The rate of change of momentum is directly proportional to the impress...
Newton's Second Law of Motion
According to Newton's second law of motion, the rate of change of momentum is directly proportional to the impressed force and takes place in the same direction in which the force acts. This law is one of the fundamental principles of classical mechanics and it provides a mathematical relationship between force, mass, and acceleration.
Rate of Change of Momentum
Momentum is defined as the product of an object's mass and its velocity. Mathematically, momentum (p) can be expressed as:
p = m * v
where p is the momentum, m is the mass of the object, and v is the velocity of the object.
The rate of change of momentum (dp/dt) is the derivative of momentum with respect to time. It represents how quickly the momentum of an object is changing. Mathematically, it can be expressed as:
dp/dt = m * dv/dt
where dp/dt is the rate of change of momentum, m is the mass of the object, and dv/dt is the rate of change of velocity.
Impressed Force
When a force is applied to an object, it causes a change in the object's velocity. This change in velocity results in a change in momentum. The impressed force is the external force acting on an object that causes this change in momentum. According to Newton's second law, the impressed force (F) is directly proportional to the rate of change of momentum. Mathematically, it can be expressed as:
F = k * (dp/dt)
where F is the impressed force, k is the proportionality constant, and (dp/dt) is the rate of change of momentum.
Direction of Force and Change in Momentum
According to Newton's second law, the rate of change of momentum takes place in the same direction in which the force acts. This means that if an impressed force is applied in a specific direction, the resulting change in momentum will also occur in that direction. Therefore, the direction of the force and the direction of the change in momentum are the same.
Conclusion
In summary, Newton's second law of motion states that the rate of change of momentum is directly proportional to the impressed force and takes place in the same direction in which the force acts. This law provides a fundamental relationship between force, mass, and acceleration, and is widely used in the study of mechanics.
The rate of change of momentum is directly proportional to the impress...
F =ma (newtons second law of motion)
statement justified newtons second law