Understanding Linear Momentum Conservation
Linear momentum (\(\vec{p}\)) is a fundamental concept in physics, describing the mass in motion. It's defined as the product of a particle's mass (\(m\)) and its velocity (\(\vec{v}\)):
\(\vec{p} = m\vec{v}\)
The principle of linear momentum conservation states that the total linear momentum of a system remains constant if no external forces act on it. This idea is a direct consequence of Newton's laws of motion.
Relating Force and Momentum
Newton's second law of motion provides the link between force and momentum. It states that the net force (\(\vec{F}_{net}\)) acting on a particle is equal to the time rate of change of its linear momentum:
\(\vec{F}_{net} = \frac{d\vec{p}}{dt}\)
Here:
- \(\vec{F}_{net}\) is the vector sum of all external forces acting on the particle.
- \(\frac{d\vec{p}}{dt}\) represents how the linear momentum changes over time.
Condition for Momentum Conservation
For the linear momentum (\(\vec{p}\)) of a particle to be conserved, it must remain constant. This means its value does not change over time. Mathematically, this requires the rate of change of momentum to be zero:
\(\frac{d\vec{p}}{dt} = 0\)
According to Newton's second law (\(\vec{F}_{net} = \frac{d\vec{p}}{dt}\)), if the rate of change of momentum is zero, then the net force acting on the particle must also be zero:
\(\vec{F}_{net} = 0\)
Therefore, the linear momentum of a particle is conserved if and only if the net force on it is zero.
Analyzing the Options
- Option 1: the net force on it is maximum. If the net force is maximum, the momentum is changing very rapidly, so it is not conserved.
- Option 2: the net force on it is zero. This is the condition required for \(\frac{d\vec{p}}{dt} = 0\), meaning momentum is conserved. This aligns with the principle.
- Option 3: the net torque on it is zero. A zero net torque relates to the conservation of *angular* momentum, not linear momentum.
- Option 4: the net work done on it is maximum. Net work done relates to the change in kinetic energy (\(W_{net} = \Delta KE\)). While related to motion, it doesn't directly imply the conservation of linear momentum.
Based on the physics principles, the correct condition for the conservation of linear momentum is the absence of a net external force.
Similar Questions
A car of mass 800 kg is travelling at a speed of 40 km/h on a straight road. A force of 1000 N is applied on it in the direction of its velocity for 12 s. Which one among the following is the final speed of the car?
Important Questions from Laws of Motion
Which of the following is correct?
I. The mass of an object is a measure of its inertia
II. In an isolated system the total momentum remains conserved
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