There 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, 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 also that if any two of the first three columns are known, then the remaining column can be computed. 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 us to compute the remaining column. There 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 impact corresponds to a tenfold decrease in the force of impact. An examination of rows 1 and 3 show that mass and force are directly proportional; for the same time and velocity change, a fivefold increase 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 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.
Express your understanding of the impulse-momentum change theorem by answering the following questions. Click the button to view the answers. Which cart 1 or 2 has the greatest acceleration? See Answer Cart 2 has the greatest acceleration. Recall that acceleration depends on force and mass.
They each have the same mass, yet cart 2 has the greater force. See Answer The impulse is the same for each cart. See Answer The momentum change is the same for each cart. Momentum change equals the impulse; if each cart has the same impulse, then it would follow that they have the same momentum change. 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. See Answer Balloon B has the greatest acceleration. See Answer Balloon B has the greatest final velocity. At the end of the diagram, the distance traveled in the last interval is greatest for Balloon B. See Answer Balloon B has the greatest momentum change. Since the final velocity is greatest for Balloon B, its velocity change is also the greatest. Momentum change depends on velocity change.
The balloon with the greatest velocity change will have the greatest momentum change. See Answer Balloon B has the greatest impulse. Impulse is equal to momentum change. If balloon B has the greatest momentum change, then it must also have the greatest impulse. 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 car are shown on the diagram below. At what approximate location on the diagram in terms of dots does each car begin to experience the impulse?
See Answer The collision occurs at approximately the ninth dot plus or minus a dot. The diagram shows that it is at that location that the cars begin to slow down. See Answer Car A has the greatest acceleration. The velocity change of each car is the same. They start with the same velocity and each finish with zero velocity. Yet car A accomplishes this change in less time.
Car A accelerates "most rapidly. See Answer The momentum change is the same for each car. The velocity change of each car is the same they start with the same velocity and each finish with zero velocity , and the mass of each car is the same. Thus, the momentum change is the same for each car. See Answer The impulse is the same for each car. The impulse equals the momentum change. If the momentum change is the same for each car, then so must be the impulse. The diagram to the right depicts the before- and after-collision speeds of a car that undergoes a head-on-collision with a wall.
In Case A, the car bounces off the wall. In Case B, the car crumples up and sticks to the wall. See Answer Case A has the greatest velocity change. See Answer Case A has the greatest momentum change. To determine the change in momentum, insert the values for the initial and final velocities into the equation above:. Is it possible for a small force to produce a larger impulse on a given object than a large force?
Why is a m fall onto concrete far more dangerous than a m fall onto water? What external force is responsible for changing the momentum of a car moving along a horizontal road?
By friction, the road exerts a horizontal force on the tires of the car, which changes the momentum of the car. A piece of putty and a tennis ball with the same mass are thrown against a wall with the same velocity. Which object experience a greater impulse from the wall or are the impulses equal? One hazard of space travel is debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint.
Calculate the force exerted by a 0. A cruise ship with a mass of [latex] 1. It comes to rest after traveling 6. Calculate the average force exerted on the pier using the concept of impulse. Hint : First calculate the time it took to bring the ship to rest, assuming a constant force. Calculate the final speed of a kg rugby player who is initially running at 8. Water from a fire hose is directed horizontally against a wall at a rate of Assume constant acceleration of the hammer-nail pair.
What is the momentum as a function of time of a 5. What is the net force acting on this particle? The x -component of a force on a g golf ball by a 7-iron versus time is plotted in the following figure:. Suddenly, a constant force of magnitude 5 N and direction due north is applied to the puck for 1. Find the north and east components of the momentum at the end of the 1. Ignore air resistance. What is the momentum of the ball after 0. Do this problem by finding the components of the momentum first, and then constructing the magnitude and direction of the momentum vector from the components.
Privacy Policy. Skip to main content. Search for:. Example The Arizona Meteor Crater Approximately 50, years ago, a large radius of 25 m iron-nickel meteorite collided with Earth at an estimated speed of [latex] 1. What average force does the driver experience during the collision?
Without the seatbelt and airbag, his collision time with the steering wheel would have been approximately 0. What force would he experience in this case? Equate these and solve for the desired quantity. Example Moving the Enterprise Figure 9. Check Your Understanding The U.
Strategy The force the phone experiences is due to the impulse applied to it by the floor when the phone collides with the floor. Check Your Understanding What if we had assumed the phone did bounce on impact? Summary When a force is applied on an object for some amount of time, the object experiences an impulse. Conceptual Questions Is it possible for a small force to produce a larger impulse on a given object than a large force?
Show Solution By friction, the road exerts a horizontal force on the tires of the car, which changes the momentum of the car. Problems A Calculate the average force on the person if he is stopped by a padded dashboard that compresses an average of 1. Calculate the average force on the person if he is stopped by an air bag that compresses an average of Show Solution a. Show Solution [latex] 4.
Show Solution [latex] 2. Calculate the duration of the impact. What was the average force exerted on the nail? The x -component of a force on a g golf ball by a 7-iron versus time is plotted in the following figure: Find the x -component of the impulse during the intervals [0, 50 ms], and [50 ms, ms] Find the change in the x -component of the momentum during the intervals [0, 50 ms], and [50 ms, ms].
Show Solution Let the positive x-axis be in the direction of the original momentum. Glossary impulse effect of applying a force on a system for a time interval; this time interval is usually small, but does not have to be impulse-momentum theorem change of momentum of a system is equal to the impulse applied to the system. Licenses and Attributions. CC licensed content, Shared previously. FALSE - A less massive object would have a greater momentum owing to a velocity which is greater than that of the more massive object.
Both are equally important. The direction of any vector would never enter into a size comparison. TRUE - Objects with a changing speed also have a changing velocity. As such, an object with a changing speed also has a changing momentum. Which of the following are true about the relationship between momentum end energy? Momentum is momentum and energy is energy. Momentum is NOT a form of energy; it is simply a quantity which proves to be useful in the analysis of situations involving forces and impulses.
TRUE - If an object has momentum, then it is moving. If it is moving, then it has kinetic energy. And if an object has kinetic energy, then it definitely has mechanical energy.
However, it could have some potential energy and thus have mechanical energy. Object A clearly has more momentum. However, Object B has the greatest kinetic energy. The kinetic energy of A is 45 J and the kinetic energy of B is J.
TRUE - When comparing the momentum of two objects to each other, one must consider both mass and velocity; both are of equal importance when determining the momentum value of an object. When comparing the kinetic energy of two objects, the velocity of an object is of double importance. So if two objects of different mass have the same momentum, then the object with the least mass has a greater velocity.
This greater velocity will tip the scales in favor of the least massive object when a kinetic energy comparison is made. Impulse is a quantity which depends upon both force and time to change the momentum of an object. Impulse is a force acting over time. TRUE - Impulse is a vector quantity Like momentum, impulse is not fully described unless a direction is associated with it.
FALSE - An object which is traveling east could encounter a collision from the side, from behind by a faster-moving object or from the front. The direction of the impulse is dependent upon the direction of the force exerted upon the object. In each of these scenarios, the direction of the force would be different.
TRUE - In a collision, there is a collision force which endures for some amount of time. The combination of force and time is what is referred to as an impulse. TRUE - In a collision, there is a collision force which endures for some amount of time to cause an impulse.
This impulse acts upon the object to change its velocity and thus its momentum. TRUE - Yes!!!
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