Collision Speed Calculator

Formula

The formula to calculate the collision speed is:

\[ \text{CS} = \left| \frac{m_1 \cdot v_1 + m_2 \cdot v_2}{m_1 + m_2} \right| \]

Where:

CS – The collision speed (m/s).
m1 – The mass of object 1 (kg).
v1 – The velocity of object 1 (m/s).
m2 – The mass of object 2 (kg).
v2 – The velocity of object 2 (m/s).

Definition

Collision Speed: The speed at which two objects move together after a perfectly inelastic collision, where they stick together and move as a single object. This speed is a result of the conservation of momentum, assuming no external forces act on the system of the two objects. It is an important concept in physics, particularly in the study of momentum and collisions.

Example

Let's say the mass of object 1 is 5 kg, its velocity is 3 m/s, the mass of object 2 is 10 kg, and its velocity is -2 m/s. Using the formula:

\[ \text{CS} = \left| \frac{(5 \times 3) + (10 \times -2)}{5 + 10} \right| = \left| \frac{15 - 20}{15} \right| = \left| \frac{-5}{15} \right| = 0.33 \, \text{m/s} \]

So, the collision speed is 0.33 m/s.

Extended information about Collision-Speed-Calculator

Extended information about Calculate Speed of Car Before Collision

Definition: The speed of a car before a collision can be calculated using the principles of conservation of momentum and energy.

Formula: \( v = \frac{(m_1 + m_2) \cdot v_f}{m_1} \)

\( v \): Speed before collision
\( m_1 \): Mass of the first car
\( m_2 \): Mass of the second car
\( v_f \): Final speed after collision

Example: \( v = \frac{(1500 + 1200) \cdot 10}{1500} \)

\( m_1 \): 1500 kg
\( m_2 \): 1200 kg
\( v_f \): 10 m/s

Extended information about Formula for Speed After Collision

Definition: The speed after a collision can be determined using the conservation of momentum.

Formula: \( v_f = \frac{m_1 \cdot v_1 + m_2 \cdot v_2}{m_1 + m_2} \)

\( v_f \): Final speed after collision
\( m_1 \): Mass of the first car
\( v_1 \): Initial speed of the first car
\( m_2 \): Mass of the second car
\( v_2 \): Initial speed of the second car

Example: \( v_f = \frac{1500 \cdot 20 + 1200 \cdot 15}{1500 + 1200} \)

\( m_1 \): 1500 kg
\( v_1 \): 20 m/s
\( m_2 \): 1200 kg
\( v_2 \): 15 m/s

Extended information about Average Collision Rate Formula

Definition: The average collision rate is the frequency at which collisions occur in a given system.

Formula: \( R = \frac{N \cdot v}{V} \)

\( R \): Collision rate
\( N \): Number of particles
\( v \): Average velocity
\( V \): Volume of the system

Example: \( R = \frac{1000 \cdot 5}{50} \)

\( N \): 1000 particles
\( v \): 5 m/s
\( V \): 50 m³

Extended information about Time to Collision Calculation

Definition: The time to collision is the time remaining before two objects collide, given their current speeds and distance apart.

Formula: \( t = \frac{d}{v_1 + v_2} \)

\( t \): Time to collision
\( d \): Distance between the objects
\( v_1 \): Speed of the first object
\( v_2 \): Speed of the second object

Example: \( t = \frac{100}{20 + 30} \)

\( d \): 100 m
\( v_1 \): 20 m/s
\( v_2 \): 30 m/s