As mentioned in the previous role of this lesson, momentum is a ordinarily used term in sports. 
When a sports announcer says that a team has the momentum they mean that the squad is really on the move and is going to be hard to stop. The term momentum is a physics concept. Whatsoever object with momentum is going to be hard to stop. To stop such an object, it is necessary to use a force against its motion for a given period of time. The more momentum that an object has, the harder that it is to stop. Thus, information technology would require a greater amount of force or a longer amount of time or both to bring such an object to a halt. As the forcefulness acts upon the object for a given amount of time, the object's velocity is changed; and hence, the object's momentum is inverse.
The concepts in the to a higher place paragraph should not seem like abstruse information to you. You have observed this a number of times if yous accept watched the sport of football game. In football, the defensive players utilize a force for a given corporeality of time to stop the momentum of the offensive player who has the ball. You accept likewise experienced this a multitude of times while driving. Equally you bring your car to a halt when budgeted a stop sign or stoplight, the brakes serve to employ a strength to the motorcar for a given amount of time to change the car's momentum. An object with momentum can be stopped if a strength is applied against it for a given corporeality of time.
A force acting for a given corporeality of fourth dimension will modify an object's momentum. Put another way, an unbalanced force e'er accelerates an object - either speeding it up or slowing it downward. If the forcefulness acts contrary the object's motility, it slows the object downwards. If a force acts in the aforementioned direction every bit the object's motion, and then the strength speeds the object up. Either mode, a force will change the velocity of an object. And if the velocity of the object is changed, then the momentum of the object is inverse.
Impulse
These concepts are merely an outgrowth of Newton's 2nd law as discussed in an before unit of measurement. Newton'southward second constabulary (Fnet = m • a) stated that the dispatch of an object is directly proportional to the internet force 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 issue.
F = g • a or
F = m • ∆five / t
If both sides of the above equation are multiplied by the quantity t, a new equation results.
F • t = m • ∆5
This equation represents 1 of 2 master principles to be used in the assay of collisions during this unit of measurement. To truly empathise the equation, it is important to understand its pregnant in words. In words, it could be said that the forcefulness times the time equals the mass times the change in velocity. In physics, the quantity Force • time is known as impulse . And since the quantity chiliad•v is the momentum, the quantity m•Δv must be the change in momentum . The equation really says that the
Impulse = Change in momentum One focus of this unit is to empathise the physics of collisions. The physics of collisions are governed by the laws of momentum; and the start police force that we talk over in this unit of measurement is expressed in the higher up equation. The equation is known as the impulse-momentum change equation . The law can be expressed this way:
In a collision, an object experiences a force for a specific amount of time that results in a alter in momentum. The event of the force acting for the given amount of fourth dimension is that the object'due south mass either speeds upwards or slows downwardly (or changes direction). The impulse experienced by the object equals the change in momentum of the object. In equation course, F • t = 1000 • Δ v.
In a collision, objects experience an impulse; the impulse causes and is equal to the modify in momentum. Consider a football halfback running down the football field and encountering a standoff with a defensive back. The collision would change the halfback'due south speed and thus his momentum. If the movement was represented past a ticker record diagram, information technology might appear as follows:
At approximately the 10th dot on the diagram, the collision occurs and lasts for a certain amount of fourth dimension; in terms of dots, the standoff 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 slow downward, 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 Northward•s. This impulse would crusade a momentum change of 720 kg•m/due south. In a standoff, the impulse experienced by an object is always equal to the momentum modify.
Representing aRebounding Collision
Now consider a standoff of a tennis ball with a wall. Depending on the physical properties of the ball 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 design), indicate which example (A or B) has the greatest change in velocity, greatest acceleration, greatest momentum change, and greatest impulse. Support each respond. Click the button to cheque 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? |
| |
Observe that each of the collisions above involve the rebound of a ball off a wall. Find that the greater the rebound effect, the greater the acceleration, momentum alter, and impulse. A rebound is a special type of collision involving a direction change in addition to a speed modify. The effect of the direction change is a big velocity change. On occasions in a rebound collision, an object will maintain the same or almost the same speed equally it had before the standoff. Collisions in which objects rebound with the same speed (and thus, the same momentum and kinetic energy) as they had prior to the collision are known as elastic collisions . In general, elastic collisions are characterized past a large velocity change, a large momentum change, a big impulse, and a large force.
Use the impulse-momentum change principle to fill in the blanks in the post-obit rows of the table. Equally you do, keep these three major truths in listen:
- The impulse experienced past an object is the force•time.
- The momentum change of an object is the mass•velocity change.
- The impulse equals the momentum alter.
Click the button to view answers.
| | Force
(Due north) | Fourth dimension
(due south) | Impulse
(Northward*s) | Mom. Change
(kg*m/s) | Mass
(kg) | Vel. Alter
(one thousand/s) |
| one. | | 0.010 | | | 10 | -4 |
| ii. | | 0.100 | -40 | | 10 | |
| 3. | | 0.010 | | -200 | fifty | |
| four. | -xx 000 | | | -200 | | -eight |
| v. | -200 | 1.0 | | | fifty | |
There are a few observations that can be made in the in a higher place table that relate to the computational nature of the impulse-momentum change theorem. First, observe that the answers in the table above reveal that the third and fourth columns are always equal; that is, the impulse is always equal to the momentum change. Observe likewise that if any two of the first three columns are known, then the remaining column can be computed. This is truthful because the impulse=strength • time. Knowing two of these three quantities allows us to compute the third quantity. And finally, observe that knowing any two of the last three columns allows usa to compute the remaining cavalcade. This is truthful since momentum change = mass • velocity modify.
At that place are besides a few observations that can exist made that relate to the qualitative nature of the impulse-momentum alter theorem. An examination of rows 1 and 2 show that strength and time are inversely proportional; for the same mass and velocity change, a tenfold increase in the fourth dimension of impact corresponds to a tenfold subtract in the strength of impact. An examination of rows one and 3 show that mass and forcefulness are directly proportional; for the aforementioned time and velocity alter, a fivefold increment in the mass corresponds to a fivefold increase in the force required to stop that mass. Finally, an examination of rows 3 and 4 illustrate that mass and velocity modify are inversely proportional; for the same force and time, a twofold subtract in the mass corresponds to a twofold increase in the velocity change.
We Would Like to Advise ...
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Check Your Understanding
Express your understanding of the impulse-momentum change theorem by answering the following questions. Click the button to view the answers.
1. A 0.fifty-kg cart (#1) is pulled with a one.0-N force for 1 second; another 0.50 kg cart (#ii) is pulled with a 2.0 N-strength for 0.l seconds. Which cart (#1 or #2) has the greatest dispatch? Explain.
Which cart (#ane or #ii) has the greatest impulse? Explain.
Which cart (#i or #ii) has the greatest change in momentum? Explicate.
2. In a physics demonstration, two identical balloons (A and B) are propelled across the room on horizontal guide wires. The motility 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? Explain.
Which balloon (A or B) has the greatest final velocity? Explain.
Which balloon (A or B) has the greatest momentum change? Explain.
Which balloon (A or B) experiences the greatest impulse? Explain.
3. Two cars of equal mass are traveling down Lake Avenue with equal velocities. They both come to a stop over different lengths of time. The ticker tape patterns for each motorcar are shown on the diagram below.
At what guess location on the diagram (in terms of dots) does each car brainstorm to experience the impulse?
Which machine (A or B) experiences the greatest acceleration? Explain.
Which car (A or B) experiences the greatest alter in momentum? Explain.
Which auto (A or B) experiences the greatest impulse? Explain.
iv. The diagram to the right depicts the before- and subsequently-collision speeds of a machine that undergoes a head-on-standoff with a wall. In Instance A, the car bounces off the wall. In Example B, the car crumples up and sticks to the wall.
a. In which case (A or B) is the alter in velocity the greatest? Explain.
b. In which case (A or B) is the change in momentum the greatest? Explicate.
c. In which case (A or B) is the impulse the greatest? Explicate.
d. In which case (A or B) is the strength that acts upon the car the greatest (assume contact times are the aforementioned in both cases)? Explicate.
5. Jennifer, who has a mass of 50.0 kg, is riding at 35.0 m/s in her blood-red sports automobile when she must suddenly slam on the brakes to avoid striking a deer crossing the road. She strikes the air pocketbook, that brings her body to a cease in 0.500 s. What average force does the seat belt exert on her?
If Jennifer had not been wearing her seat belt and not had an air bag, then the windshield would accept stopped her head in 0.002 s. What boilerplate force would the windshield accept exerted on her?
6. A hockey player applies an average forcefulness of 80.0 N to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced past the hockey puck.
7. If a five-kg object experiences a x-North strength for a duration of 0.x-second, then what is the momentum change of the object?
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