What is impulse of a force?Prove that impulse of force equals to change of momentum?
Answers
In classical mechanics, impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector in the same direction. ... A resultant force causes acceleration and a change in the velocity of the body for as long as it acts.
Impulse…
is a quantity that describes the effect of a net force acting on an object (a kind of "moving force").
is represented by the symbol J (boldface).
is the product of the average net force acting on an object and its duration.
J = FΔt
is the force-time integral.
J = ⌠
⌡ F dt
is a vector quantity (since force is a vector and time is a scalar).
Impulse-Momentum Theorem
The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it.
J = Δp
If mass is constant, then…
FΔt = mΔv
If mass is changing, then…
F dt = m dv + v dm
The impulse-momentum theorem is logically equivalent to Newton's second law of motion (the force law).
Units
The SI unit of impulse is the newton second.
The SI unit of momentum is the kilogram meter per second.
These units of impulse and momentum are equivalent.
[N s = kg m/s]
Related concepts of dynamics
I II
1st law inertia
m momentum
p = mv
2nd law force law
F = ma impulse-momentum theorem
J = Δp
3rd law action-reaction
+F1 = −F2 conservation of momentum
∑p = ∑p0
Specific impulse
is a measure of the efficacy of rocket propellants.
if defined as impulse per mass (or thrust per mass flow rate)
is equal to exhaust velocity and has the SI unit of meter per second.
Jsp[m/s] = J = T = v
m qm
if defined as impulse per weight (or thrust per weight flow rate)
is equal to exhaust velocity divided by acceleration due to gravity and has the SI unit of second.
Jsp[s] = J = T = v
mg qmg g