Equally mentioned in the previous part of this lesson, momentum is a normally used term in sports. 
When a sports announcer says that a squad has the momentum they mean that the team is really on the movement and is going to be hard to stop. The term momentum is a physics concept. Whatever object with momentum is going to be hard to end. To stop such an object, it is necessary to apply a force confronting its movement for a given period of time. The more momentum that an object has, the harder that it is to finish. Thus, information technology would require a greater corporeality of force or a longer corporeality of time or both to bring such an object to a halt. Every bit the force acts upon the object for a given amount of time, the object's velocity is changed; and hence, the object's momentum is changed.
The concepts in the in a higher place paragraph should not seem like abstract information to you. You have observed this a number of times if you have watched the sport of football. In football, the defensive players apply a forcefulness for a given corporeality of time to end the momentum of the offensive player who has the ball. You have likewise experienced this a multitude of times while driving. As you bring your car to a halt when approaching a finish sign or stoplight, the brakes serve to utilize a force to the machine for a given amount of fourth dimension to change the car's momentum. An object with momentum can be stopped if a force is applied against information technology for a given amount of time.
A force acting for a given amount of fourth dimension will change an object's momentum. Put another mode, an unbalanced force ever accelerates an object - either speeding it upwards or slowing it down. If the force acts reverse the object's move, it slows the object down. If a force acts in the same direction every bit the object's motility, and so the strength speeds the object up. Either way, a force will change the velocity of an object. And if the velocity of the object is changed, and then the momentum of the object is changed.
Impulse
These concepts are merely an outgrowth of Newton'southward second police force as discussed in an before unit. Newton's 2d law (Fnet = k • a) stated that the acceleration of an object is straight proportional to the internet force acting 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 result.
F = m • a or
F = m • ∆v / 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 i of two primary principles to be used in the analysis of collisions during this unit. To truly sympathize the equation, it is of import to understand its meaning in words. In words, it could be said that the force times the time equals the mass times the change in velocity. In physics, the quantity Forcefulness • fourth dimension is known equally impulse . And since the quantity m•five is the momentum, the quantity thou•Δv must be the change in momentum . The equation actually says that the
Impulse = Change in momentum One focus of this unit is to empathize the physics of collisions. The physics of collisions are governed by the laws of momentum; and the first law that we hash out in this unit is expressed in the above equation. The equation is known as the impulse-momentum alter equation . The law can be expressed this fashion:
In a standoff, an object experiences a force for a specific amount of fourth dimension that results in a alter in momentum. The outcome of the force acting for the given amount of fourth dimension is that the object'south mass either speeds upwardly or slows down (or changes direction). The impulse experienced by the object equals the alter in momentum of the object. In equation form, F • t = thou • Δ 5.
In a collision, objects experience an impulse; the impulse causes and is equal to the modify in momentum. Consider a football halfback running downwards the football field and encountering a collision 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, information technology might appear every bit follows:
At approximately the 10th dot on the diagram, the collision occurs and lasts for a certain amount of time; in terms of dots, the collision lasts for a fourth dimension equivalent to approximately nine dots. In the halfback-defensive back collision, the halfback experiences a forcefulness that lasts for a certain amount of time to modify his momentum. Since the collision causes the rightward-moving halfback to slow downwards, the force on the halfback must have been directed leftward. If the halfback experienced a force of 800 North for 0.9 seconds, then nosotros could say that the impulse was 720 North•s. This impulse would cause a momentum alter of 720 kg•m/southward. In a collision, the impulse experienced by an object is ever equal to the momentum modify.
Representing aRebounding Standoff
Now consider a collision of a lawn 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 information technology will vary. The diagrams below describe the changes in velocity of the aforementioned ball. For each representation (vector diagram, velocity-time graph, and ticker tape pattern), indicate which example (A or B) has the greatest change in velocity, greatest acceleration, greatest momentum change, and greatest impulse. Support each answer. Click the button to cheque your answer.
Vector Diagram 
| Greatest velocity change? |
| Greatest dispatch? |
| Greatest momentum change? |
| Greatest Impulse? |
Velocity-Time Graph 
| Greatest velocity modify? |
| Greatest acceleration? |
| Greatest momentum change? |
| Greatest Impulse? |
Ticker Tape Diagram 
| Greatest velocity change? |
| Greatest acceleration? |
| Greatest momentum change? |
| |
Observe that each of the collisions in a higher place involve the rebound of a ball off a wall. Detect that the greater the rebound effect, the greater the dispatch, momentum change, and impulse. A rebound is a special type of collision involving a direction modify in addition to a speed alter. The upshot of the direction change is a large velocity change. 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 aforementioned speed (and thus, the same momentum and kinetic energy) as they had prior to the standoff are known as elastic collisions . In general, elastic collisions are characterized by a big velocity change, a big momentum change, a large impulse, and a large force.
Use the impulse-momentum change principle to make full in the blanks in the following rows of the table. Every bit yous do, proceed these three major truths in heed:
- The impulse experienced by an object is the forcefulness•fourth dimension.
- The momentum change of an object is the mass•velocity change.
- The impulse equals the momentum change.
Click the button to view answers.
| | Forcefulness
(N) | Time
(s) | Impulse
(N*south) | Mom. Alter
(kg*m/s) | Mass
(kg) | Vel. Modify
(m/southward) |
| 1. | | 0.010 | | | 10 | -four |
| 2. | | 0.100 | -forty | | x | |
| 3. | | 0.010 | | -200 | l | |
| 4. | -20 000 | | | -200 | | -8 |
| 5. | -200 | 1.0 | | | 50 | |
There are a few observations that can exist made in the to a higher place table that relate to the computational nature of the impulse-momentum change theorem. First, detect that the answers in the table above reveal that the 3rd and quaternary columns are always equal; that is, the impulse is e'er equal to the momentum modify. Observe as well that if whatever two of the kickoff three columns are known, and then the remaining cavalcade tin can exist computed. This is true considering the impulse=force • time. Knowing 2 of these three quantities allows us to compute the 3rd quantity. And finally, detect that knowing whatever ii of the last three columns allows us to compute the remaining column. This is true since momentum alter = mass • velocity change.
There are as well a few observations that can be made that chronicle to the qualitative nature of the impulse-momentum change theorem. An test of rows 1 and 2 testify that strength and time are inversely proportional; for the same mass and velocity modify, a tenfold increase in the time of affect corresponds to a tenfold decrease in the forcefulness of bear on. An examination of rows 1 and iii show that mass and force are direct proportional; for the aforementioned time and velocity change, a fivefold increase in the mass corresponds to a fivefold increment 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 aforementioned force and fourth dimension, a twofold decrease in the mass corresponds to a twofold increment in the velocity change.
We Would Similar to Advise ...
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Cheque Your Agreement
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 (#ane) is pulled with a one.0-N force for ane second; another 0.l kg cart (#2) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #two) has the greatest acceleration? Explain.
Which cart (#i or #2) has the greatest impulse? Explicate.
Which cart (#i or #ii) has the greatest change in momentum? Explain.
2. In a physics demonstration, ii 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 2 balloons are shown below.
Which balloon (A or B) has the greatest acceleration? Explicate.
Which balloon (A or B) has the greatest final velocity? Explain.
Which airship (A or B) has the greatest momentum modify? Explain.
Which balloon (A or B) experiences the greatest impulse? Explicate.
3. Ii cars of equal mass are traveling downwardly Lake Artery with equal velocities. They both come to a stop over different lengths of time. The ticker tape patterns for each auto are shown on the diagram below.
At what approximate location on the diagram (in terms of dots) does each motorcar begin to feel the impulse?
Which car (A or B) experiences the greatest acceleration? Explain.
Which car (A or B) experiences the greatest modify in momentum? Explain.
Which car (A or B) experiences the greatest impulse? Explicate.
4. The diagram to the correct depicts the earlier- and after-collision speeds of a car that undergoes a head-on-standoff with a wall. In Case A, the machine 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 change in velocity the greatest? Explain.
b. In which case (A or B) is the change in momentum the greatest? Explain.
c. In which case (A or B) is the impulse the greatest? Explicate.
d. In which instance (A or B) is the strength that acts upon the car the greatest (assume contact times are the same in both cases)? Explain.
5. Jennifer, who has a mass of l.0 kg, is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoid hitting a deer crossing the road. She strikes the air purse, that brings her body to a cease in 0.500 southward. What boilerplate force does the seat belt exert on her?
If Jennifer had not been wearing her seat chugalug and not had an air bag, then the windshield would have stopped her head in 0.002 south. What average forcefulness would the windshield accept exerted on her?
6. A hockey thespian applies an average force of eighty.0 Due north to a 0.25 kg hockey puck for a time of 0.10 seconds. Determine the impulse experienced by the hockey puck.
7. If a 5-kg object experiences a x-N force for a elapsing of 0.x-2d, then what is the momentum change of the object?
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