As mentioned in the previous part of this lesson, momentum is a commonly used term in sports. 
When a sports journalist says that a team has the momentum they mean that the team is actually on the movement and is going to be difficult to finish. The term momentum is a physics concept. Any object with momentum is going to be hard to finish. To stop such an object, information technology is necessary to apply a force against its move for a given period of time. The more momentum that an object has, the harder that it is to stop. Thus, it would require a greater amount of force or a longer amount of fourth dimension or both to bring such an object to a halt. As the force acts upon the object for a given amount of fourth dimension, the object's velocity is inverse; and hence, the object'due south momentum is changed.
The concepts in the above paragraph should not seem like abstract information to y'all. You have observed this a number of times if yous accept watched the sport of football. In football, the defensive players apply a force for a given amount of time to terminate the momentum of the offensive player who has the brawl. You have also experienced this a multitude of times while driving. Equally you bring your car to a halt when budgeted a terminate sign or stoplight, the brakes serve to use a force to the auto for a given corporeality of time to change the car'due south momentum. An object with momentum can exist stopped if a force is applied against it for a given amount of time.
A forcefulness acting for a given amount of fourth dimension volition change an object's momentum. Put some other way, an unbalanced forcefulness ever accelerates an object - either speeding it up or slowing it downwardly. If the force acts contrary the object'south motion, it slows the object down. If a strength acts in the same direction as the object's motion, and then the force speeds the object up. Either way, a strength will change the velocity of an object. And if the velocity of the object is inverse, so the momentum of the object is changed.
Impulse
These concepts are merely an outgrowth of Newton's second police force as discussed in an earlier unit. Newton's second police (Fnet = k • a) stated that the dispatch of an object is direct proportional to the cyberspace forcefulness interim upon the object and inversely proportional to the mass of the object. When combined with the definition of acceleration (a = change in velocity / time), the post-obit equalities consequence.
F = m • a or
F = 1000 • ∆v / t
If both sides of the higher up equation are multiplied by the quantity t, a new equation results.
F • t = m • ∆v
This equation represents ane of two primary principles to be used in the analysis of collisions during this unit. To truly understand the equation, information technology is important to understand its significant in words. In words, information technology could be said that the strength times the fourth dimension equals the mass times the modify in velocity. In physics, the quantity Strength • time is known as impulse . And since the quantity grand•v is the momentum, the quantity k•Δv must be the alter in momentum . The equation really says that the
Impulse = Change in momentum One focus of this unit of measurement is to sympathise the physics of collisions. The physics of collisions are governed by the laws of momentum; and the first law that we discuss in this unit is expressed in the above equation. The equation is known as the impulse-momentum change equation . The law can be expressed this way:
In a standoff, an object experiences a force for a specific amount of time that results in a change in momentum. The result of the strength acting for the given amount of time is that the object's mass either speeds up or slows down (or changes direction). The impulse experienced by the object equals the change in momentum of the object. In equation form, F • t = m • Δ v.
In a collision, objects feel an impulse; the impulse causes and is equal to the change in momentum. Consider a football halfback running down the football field and encountering a standoff with a defensive dorsum. The collision would change the halfback'southward speed and thus his momentum. If the movement was represented by a ticker tape diagram, it might appear as follows:
At approximately the tenth dot on the diagram, the collision occurs and lasts for a certain corporeality of time; in terms of dots, the collision lasts for a time equivalent to approximately nine dots. In the halfback-defensive back collision, the halfback experiences a force that lasts for a certain amount of time to change his momentum. Since the collision causes the rightward-moving halfback to dull down, the force on the halfback must have been directed leftward. If the halfback experienced a forcefulness of 800 N for 0.9 seconds, then we could say that the impulse was 720 N•southward. This impulse would cause a momentum change of 720 kg•m/south. In a standoff, the impulse experienced by an object is always equal to the momentum change.
Representing aRebounding Standoff
Now consider a collision of a tennis brawl with a wall. Depending on the physical properties of the brawl and wall, the speed at which the ball rebounds from the wall upon colliding with it will vary. The diagrams below depict the changes in velocity of the same ball. For each representation (vector diagram, velocity-time graph, and ticker tape blueprint), indicate which case (A or B) has the greatest alter in velocity, greatest acceleration, greatest momentum change, and greatest impulse. Back up each answer. Click the push to check your answer.
Vector Diagram 
| Greatest velocity change? |
| Greatest acceleration? |
| Greatest momentum change? |
| Greatest Impulse? |
Velocity-Time Graph 
| Greatest velocity change? |
| Greatest acceleration? |
| Greatest momentum modify? |
| Greatest Impulse? |
Ticker Tape Diagram 
| Greatest velocity change? |
| Greatest acceleration? |
| Greatest momentum change? |
| |
Discover that each of the collisions above involve the rebound of a ball off a wall. Notice that the greater the rebound consequence, the greater the dispatch, momentum change, and impulse. A rebound is a special type of collision involving a direction change in addition to a speed alter. The consequence of the management change is a large velocity alter. On occasions in a rebound standoff, an object will maintain the same or nearly the aforementioned speed as it had before the collision. Collisions in which objects rebound with the same speed (and thus, the same momentum and kinetic energy) every bit they had prior to the standoff are known as elastic collisions . In general, elastic collisions are characterized by a large velocity alter, a big momentum change, a large impulse, and a big force.
Use the impulse-momentum alter principle to fill up in the blanks in the following rows of the tabular array. Equally y'all do, keep these three major truths in heed:
- The impulse experienced by an object is the strength•fourth dimension.
- The momentum change of an object is the mass•velocity change.
- The impulse equals the momentum modify.
Click the button to view answers.
| | Forcefulness
(N) | Fourth dimension
(south) | Impulse
(North*southward) | Mom. Change
(kg*m/s) | Mass
(kg) | Vel. Change
(m/s) |
| 1. | | 0.010 | | | 10 | -four |
| 2. | | 0.100 | -xl | | ten | |
| three. | | 0.010 | | -200 | 50 | |
| 4. | -xx 000 | | | -200 | | -8 |
| 5. | -200 | one.0 | | | 50 | |
There are a few observations that can exist fabricated in the above table that relate to the computational nature of the impulse-momentum change theorem. Beginning, observe that the answers in the table above reveal that the 3rd and fourth columns are always equal; that is, the impulse is always equal to the momentum change. Find also that if any two of the beginning three columns are known, and then the remaining column can exist computed. This is true considering the impulse=force • time. Knowing two of these three quantities allows united states to compute the tertiary quantity. And finally, observe that knowing any ii of the concluding three columns allows us to compute the remaining column. This is true since momentum alter = mass • velocity change.
In that location are also a few observations that can be made that relate to the qualitative nature of the impulse-momentum change theorem. An examination of rows 1 and 2 show that force and time are inversely proportional; for the same mass and velocity change, a tenfold increase in the time of touch corresponds to a tenfold decrease in the force of touch on. An examination of rows 1 and iii show that mass and force are directly proportional; for the same fourth dimension and velocity change, a fivefold increment in the mass corresponds to a fivefold increase in the force required to cease that mass. Finally, an examination of rows 3 and 4 illustrate that mass and velocity change are inversely proportional; for the same force and time, a twofold decrease in the mass corresponds to a twofold increase in the velocity change.
We Would Similar to Suggest ...
Sometimes information technology isn't enough to but read nearly it. You accept to collaborate with it! And that's exactly what you practice when you use 1 of The Physics Classroom's Interactives. We would similar to advise that you lot combine the reading of this folio with the use of our Egg Drib Interactive. Yous can observe it in the Physics Interactives department of our website. The Egg Driblet Interactive immerses a learner into a Virtual Egg Drop activity in club to explore the effect of driblet height, egg mass, and landing surface upon the outcome of the egg.
Check Your Understanding
Express your understanding of the impulse-momentum change theorem past answering the post-obit questions. Click the button to view the answers.
i. A 0.l-kg cart (#1) is pulled with a one.0-North force for one second; another 0.l kg cart (#two) is pulled with a 2.0 Northward-strength for 0.50 seconds. Which cart (#ane or #2) has the greatest acceleration? Explain.
Which cart (#i or #2) has the greatest impulse? Explain.
Which cart (#1 or #two) has the greatest change in momentum? Explain.
2. In a physics demonstration, two identical balloons (A and B) are propelled across the room on horizontal guide wires. The motion diagrams (depicting the relative position of the balloons at time intervals of 0.05 seconds) for these two balloons are shown below.
Which balloon (A or B) has the greatest dispatch? Explicate.
Which balloon (A or B) has the greatest final velocity? Explain.
Which airship (A or B) has the greatest momentum change? Explain.
Which balloon (A or B) experiences the greatest impulse? Explain.
3. 2 cars of equal mass are traveling downwardly Lake Avenue with equal velocities. They both come to a end over different lengths of time. The ticker tape patterns for each automobile are shown on the diagram below.
At what approximate location on the diagram (in terms of dots) does each car brainstorm to experience the impulse?
Which car (A or B) experiences the greatest acceleration? Explain.
Which car (A or B) experiences the greatest change in momentum? Explain.
Which car (A or B) experiences the greatest impulse? Explicate.
4. The diagram to the right depicts the earlier- and after-collision speeds of a auto that undergoes a head-on-standoff with a wall. In Case A, the motorcar bounces off the wall. In Case B, the machine crumples up and sticks to the wall.
a. In which case (A or B) is the change in velocity the greatest? Explain.
b. In which example (A or B) is the alter in momentum the greatest? Explain.
c. In which case (A or B) is the impulse the greatest? Explain.
d. In which case (A or B) is the force that acts upon the automobile the greatest (assume contact times are the same in both cases)? Explain.
v. Jennifer, who has a mass of fifty.0 kg, is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avert hitting a deer crossing the road. She strikes the air bag, that brings her body to a stop in 0.500 s. What average force does the seat chugalug exert on her?
If Jennifer had non been wearing her seat belt and not had an air purse, then the windshield would take stopped her head in 0.002 s. What boilerplate force would the windshield accept exerted on her?
6. A hockey histrion applies an average forcefulness of 80.0 North to a 0.25 kg hockey puck for a fourth dimension of 0.10 seconds. Determine the impulse experienced past the hockey puck.
seven. If a 5-kg object experiences a 10-N force for a elapsing of 0.10-second, then what is the momentum change of the object?
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