A body of mass 40 kg is accelerating at a rate of 9 m/s². What is the rate of change of linear momentum?
Answer (3)
Momentum = (mass) x (speed)
Mass is constant, so the rate of change of momentum is (mass) x (rate of change of speed) .
But (rate of change of speed ) is just acceleration.
So the rate of change of momentum is (mass) x (acceleration).
But (mass) x (acceleration) is Force.
So Force is the rate of change of momentum. Verrrrrrrry interesting !
In this problem, Force = (40 kg) x (9 m/s²) = 360 newtons.
One 'Newton' is one kilogram-meter per second² . Unit of momentum is (kilogram)-(meter per second), so 'newton' is also a unit of time rate of change of momentum.
Rate of change of momentum is 360 momentum units per second.
Momentum = mass * velocity : p = mv Time Rate of change of linear momentum of an object Δp / Δt ***
*** = Δ (m v ) / Δt = m Δv / Δt = m a ***
*** = Force acting on the object *** = 40 Kg * 9 m /sec² = 360 Newtons***
Δ denotes change in a quantity. Δp = p2 - p1 Δt = t2 - t1 p2 = momentum at time t2 and p1 = momentum at time t1 v2 = velocity at time t2 v1 = velocity at time t1 a = acceleration, constant and same at t1 and t2 let u = velocity at time t = 0
Time rate of change of moment um is actually = (p2 - p1) / (t2 - t1) p2 = m v2 p1 = m v1 So p2 - p1 = Δp = m (v2 - v1)
v2 = u + a t2 v1 = u + a t1 so, v2 - v1 = Δv = a (t2 - t1 ) = a Δt
So p2 - p1 = m (v2 - v1 ) = m a ( t2 - t1) So ( p2 - p1 ) / (t2 - t1 ) = Δp / Δt = m a = 40 * 9 = 360 Newtons
The rate of change of linear momentum for a body with a mass of 40 kg and an acceleration of 9 m/s² is 360 kg·m/s², which is equivalent to 360 Newtons. Momentum changes due to acceleration, and in this case, we calculated it using the formula d t d p = m ⋅ a .
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