Momentum is a property of moving objects. It is a measure of how hard it is to stop a moving object. It depends on both the mass and the velocity of the object.
The formula for momentum \(p\) is: \( p = mv \)
Impulse is the change in momentum of an object when a force is applied over a period of time. It is equal to the force multiplied by the time it acts for.
\( \text{Impulse} = F \cdot t = \Delta p \)
We start with Newton’s second law:
\[ F = m \cdot a \]
Since acceleration is the change in velocity over time:
\[ F = m \cdot \frac{\Delta v}{\Delta t} \]
Multiplying the numerator:
\[ F = \frac{m \cdot \Delta v}{\Delta t} \]
Recognizing that momentum \( p = mv \), we substitute:
\[ F = \frac{\Delta p}{\Delta t} \]
Finally, multiplying both sides by \( \Delta t \):
\[ F \cdot \Delta t = \Delta p \]
This shows that Impulse = Change in Momentum.
The total momentum of a closed system is conserved, meaning it does not change unless acted on by an external force.
In a collision between two objects:
\( m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2 \)
Where:
\( m_1, m_2 \) = masses of the two objects
\( u_1, u_2 \) = initial velocities
\( v_1, v_2 \) = final velocities
Cart A of mass 2kg is moving at 3 m/s. Cart B of mass 1kg is stationary. They collide and stick together. What is their common velocity after the collision?
Written by Pavle Ignjatovic