Momentum is a fundamental concept in physics that describes the quantity of motion an object possesses. Every moving object has momentum, which depends directly on both its mass and its velocity. An object with a larger mass or moving at a higher velocity is more difficult to stop because it possesses a greater momentum. Furthermore, when objects interact through collisions or explosions in a closed system with no external forces, their total momentum remains conserved.
Compare how momentum is conserved when objects collide and when a stationary object explodes into parts moving in opposite directions.
Two spheres approach each other with velocities \(u_1\) and \(u_2\), then separate with velocities \(v_1\) and \(v_2\).
\(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\)
A rocket at rest (\(p = 0\)) splits into downward exhaust gases (\(m_1v_1\)) and an upward rocket body (\(m_2v_2\)).
\(m_1v_1 = -m_2v_2\)
Momentum is the product of an object's mass and its velocity. It is a vector quantity, so its direction is the same as the direction of the object's velocity.
\(p = mv\) where \(p\) is momentum, \(m\) is mass and \(v\) is velocity. The S.I. unit is \(\text{kg m s}^{-1}\) or \(\text{N s}\).
The total momentum before collision is equal to the total momentum after collision if no external force is acting on the system.
An explosion refers to a situation where an object at rest breaks up into two or more parts. Before explosion, total momentum is \(0\) because the object is at rest.
Collision formula
If two objects stick together after collision, they share a common velocity \(v\): \(m_1u_1 + m_2u_2 = (m_1 + m_2)v\).
Explosion formula
This can be written as \(m_1v_1 = -m_2v_2\). The negative sign indicates that the two parts move in opposite directions.
A lorry of mass \(20\,000\text{ kg}\) moves at \(22\text{ m s}^{-1}\). Its momentum is \(p = mv = 20\,000\text{ kg} \times 22\text{ m s}^{-1} = 440\,000\text{ kg m s}^{-1} = 440\,000\text{ N s}\).
Fire hose: Water gushing out of the hose at high speed has a high forward momentum. To balance this backward reaction momentum, two or more firemen are needed to hold the hose tightly.
Answer in your mind, then press “Check Answer”.
What is the momentum of an \(800\text{ kg}\) car moving with a velocity of \(25\text{ m s}^{-1}\)?
State the condition required for the total momentum of a system to be conserved.
A lorry of mass \(1\,000\text{ kg}\) moving at \(5.0\text{ m s}^{-1}\) collides with a car of mass \(800\text{ kg}\) moving at \(2.0\text{ m s}^{-1}\) in the same direction. If the lorry continues moving at \(3.4\text{ m s}^{-1}\) in the same direction after the collision, calculate the velocity of the car.
A stationary object with an enormous mass has high momentum.
An object at rest has zero velocity (\(v = 0\)), so its momentum is strictly zero, regardless of how massive it is.
In an explosion, momentum is created from nothing because objects suddenly gain speed.
The initial momentum is zero. After the explosion, parts move in opposite directions; when added as vectors, the opposite momenta cancel each other out, keeping the total momentum zero.
The displacement of an obstacle hit by an object depends only on the object's speed.
The displacement depends on both the mass and velocity (the momentum) of the moving object.
Objective: Identify momentum, conservation of momentum, collisions and explosions.
1 Which of the following is an S.I. unit for momentum?
2 Under what condition is the total momentum of a colliding system conserved?
3 Isaac Newton described momentum as the "quantity of ".
4 In an explosion where an object initially at rest breaks into two parts of masses \(m_1\) and \(m_2\), the equation relating their momenta after explosion is \(m_1v_1 = \) .
Match each momentum term or phenomenon to its correct textbook description. If using a phone, tap the answer first, then tap the matching box.
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