show that impulse =∆momentum
Answers
Answer:
Momentum…
is a quantity that describes an object's resistance to stopping (a kind of "moving inertia").
is represented by the symbol p (boldface).
is the product of an object's mass and velocity.
p = mv
is a vector quantity (since velocity is a vector and mass is a scalar).
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 = F∆t
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 = ∆p
If mass is constant, then…
F∆t = m∆v
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 = ∆p
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