State and prove impulse momentum theorem using calculus method..
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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 = F̅Δt
is the force–time integral.J = ⌠
⌡F dtis a vector quantity (since force is a vector and time is a scalar).Impulse-Momentum TheoremThe 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…
F̅Δt = 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).UnitsThe 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 III1st lawinertia
mmomentum
p = mv2nd lawforce law
F = maimpulse-momentum theorem
J = Δp3rd lawaction-reaction
+F1 = −F2conservation of momentum
∑p = ∑p0Specific Impulseis 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 = vmqmif 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 = vmgqmgg
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 = F̅Δt
is the force–time integral.J = ⌠
⌡F dtis a vector quantity (since force is a vector and time is a scalar).Impulse-Momentum TheoremThe 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…
F̅Δt = 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).UnitsThe 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 III1st lawinertia
mmomentum
p = mv2nd lawforce law
F = maimpulse-momentum theorem
J = Δp3rd lawaction-reaction
+F1 = −F2conservation of momentum
∑p = ∑p0Specific Impulseis 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 = vmqmif 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 = vmgqmgg
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