Impulse and Newton’s second law

We often think of Newton’s second law as F = ma. But Newton originally expressed his second law in a way that relates to momentum. Newton defined force as the rate of change of momentum—the change in momentum divided by the time interval. Just as velocity is the rate at which displacement changes, force can be expressed as the rate at which momentum changes. Read the text aloud
F= Δp Δt
F  = force (N)
Δp  = change in momentum (kg m/s)
Δt  = change in time (s)
rate of change of momentum
Newton’s definition of force in terms of momentum leads to a new quantity: impulse. Multiplying both sides of F = ∆p/∆t by ∆t gives Ft = ∆p. The product of force and the duration of time the force is applied is called impulse and is usually denoted with the letter J. An impulse applied to an object causes a change in its momentum, ∆p, equal to Ft. Read the text aloud
(11.2) J=Δp=FΔt
J  = impulse (kg m/s)
Δp  = momentum (kg m/s)
F  = force (N)
Δt  = time (s)
force applied over time interval
Read the text aloud
The equation above assumes that the applied force F is constant. However, most impulses are from variable forces. For our purposes an acceptable approximation for equation 11.2 is that F represents the average force acting on an object to change its momentum. This approximation modifies the equation to address both variable and constant forces.
Impulse, applied force, and the time interval over which it is appliedThe same impulse can be applied with different forces. Braking gently applies a small average force, whereas slamming on the brakes applies a large average force. Both stop the car, so both apply the same impulse. They are different because braking gently stops the car over a long time Δt, while slamming on the brakes does it over a short time. In both cases the car changes its momentum from a large value to zero! Read the text aloud
Cushioning increases impact timeFalling on a hard surface causes a rapid change in momentum in a short time interval Δt. As a result, the force is large. Cushioning increases the time interval over which a force is applied, without changing the total impulse. Falling on a cushion spreads the impulse over a longer time interval as the cushion collapses. This dramatically decreases the impact force. One hurts, and the other doesn't! The same thing happens when you bend your legs while landing. Bending your knees extends the time the impulse is applied, reducing the force you experience. Read the text aloud

As Jane approaches a stop sign, she applies a braking force of 10,000 N. Her car has a mass of 2,000 kg and is moving with a velocity of +20 m/s. What is the impulse imparted to bring the car to a stop?

  1. −400,000 kg m/s
  2. −40,000 kg m/s
  3. −4,000 kg m/s
  4. −400 kg m/s

Using the impulse you found above, how long will it take for Jane’s car to stop?

  1. 4 s
  2. 40 s
  3. 0.04 s
  4. 0.4 s

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