= A 2.0-kg object moves with v, -, vy=v₂ = 0. Find the components of the object's four-momentum. R8B.3
= A 2.0-kg object moves with v, -, vy=v₂ = 0. Find the components of the object's four-momentum. R8B.3
Related questions
Question
![**Problem R8B.3:** A 2.0-kg object moves with \( v_x = \frac{3}{5} \), \( v_y = v_z = 0 \). Find the components of the object's four-momentum.
**Explanation:**
This problem involves calculating the four-momentum of an object in a relativistic context. The four-momentum (\( P^\mu \)) is a four-vector consisting of energy and momentum, expressed as:
\[
P^\mu = (E/c, p_x, p_y, p_z)
\]
where:
- \( E \) is the energy of the object,
- \( c \) is the speed of light,
- \( p_x \), \( p_y \), \( p_z \) are the components of the momentum vector.
Given:
- Mass \( m = 2.0 \) kg
- Velocity components \( v_x = \frac{3}{5} \), \( v_y = 0 \), \( v_z = 0 \)
We need to calculate these components using the following formulas:
1. **Relativistic momentum**:
\[
p_x = \gamma m v_x
\]
\[
p_y = \gamma m v_y = 0
\]
\[
p_z = \gamma m v_z = 0
\]
2. **Lorentz factor (\( \gamma \))**:
\[
\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}
\]
Here, \( v = v_x \) since \( v_y \) and \( v_z \) are zero.
3. **Energy**:
\[
E = \gamma mc^2
\]
**Steps to solve:**
- Compute \( \gamma \) using the given \( v_x \).
- Find \( p_x \) using the calculated \( \gamma \).
- Calculate \( E \) with the energy formula \( E = \gamma mc^2 \).
This approach gives you the four components of the four-momentum needed for understanding relativistic motion in physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7344b6c-fa41-48a4-a128-c90aad5b9705%2F132b3028-06b9-4eef-b6c1-8279d7122571%2Fa04ix68_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem R8B.3:** A 2.0-kg object moves with \( v_x = \frac{3}{5} \), \( v_y = v_z = 0 \). Find the components of the object's four-momentum.
**Explanation:**
This problem involves calculating the four-momentum of an object in a relativistic context. The four-momentum (\( P^\mu \)) is a four-vector consisting of energy and momentum, expressed as:
\[
P^\mu = (E/c, p_x, p_y, p_z)
\]
where:
- \( E \) is the energy of the object,
- \( c \) is the speed of light,
- \( p_x \), \( p_y \), \( p_z \) are the components of the momentum vector.
Given:
- Mass \( m = 2.0 \) kg
- Velocity components \( v_x = \frac{3}{5} \), \( v_y = 0 \), \( v_z = 0 \)
We need to calculate these components using the following formulas:
1. **Relativistic momentum**:
\[
p_x = \gamma m v_x
\]
\[
p_y = \gamma m v_y = 0
\]
\[
p_z = \gamma m v_z = 0
\]
2. **Lorentz factor (\( \gamma \))**:
\[
\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}
\]
Here, \( v = v_x \) since \( v_y \) and \( v_z \) are zero.
3. **Energy**:
\[
E = \gamma mc^2
\]
**Steps to solve:**
- Compute \( \gamma \) using the given \( v_x \).
- Find \( p_x \) using the calculated \( \gamma \).
- Calculate \( E \) with the energy formula \( E = \gamma mc^2 \).
This approach gives you the four components of the four-momentum needed for understanding relativistic motion in physics.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 9 images
