<< Chapter < Page Chapter >> Page >
  • Define impulse.
  • Describe effects of impulses in everyday life.
  • Determine the average effective force using graphical representation.
  • Calculate average force and impulse given mass, velocity, and time.

The effect of a force on an object depends on how long it acts, as well as how great the force is. In previous examples, a very large force acting for a short time had a great effect on the momentum of the tennis ball. A small force could cause the same change in momentum    , but it would have to act for a much longer time. For example, if the ball were thrown upward, the gravitational force (which is much smaller than the tennis racquet’s force) would eventually reverse the momentum of the ball. Quantitatively, the effect we are talking about is the change in momentum Δ p size 12{Δp} {} .

By rearranging the equation F net = Δ p Δ t to be

Δ p = F net Δ t , size 12{Δp= F rSub { size 8{"net"} } Δt} {}

we can see how the change in momentum equals the average net external force multiplied by the time this force acts. The quantity F net Δ t size 12{F rSub { size 8{"net"} } Δt} {} is given the name impulse    . Impulse is the same as the change in momentum.

Impulse: change in momentum

Change in momentum equals the average net external force multiplied by the time this force acts.

Δ p = F net Δ t

The quantity F net Δ t size 12{F rSub { size 8{"net"} } Δt} {} is given the name impulse.

There are many ways in which an understanding of impulse can save lives, or at least limbs. The dashboard padding in a car, and certainly the airbags, allow the net force on the occupants in the car to act over a much longer time when there is a sudden stop. The momentum change is the same for an occupant, whether an air bag is deployed or not, but the force (to bring the occupant to a stop) will be much less if it acts over a larger time. Cars today have many plastic components. One advantage of plastics is their lighter weight, which results in better gas mileage. Another advantage is that a car will crumple in a collision, especially in the event of a head-on collision. A longer collision time means the force on the car will be less. Deaths during car races decreased dramatically when the rigid frames of racing cars were replaced with parts that could crumple or collapse in the event of an accident.

Bones in a body will fracture if the force on them is too large. If you jump onto the floor from a table, the force on your legs can be immense if you land stiff-legged on a hard surface. Rolling on the ground after jumping from the table, or landing with a parachute, extends the time over which the force (on you from the ground) acts.

Our definition of impulse includes an assumption that the force is constant over the time interval Δ t size 12{Δt} {} . Forces are usually not constant . Forces vary considerably even during the brief time intervals considered. It is, however, possible to find an average effective force F eff that produces the same result as the corresponding time-varying force. [link] shows a graph of what an actual force looks like as a function of time for a ball bouncing off the floor. The area under the curve has units of momentum and is equal to the impulse or change in momentum between times t 1 and t 2 size 12{t rSub { size 8{2} } } {} . That area is equal to the area inside the rectangle bounded by F eff , t 1 , and t 2 . Thus the impulses and their effects are the same for both the actual and effective forces.

Practice Key Terms 2

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Concepts of physics with linear momentum. OpenStax CNX. Aug 11, 2016 Download for free at http://legacy.cnx.org/content/col11960/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Concepts of physics with linear momentum' conversation and receive update notifications?

Ask