As mentioned in the previous part of this lesson, momentum is a commonly used term in sports. 
When a sports announcer says that a team has the momentum they hateful that the squad is actually on the move and is going to exist hard to cease. The term momentum is a physics concept. Whatsoever object with momentum is going to be hard to cease. To stop such an object, information technology is necessary to apply a force against its move for a given catamenia 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 time or both to bring such an object to a halt. Every bit 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 changed.
The concepts in the above paragraph should not seem like abstruse information to yous. You take observed this a number of times if y'all accept watched the sport of football game. In football, the defensive players utilize a force for a given amount of time to finish the momentum of the offensive player who has the ball. Y'all have also experienced this a multitude of times while driving. As you bring your car to a halt when budgeted a stop sign or stoplight, the brakes serve to use a strength to the automobile for a given amount of fourth dimension to change the car's momentum. An object with momentum tin be stopped if a force is applied against it for a given amount of fourth dimension.
A forcefulness acting for a given amount of time volition change an object's momentum. Put another fashion, an unbalanced force always accelerates an object - either speeding it upwards or slowing it down. If the forcefulness acts opposite the object'due south motion, it slows the object downwardly. If a force acts in the aforementioned direction as the object'south motion, then the force speeds the object up. Either fashion, a force will change the velocity of an object. And if the velocity of the object is changed, so the momentum of the object is changed.
Impulse
These concepts are merely an outgrowth of Newton'due south second law equally discussed in an earlier unit of measurement. Newton's second police force (Fnet = m • a) stated that the dispatch of an object is directly proportional to the net forcefulness acting upon the object and inversely proportional to the mass of the object. When combined with the definition of acceleration (a = modify in velocity / time), the following equalities upshot.
F = chiliad • a or
F = m • ∆v / t
If both sides of the higher up equation are multiplied past the quantity t, a new equation results.
F • t = thou • ∆5
This equation represents one of two primary principles to exist used in the analysis of collisions during this unit. To truly understand the equation, it is important to understand its meaning in words. In words, it could exist said that the force times the fourth dimension equals the mass times the change in velocity. In physics, the quantity Force • time is known as impulse . And since the quantity m•5 is the momentum, the quantity k•Δv must exist the change in momentum . The equation really says that the
Impulse = Change in momentum One focus of this unit is to understand the physics of collisions. The physics of collisions are governed by the laws of momentum; and the outset law that we hash out in this unit is expressed in the in a higher place equation. The equation is known as the impulse-momentum modify equation . The police force can exist expressed this way:
In a collision, an object experiences a force for a specific amount of time that results in a modify in momentum. The result of the force acting for the given corporeality of time is that the object's mass either speeds upward or slows down (or changes direction). The impulse experienced by the object equals the modify in momentum of the object. In equation form, F • t = m • Δ five.
In a collision, objects experience 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 collision with a defensive back. The collision would change the halfback's speed and thus his momentum. If the motility was represented past a ticker tape diagram, it might appear as follows:
At approximately the tenth dot on the diagram, the collision occurs and lasts for a sure amount of time; in terms of dots, the standoff lasts for a fourth dimension equivalent to approximately nine dots. In the halfback-defensive dorsum standoff, the halfback experiences a strength that lasts for a certain corporeality of time to change his momentum. Since the collision causes the rightward-moving halfback to wearisome downwards, the force on the halfback must take been directed leftward. If the halfback experienced a force of 800 Northward for 0.9 seconds, then we could say that the impulse was 720 Due north•s. This impulse would cause a momentum modify of 720 kg•g/s. In a collision, the impulse experienced by an object is always equal to the momentum change.
Representing aRebounding Standoff
At present consider a collision of a tennis ball with a wall. Depending on the physical properties of the ball and wall, the speed at which the brawl rebounds from the wall upon colliding with information technology 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), betoken which instance (A or B) has the greatest change in velocity, greatest dispatch, greatest momentum change, and greatest impulse. Support each answer. Click the push button to check your answer.
Vector Diagram 
| Greatest velocity change? |
| Greatest acceleration? |
| Greatest momentum modify? |
| Greatest Impulse? |
Velocity-Fourth dimension Graph 
| Greatest velocity change? |
| Greatest dispatch? |
| Greatest momentum alter? |
| Greatest Impulse? |
Ticker Record Diagram 
| Greatest velocity alter? |
| Greatest dispatch? |
| Greatest momentum alter? |
| |
Observe that each of the collisions above involve the rebound of a ball off a wall. Detect that the greater the rebound consequence, the greater the acceleration, momentum change, and impulse. A rebound is a special type of collision involving a management change in add-on to a speed change. The issue of the management modify is a large velocity change. On occasions in a rebound collision, an object will maintain the same or almost the aforementioned speed as it had earlier 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 collision are known as elastic collisions . In general, elastic collisions are characterized by a large velocity change, a large momentum change, a big impulse, and a large force.
Use the impulse-momentum change principle to make full in the blanks in the following rows of the tabular array. As yous do, continue these three major truths in mind:
- The impulse experienced by an object is the force•time.
- The momentum change of an object is the mass•velocity modify.
- The impulse equals the momentum change.
Click the button to view answers.
| | Forcefulness
(N) | Time
(s) | Impulse
(N*s) | Mom. Alter
(kg*1000/s) | Mass
(kg) | Vel. Change
(m/s) |
| 1. | | 0.010 | | | x | -4 |
| 2. | | 0.100 | -40 | | 10 | |
| 3. | | 0.010 | | -200 | 50 | |
| 4. | -twenty 000 | | | -200 | | -8 |
| five. | -200 | ane.0 | | | 50 | |
In that location are a few observations that can be made in the above table that relate to the computational nature of the impulse-momentum change theorem. First, notice that the answers in the table above reveal that the tertiary and fourth columns are e'er equal; that is, the impulse is always equal to the momentum modify. Observe also that if any ii of the first three columns are known, so the remaining column can be computed. This is true because the impulse=forcefulness • time. Knowing 2 of these three quantities allows us to compute the third quantity. And finally, observe that knowing any two of the final three columns allows us to compute the remaining column. This is true since momentum modify = mass • velocity change.
In that location are also a few observations that can exist made that relate to the qualitative nature of the impulse-momentum change theorem. An examination of rows 1 and two show that force and time are inversely proportional; for the aforementioned mass and velocity change, a tenfold increase in the time of bear upon corresponds to a tenfold subtract in the force of touch. An test of rows 1 and 3 show that mass and force are direct proportional; for the same time and velocity change, a fivefold increase in the mass corresponds to a fivefold increase in the forcefulness required to stop that mass. Finally, an examination of rows iii and 4 illustrate that mass and velocity change are inversely proportional; for the same force and fourth dimension, a twofold decrease in the mass corresponds to a twofold increase in the velocity change.
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Check Your Agreement
Express your understanding of the impulse-momentum change theorem by answering the post-obit questions. Click the button to view the answers.
one. A 0.50-kg cart (#one) is pulled with a 1.0-Northward force for 1 second; another 0.50 kg cart (#2) is pulled with a ii.0 Northward-force for 0.fifty seconds. Which cart (#1 or #2) has the greatest acceleration? Explain.
Which cart (#ane or #2) has the greatest impulse? Explicate.
Which cart (#1 or #two) has the greatest change in momentum? Explain.
ii. In a physics demonstration, two identical balloons (A and B) are propelled beyond 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 ii balloons are shown below.
Which balloon (A or B) has the greatest dispatch? Explain.
Which balloon (A or B) has the greatest final velocity? Explicate.
Which balloon (A or B) has the greatest momentum change? Explicate.
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 end over unlike lengths of fourth dimension. The ticker tape patterns for each car are shown on the diagram below.
At what judge 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? Explicate.
Which car (A or B) experiences the greatest change in momentum? Explain.
Which car (A or B) experiences the greatest impulse? Explain.
4. The diagram to the right depicts the before- and after-collision speeds of a motorcar that undergoes a head-on-collision with a wall. In Example A, the car bounces off the wall. In Case 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? Explicate.
c. In which case (A or B) is the impulse the greatest? Explicate.
d. In which example (A or B) is the force that acts upon the automobile the greatest (assume contact times are the aforementioned in both cases)? Explain.
5. Jennifer, who has a mass of fifty.0 kg, is riding at 35.0 m/southward in her red sports car when she must all of a sudden slam on the brakes to avert striking a deer crossing the road. She strikes the air bag, that brings her body to a end in 0.500 s. What boilerplate 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 take stopped her head in 0.002 s. What average strength 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. Decide the impulse experienced by the hockey puck.
seven. If a five-kg object experiences a 10-Northward force for a duration of 0.10-second, then what is the momentum change of the object?
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