Mathematical relationship between the change in momentum of an object and the time over which over which net force is applied to the object
The mathematical relationship between the change in momentum of an object and the time over which a net force is applied to the object is given by the equation:
Δp = F * t
where Δp is the change in momentum, F is the net force applied, and t is the time over which the force is applied.
Called "impulse".
The mathematical relationship between the change in momentum of an object and the time over which the net force is applied to the object can be described using Newton's second law of motion. According to this law, the net force acting on an object is equal to the rate of change of momentum.
Mathematically, we can represent this relationship as:
F = Δp / Δt
where:
F is the net force exerted on the object,
Δp is the change in momentum of the object,
and Δt is the time interval over which the net force is applied.
This equation shows that the net force acting on an object is directly proportional to the change in momentum and inversely proportional to the time interval over which that force is applied.
The mathematical relationship between the change in momentum of an object and the time over which a net force is applied to the object is defined by the concept of impulse.
Impulse is the product of the force applied to an object and the time interval over which the force is applied. It is mathematically expressed by the equation:
Impulse = Force × Time
In terms of momentum, impulse is also defined as the change in momentum of an object. The equation relating impulse and change in momentum is:
Impulse = Change in Momentum
Therefore, we can write:
Force × Time = Change in Momentum
To isolate the change in momentum, we rearrange the equation as follows:
Change in Momentum = Force × Time
This equation shows that the change in momentum of an object is directly proportional to the force applied to it and the time interval over which the force acts. Consequently, if the force or the time increases, the change in momentum will also increase.
It is important to note that momentum is a vector quantity, and its change in direction must also be taken into account when considering the relationship between force, time, and impulse.