1. Indicate ALL the spacetime diagrams with worldlines that are physically realizable: a) b) d) e) None of these LL MY * (s) x (s) c) t(s) x (s)

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### Spacetime Diagrams and 4-Momentum Vectors

#### Question 1:
**Indicate ALL the spacetime diagrams with worldlines that are physically realizable:**

a)
- Diagram with a straight line moving upwards diagonally from left to right.

b)
- Diagram with a right-angled path moving up then horizontally to the right.

c)
- Diagram with a zigzag path moving up and down repeatedly.

d)
- Diagram with a bent line starting up then sharply turning right and continuing diagonally.

e)
- None of these.
    
**Answer:**

- **Realizable Diagrams:** a) and d)

#### Question 2:
**Which of these 4-momentum vectors represent an object with mass? Indicate all that apply:**

a) 
\[ 
\begin{bmatrix}
5\, \text{kg} \\
0 \\
0 \\
-3\, \text{kg}
\end{bmatrix} 
\]

b)
\[ 
\begin{bmatrix}
3\, \text{kg} \\
3\, \text{kg} \\
0 \\
0
\end{bmatrix} 
\]

c)
\[ 
\begin{bmatrix}
5\, \text{kg} \\
0 \\
0 \\
-5\, \text{kg}
\end{bmatrix} 
\]

d)
\[ 
\begin{bmatrix}
3\, \text{kg} \\
0 \\
0 \\
0
\end{bmatrix} 
\]

e)
\[ 
\begin{bmatrix}
5\, \text{kg} \\
0 \\
3\, \text{kg} \\
0
\end{bmatrix} 
\]

f)
\[ 
\begin{bmatrix}
5\, \text{kg} \\
0 \\
0 \\
-5\, \text{kg}
\end{bmatrix} 
\]

**Answer:**

- **Represent an Object with Mass:** a), b), d), e)

#### Question 3:
**A 1 meter stick with a speed of 4/5 moves past an observer. In the observer’s reference frame, how long does it take the stick to completely pass the observer?**

a) 1.6 ns

b) 2.5 ns

c) 4.2 ns

d) 2.0 ns
Transcribed Image Text:### Spacetime Diagrams and 4-Momentum Vectors #### Question 1: **Indicate ALL the spacetime diagrams with worldlines that are physically realizable:** a) - Diagram with a straight line moving upwards diagonally from left to right. b) - Diagram with a right-angled path moving up then horizontally to the right. c) - Diagram with a zigzag path moving up and down repeatedly. d) - Diagram with a bent line starting up then sharply turning right and continuing diagonally. e) - None of these. **Answer:** - **Realizable Diagrams:** a) and d) #### Question 2: **Which of these 4-momentum vectors represent an object with mass? Indicate all that apply:** a) \[ \begin{bmatrix} 5\, \text{kg} \\ 0 \\ 0 \\ -3\, \text{kg} \end{bmatrix} \] b) \[ \begin{bmatrix} 3\, \text{kg} \\ 3\, \text{kg} \\ 0 \\ 0 \end{bmatrix} \] c) \[ \begin{bmatrix} 5\, \text{kg} \\ 0 \\ 0 \\ -5\, \text{kg} \end{bmatrix} \] d) \[ \begin{bmatrix} 3\, \text{kg} \\ 0 \\ 0 \\ 0 \end{bmatrix} \] e) \[ \begin{bmatrix} 5\, \text{kg} \\ 0 \\ 3\, \text{kg} \\ 0 \end{bmatrix} \] f) \[ \begin{bmatrix} 5\, \text{kg} \\ 0 \\ 0 \\ -5\, \text{kg} \end{bmatrix} \] **Answer:** - **Represent an Object with Mass:** a), b), d), e) #### Question 3: **A 1 meter stick with a speed of 4/5 moves past an observer. In the observer’s reference frame, how long does it take the stick to completely pass the observer?** a) 1.6 ns b) 2.5 ns c) 4.2 ns d) 2.0 ns
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