The question asks about the fundamental principle of the law of conservation of momentum. This law is a core concept in physics, particularly in mechanics, and it applies to isolated systems. Understanding what an "isolated system" means is key to correctly answering this question.
Define Momentum: Momentum (\(p\)) is a vector quantity defined as the product of an object's mass (\(m\)) and its velocity (\(v\)). Mathematically, it is expressed as \(p = mv\).
Define an Isolated System: An isolated system is a system where no external forces act on it. This means there is no net force from outside the system influencing its motion or the motion of its components.
State the Law of Conservation of Momentum: The law of conservation of momentum states that if the net external force acting on a system is zero (i.e., it's an isolated system), then the total momentum of the system remains constant.
Relate to Newton's Second Law: Newton's Second Law of Motion can be stated in terms of momentum as the net external force (\(F_{\text{net}}\)) being equal to the rate of change of momentum (\(\frac{dp}{dt}\)).
\[ F_{\text{net}} = \frac{dp}{dt} \]If the system is isolated, then \(F_{\text{net}} = 0\). Therefore,
\[ 0 = \frac{dp}{dt} \]This implies that the change in momentum over time is zero, which means the momentum \(p\) must be constant.
Conclusion: For an isolated system, the total momentum does not change; it remains constant over time.
Correct Option: C) Remains constant
The question asks to identify the type of collision where the total momentum before the collision is equal to the total momentum after the collision. This is a fundamental concept in the conservation of momentum.
Where \(\vec{p}\) represents momentum.
Correct Option: B) Elastic collision. In an elastic collision, both the total momentum and the total kinetic energy of the system are conserved. Therefore, the total momentum before the collision is equal to the total momentum after the collision.
This question tests the fundamental definition of momentum in physics. Momentum is a key concept in classical mechanics, representing the quantity of motion an object has. Understanding its definition is crucial for solving problems related to collisions, impulses, and conservation laws.
Correct Option: B) Velocity
This question tests the fundamental concept of equilibrium in physics. An object is said to be in equilibrium when its state of motion (either at rest or moving with constant velocity) does not change. This condition is directly related to Newton's First Law of Motion.
Correct Option: A) Zero
When an object is in equilibrium, its acceleration is zero. According to Newton's Second Law of Motion (\(F_{\text{net}} = ma\)), if acceleration \(a=0\), then the net force \(F_{\text{net}}\) acting on the object must also be zero. This means all forces acting on the object cancel each other out.
The question asks about Newton's second law of motion, specifically the relationship between acceleration, net force, and another physical quantity. We need to recall the mathematical formulation of this law.
Correct Option: A) Mass — According to Newton's second law (\(F=ma\)), acceleration (\(a\)) is inversely proportional to the mass (\(m\)) of the object when the net force (\(F\)) is constant.
A 100 kg person jumps from a height of 5 m and comes to a stop on landing. What is the magnitude of the change in the person's momentum (the net impulse) during the landing? (Take g = 10 m/s²)
To find the change in momentum (net impulse), we first need to determine the person's velocity just before landing. This can be found using the principles of conservation of energy or kinematics. Once the velocity is known, the initial momentum can be calculated. Since the person comes to a stop, the final momentum is zero. The change in momentum is the final momentum minus the initial momentum.
C) 1000 N·s is the magnitude of the change in the person's momentum (net impulse) during the landing.