How to Identify the Type of Collision: Videos & Practice Problems

To determine the type of collision between two blocks, first check if momentum is conserved using the equation m_1 × v_1initial + m_2 × v_2initial = m_1 × v_1final + m_2 × v_2final . If momentum is conserved, check if the blocks stick together (completely inelastic) or have different final velocities. Finally, assess if the collision is elastic or inelastic by comparing total initial and final velocities. This systematic approach clarifies the collision type effectively.

How to Identify the Type of Collision

Understanding the types of collisions is essential in physics, particularly when analyzing momentum and energy transfer. Collisions can be categorized into three main types: perfectly inelastic, elastic, and inelastic. To determine the type of collision occurring in a given scenario, a systematic approach can be employed using a flowchart that guides through a series of checks based on the conservation of momentum and kinetic energy.

The first step in this process is to verify whether momentum is conserved during the collision. This is done by comparing the total initial momentum of the system to the total final momentum. The equation for momentum conservation is expressed as:

$$m_1 v_{1,\text{initial}} + m_2 v_{2,\text{initial}} = m_1 v_{1,\text{final}} + m_2 v_{2,\text{final}}$$

If the initial momentum equals the final momentum, it indicates that the collision is possible, and we can proceed to the next check. If not, the collision cannot occur as described.

The second check focuses on determining if the collision is perfectly inelastic, which occurs when the colliding objects stick together after the collision. This can be assessed by checking if the final velocities of both objects are the same. If the final velocities differ, as indicated by:

$$v_{1,\text{final}} \neq v_{2,\text{final}}$$

then the collision is not perfectly inelastic. In this case, we can eliminate the possibility of the collision being one of the first two types.

The final check involves determining whether the collision is elastic or inelastic. An elastic collision is characterized by the conservation of kinetic energy, which can be checked using the equation:

$$v_{1,\text{initial}} + v_{1,\text{final}} = v_{2,\text{initial}} + v_{2,\text{final}}$$

If this equation holds true, the collision is elastic. If it does not, and since we have already established that the collision is not perfectly inelastic, we conclude that the collision is inelastic.

In summary, by following this structured approach, one can effectively classify the type of collision based on the conservation of momentum and kinetic energy principles. This method not only aids in problem-solving but also reinforces the fundamental concepts of momentum and energy in physics.

Two toy carts collide head-on on a frictionless surface. Cart A has a mass of 0.50 kg and an initial velocity of 2m/s. Cart B has a mass of 0.30kg and initial velocity –2m/s. After the collision, the final velocities of A and B are –1m/s and 3m/s, respectively. What type of collision was this?

• A. Collision Not Possible
• B. Completely Inelastic
• C. Elastic
• D. Inelastic

Answer: (C)

Here’s what students ask on this topic:

How do you determine if a collision is elastic or inelastic?

To determine if a collision is elastic or inelastic, you need to check two main criteria. First, verify if momentum is conserved using the equation:

$m_1\times v_1\mathrm{initial}+m_2\times v_2\mathrm{initial}=m_1\times v_1\mathrm{final}+m_2\times v_2\mathrm{final}$

If momentum is conserved, check if kinetic energy is also conserved. For an elastic collision, both momentum and kinetic energy are conserved. For an inelastic collision, only momentum is conserved, and kinetic energy is not.

What is the difference between elastic and inelastic collisions?

The main difference between elastic and inelastic collisions lies in the conservation of kinetic energy. In an elastic collision, both momentum and kinetic energy are conserved. This means the total kinetic energy before and after the collision remains the same. In an inelastic collision, only momentum is conserved, while kinetic energy is not. Some of the kinetic energy is converted into other forms of energy, such as heat or sound, during the collision.

How can you tell if a collision is completely inelastic?

A collision is completely inelastic if the colliding objects stick together after the collision, moving with a common final velocity. To determine this, check if the final velocities of both objects are the same or look for keywords in the problem statement such as "stuck," "embedded," or "lodged." If the objects have the same final velocity, the collision is completely inelastic.

What is the first step in identifying the type of collision?

The first step in identifying the type of collision is to check if momentum is conserved. Use the equation:

$m_1\times v_1\mathrm{initial}+m_2\times v_2\mathrm{initial}=m_1\times v_1\mathrm{final}+m_2\times v_2\mathrm{final}$

If the initial momentum equals the final momentum, the collision is possible, and you can proceed to the next steps to determine the specific type of collision.

What equations are used to identify the type of collision?

To identify the type of collision, you use the following equations:

1. Conservation of Momentum:

$m_1\times v_1\mathrm{initial}+m_2\times v_2\mathrm{initial}=m_1\times v_1\mathrm{final}+m_2\times v_2\mathrm{final}$

2. Check for Completely Inelastic Collision:

Are the final velocities of both objects the same?

3. Check for Elastic Collision:

$v_1\mathrm{initial}+v_1\mathrm{final}=v_2\mathrm{initial}+v_2\mathrm{final}$

These equations help you systematically determine the type of collision.