IB MYP 4-5 Physics- Collision and Explosion- Study Notes - New Syllabus
IB MYP 4-5 Physics-Collision and Explosion- Study Notes
Key Concepts
- Collision and Explosion
Collision and Explosion
Collision
A collision occurs when two or more bodies exert forces on each other for a relatively short period of time, resulting in a change in their motion. Collisions are common in daily life (e.g., car crashes, billiard balls hitting) and can be analyzed using the principles of momentum and, in some cases, energy conservation.
Characteristics of a Collision:
- Occurs over a short time interval (\(\Delta t\))
- Involves large forces between the interacting bodies
- Momentum is always conserved if no external forces act on the system
- Kinetic energy may or may not be conserved, depending on the type of collision
Mathematical Form:
\(\text{Total Initial Momentum} = \text{Total Final Momentum}\)
\(m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2\)
Types of Collisions:
1. Elastic Collision
- Both momentum and kinetic energy are conserved.
- Occurs when no kinetic energy is transformed into other forms like heat or sound.
- Example: Ideal collisions between gas molecules, billiard balls.
\(\dfrac{1}{2} m_1 u_1^2 + \dfrac{1}{2} m_2 u_2^2 = \dfrac{1}{2} m_1 v_1^2 + \dfrac{1}{2} m_2 v_2^2\)
2. Inelastic Collision
- Momentum is conserved, but kinetic energy is not conserved.
- Some kinetic energy is transformed into heat, sound, or deformation.
- Example: Car crashes, clay balls sticking together.
3. Perfectly Inelastic Collision
- A special case of inelastic collision where the two objects stick together after impact.
- Momentum is conserved, but maximum kinetic energy is lost.
- Example: A bullet embedding into a wooden block.
Example:
Two balls, A (2 kg) moving at \(4 \, \text{m/s}\) and B (3 kg) moving at \(2 \, \text{m/s}\) in the same direction, collide elastically. Find their velocities after the collision.
▶️ Answer/Explanation
Using conservation of momentum:
\( (2)(4) + (3)(2) = 2 v_1 + 3 v_2 \)
\( 8 + 6 = 2 v_1 + 3 v_2 \)
\( 14 = 2 v_1 + 3 v_2 \) … (1)
Using conservation of kinetic energy:
\(\dfrac{1}{2}(2)(4^2) + \dfrac{1}{2}(3)(2^2) = \dfrac{1}{2}(2)v_1^2 + \dfrac{1}{2}(3)v_2^2\)
\( 16 + 6 = v_1^2 + 1.5 v_2^2 \)
\( 22 = v_1^2 + 1.5 v_2^2 \) … (2)
Solving equations (1) and (2), we get:
\( v_1 = 2 \, \text{m/s}, \quad v_2 = 4 \, \text{m/s} \)
\(\boxed{v_1 = 2 \, \text{m/s}, \, v_2 = 4 \, \text{m/s}}\)
Example:
A 1000 kg car moving at \( 20 \ \text{m/s} \) collides head-on with a stationary 1200 kg van. After the collision, both vehicles stick together. Find their common velocity immediately after impact.
▶️ Answer/Explanation
Step 1: Using conservation of momentum for a perfectly inelastic collision:
\( m_1 u_1 + m_2 u_2 = (m_1 + m_2) v \)
Step 2: Substituting values:
\( (1000)(20) + (1200)(0) = (1000 + 1200) v \)
\( 20000 = 2200 v \)
\( v = \dfrac{20000}{2200} = 9.09 \ \text{m/s} \)
Final Answer: \(\boxed{9.09 \ \text{m/s}}\)
Explosion
An explosion is the opposite of a collision: a single object breaks apart into two or more fragments due to an internal force (e.g., chemical reaction, stored energy release). The parts move away from each other after the event.
Key Characteristics of an Explosion:
- Momentum of the system is conserved (if no external forces act).
- Kinetic energy usually increases because stored potential energy is released.
- The objects move apart after the event.
Mathematical Form:
\(m_{\text{total}} u_{\text{initial}} = \sum m_i v_i\)
If initially at rest: \(0 = \sum m_i v_i\)
Example:
A 10 kg shell initially at rest explodes into two fragments of masses 6 kg and 4 kg. The 6 kg fragment moves at \(3 \, \text{m/s}\) to the right. Find the velocity of the 4 kg fragment.
▶️ Answer/Explanation
Initial momentum = Final momentum
\( 0 = (6)(3) + (4)(v) \)
\( 0 = 18 + 4v \)
\( v = -4.5 \, \text{m/s} \)
The negative sign means the 4 kg fragment moves in the opposite direction to the 6 kg fragment.
\(\boxed{v = 4.5 \, \text{m/s} \ \text{(opposite direction)}}\)
Example:
A firecracker of mass \( 0.5 \ \text{kg} \) explodes into two pieces. One piece has a mass of \( 0.2 \ \text{kg} \) and moves east with a velocity of \( 12 \ \text{m/s} \). Find the velocity of the other piece.
▶️ Answer/Explanation
Step 1: Before explosion, total momentum is zero:
\( 0 = (0.2)(12) + (0.3)(v_2) \)
Step 2: Solving for \( v_2 \):
\( 0 = 2.4 + 0.3 v_2 \)
\( 0.3 v_2 = -2.4 \)
\( v_2 = -8 \ \text{m/s} \)
Negative sign means the second piece moves west.
Final Answer: \(\boxed{8 \ \text{m/s} \ \text{west}}\)