1. Impulse and Graphical Analysis

2. Objectives
You will be able to explain, and give examples of how the concept of impulse is used in safety devices.
You will be able to perform graphical analysis of impulse.

3. Impulse
The change in an object’s momentum is known as the impulse experienced by the object.
Assumes constant (or average) net force.
Note that m or v or both can change

5. Examples
A 1.1 kg soccer ball is rolling at 2.0 m/s, south, when Tammy strikes it. Her foot is in contact for 25 ms and the ball leaves with a velocity of 8.0 m/s, north.
Determine the impulse delivered to the ball.
Determine the force applied to the ball.

6. Solution: Impulse delivered to ball

7. Solution: Force applied to ball

8. Example A 20 N stone is dropped from a height of 15 m. Calculate the:
momentum after 1.5 s
velocity at this time.

9. Momentum Solution:

10. Velocity Solution

11. Momentum revisited: Suppose we found v first and then p:
= … kg • m/s
= 30 kg•m/s
Which is the same answer!

12. Questions: Read pages 446-452 Do practice problems: p. 451 #1, 2

13. That sudden stop thing….
What happens when a stunt man/woman safely jumps from a high height?
What physics is happening?

14. A not stunt fall:

15. A safe stunt fall:

16. Force and momentum Momentum just as object hits:
Momentum after stop: zero
This is true in either fall.

17. The difference mΔv (the Δp) is the same for either fall.
The Δt is the difference.
Normal fall: very small Δt
Stunt fall: much larger Δt
Large Δt provided by the cushion (air bag) the stunt person lands on

18. The physics:
A big Fnet = OUCH or worse.

19. Safety of sudden stops
Seatbelts, airbags, cushioning, goalie pads, etc., all aim to minimize the force that stops a person (or object) by increasing the time over which the stop occurs.

20. Graphical analysis

21. Slope
Not a known relationship.

22. y-intercept … is 20 N The meaning is that the initial force was 20 N.
Horizontal line also means the force was constant.

23. Area under the graph

24. Area under the graph…
for a force-time graph represents the impulse acting on the object being graphed.

25. Example
This graph was produced using a graphing program, force sensor and timer. A cart collided with the force sensor.

26. Problem
What is the impulse delivered to the cart during the collision?
Impulse = area under a F-t graph

27. But….. Finding the area accurately requires calculus (integration).
You are not expected to find the area under such graphs in Physics 30.
You are expected to know what the graph area represents (impulse).

28. Homework:
Read p 459 – 466
Check and Reflect:
p 467 #1 - 12