A car moving with an initial speed v collides with a second stationary car that is one-half as massive After the collision the first car moves in the same direction as before with a speed v/3. a) Draw diagram b) Find the final speed of the second car. c) Compare initial and final kinetic energies of the system. d) Is collision elastic or inelastic?
A car moving with an initial speed v collides with a second stationary car that is one-half as massive After the collision the first car moves in the same direction as before with a speed v/3. a) Draw diagram b) Find the final speed of the second car. c) Compare initial and final kinetic energies of the system. d) Is collision elastic or inelastic?
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Part A and B on paper
![### Collision and Conservation of Momentum
#### Problem Statement:
A car moving with an initial speed \( v \) collides with a second stationary car that is one-half as massive. After the collision, the first car moves in the same direction as before with a speed \( \frac{v}{3} \).
### Tasks:
a) Draw a diagram
b) Find the final speed of the second car.
c) Compare the initial and final kinetic energies of the system.
d) Determine if the collision is elastic or inelastic.
#### Solution:
**a) Draw a diagram:**
**Before Collision:**
- Car 1 (mass = m, speed = v) ➔
- Car 2 (mass = 0.5m, speed = 0) (stationary)
\[ \rightarrow \ \text{Collision} \ \rightarrow \]
**After Collision:**
- Car 1 (mass = m, speed = \(\frac{v}{3}\)) ➔
- Car 2 (mass = 0.5m, speed = \(v_2\)) ➔
**b) Find the final speed of the second car:**
Using conservation of momentum:
- **Initial Momentum:**
\[
p_{initial} = m \cdot v + 0.5m \cdot 0 = mv
\]
- **Final Momentum:**
\[
p_{final} = m \cdot \frac{v}{3} + 0.5m \cdot v_2
\]
\[
mv = m \cdot \frac{v}{3} + 0.5m \cdot v_2
\]
Dividing the equation by \( m \):
\[
v = \frac{v}{3} + 0.5v_2
\]
Solving for \( v_2 \):
\[
v - \frac{v}{3} = 0.5v_2
\]
\[
\frac{2v}{3} = 0.5v_2
\]
\[
v_2 = \frac{4v}{3}
\]
Therefore, the final speed of the second car, \( v_2 \), is \( \frac{4v}{3} \).
**c) Compare initial and final kinetic energies of the system:**
- **Initial K](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F765f1446-f94a-48d3-b4ac-193b47a28028%2Fae44e568-da35-42af-bd82-0c2338e6e58f%2Fda1r6hg_processed.png&w=3840&q=75)
Transcribed Image Text:### Collision and Conservation of Momentum
#### Problem Statement:
A car moving with an initial speed \( v \) collides with a second stationary car that is one-half as massive. After the collision, the first car moves in the same direction as before with a speed \( \frac{v}{3} \).
### Tasks:
a) Draw a diagram
b) Find the final speed of the second car.
c) Compare the initial and final kinetic energies of the system.
d) Determine if the collision is elastic or inelastic.
#### Solution:
**a) Draw a diagram:**
**Before Collision:**
- Car 1 (mass = m, speed = v) ➔
- Car 2 (mass = 0.5m, speed = 0) (stationary)
\[ \rightarrow \ \text{Collision} \ \rightarrow \]
**After Collision:**
- Car 1 (mass = m, speed = \(\frac{v}{3}\)) ➔
- Car 2 (mass = 0.5m, speed = \(v_2\)) ➔
**b) Find the final speed of the second car:**
Using conservation of momentum:
- **Initial Momentum:**
\[
p_{initial} = m \cdot v + 0.5m \cdot 0 = mv
\]
- **Final Momentum:**
\[
p_{final} = m \cdot \frac{v}{3} + 0.5m \cdot v_2
\]
\[
mv = m \cdot \frac{v}{3} + 0.5m \cdot v_2
\]
Dividing the equation by \( m \):
\[
v = \frac{v}{3} + 0.5v_2
\]
Solving for \( v_2 \):
\[
v - \frac{v}{3} = 0.5v_2
\]
\[
\frac{2v}{3} = 0.5v_2
\]
\[
v_2 = \frac{4v}{3}
\]
Therefore, the final speed of the second car, \( v_2 \), is \( \frac{4v}{3} \).
**c) Compare initial and final kinetic energies of the system:**
- **Initial K
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