion:

Therefore, the total momentum associated with the car and truck after they collide is $6.65\times {10}^4\text{kg}\cdot \text{m}/\text{s ,}\text{south}$.