For simplicity, assume the meteor is traveling vertically downward prior to impact. The problem says the velocity at impact was [latex] Substituting these values gives. This is the average force applied during the collision. Next, we calculate the maximum force. The impulse is related to the force function by. We need to make a reasonable choice for the force as a function of time. Then we assume the force is a maximum at impact, and rapidly drops to zero.
A function that does this is. The average force is. The graph of this function contains important information. The areas under the curves are equal to each other, and are numerically equal to the applied impulse. Notice that the area under each plot has been filled in.
Thus, the areas are equal, and both represent the impulse that the meteor applied to Earth during the two-second impact. The average force on Earth sounds like a huge force, and it is. Nevertheless, Earth barely noticed it. The acceleration Earth obtained was just. That said, the impact created seismic waves that nowadays could be detected by modern monitoring equipment. The collision with the building causes the car to come to a stop in approximately 1 second. The driver, who weighs N, is protected by a combination of a variable-tension seatbelt and an airbag Figure.
In effect, the driver collides with the seatbelt and airbag and not with the building. The airbag and seatbelt slow his velocity, such that he comes to a stop in approximately 2.
The restrained driver experiences a large backward force from the seatbelt and airbag, which causes his velocity to decrease to zero. The forward force from the seatback is much smaller than the backward force, so we neglect it in the solution. Impulse seems the right way to tackle this; we can combine Figure and Figure.
The negative sign implies that the force slows him down. For perspective, this is about 1. Big difference! Significance You see that the value of an airbag is how greatly it reduces the force on the vehicle occupants.
For this reason, they have been required on all passenger vehicles in the United States since , and have been commonplace throughout Europe and Asia since the mids. The change of momentum in a crash is the same, with or without an airbag; the force, however, is vastly different. Recall Figure :. This gives us the following relation, called the impulse-momentum theorem or relation.
The impulse-momentum theorem is depicted graphically in Figure. The most common questions asked in relation to impulse are to calculate the applied force, or the change of velocity that occurs as a result of applying an impulse.
The general approach is the same. Assuming this maneuver is completed in 60 s, what average force did the impulse engines apply to the ship? We are asked for a force; we know the initial and final speeds and hence the change in speed , and we know the time interval over which this all happened.
In particular, we know the amount of time that the force acted. This suggests using the impulse-momentum relation. To use that, though, we need the mass of the Enterprise. Because this problem involves only one direction i. Solving for the magnitude of the force and inserting the given values leads to.
This is an unimaginably huge force. It goes almost without saying that such a force would kill everyone on board instantly, as well as destroying every piece of equipment. The U. How much time must the Enterprise spend accelerating if the humans on board are to experience an average of at most 10 g s of acceleration? Assume the inertial dampeners are offline. Apple released its iPhone 6 Plus in November According to many reports, it was originally supposed to have a screen made from sapphire, but that was changed at the last minute for a hardened glass screen.
Reportedly, this was because the sapphire screen cracked when the phone was dropped. What force did the iPhone 6 Plus experience as a result of being dropped? The force the phone experiences is due to the impulse applied to it by the floor when the phone collides with the floor. Notice that the area under each plot has been filled in. Thus, the areas are equal, and both represent the impulse that the meteor applied to Earth during the two-second impact.
The average force on Earth sounds like a huge force, and it is. Nevertheless, Earth barely noticed it. The acceleration Earth obtained was just. That said, the impact created seismic waves that nowadays could be detected by modern monitoring equipment. Recall Equation 9. This gives us the following relation, called the impulse-momentum theorem or relation. The impulse-momentum theorem is depicted graphically in Figure 9. The most common questions asked in relation to impulse are to calculate the applied force, or the change of velocity that occurs as a result of applying an impulse.
The general approach is the same. Assuming this maneuver is completed in 60 s, what average force did the impulse engines apply to the ship? Solving for the magnitude of the force and inserting the given values leads to. The U. How much time must the Enterprise spend accelerating if the humans on board are to experience an average of at most 10 g s of acceleration? Assume the inertial dampeners are offline. We need to make a couple of reasonable estimates, as well as find technical data on the phone itself.
Second, assume that it is dropped from rest, that is, with an initial vertical velocity of zero. Finally, we assume that the phone bounces very little—the height of its bounce is assumed to be negligible. We need to be careful with the velocities here; this is the change of velocity due to the collision with the floor. Figure 9.
With these definitions, the change of momentum of the phone during the collision with the floor is. We can get the speed of the phone just before it hits the floor using either kinematics or conservation of energy.
First, define the zero of potential energy to be located at the floor. Conservation of energy then gives us:. Because v 1 v 1 is a vector magnitude, it must be positive. Inserting this result into the expression for force gives. Finally, we need to estimate the collision time. One common way to estimate a collision time is to calculate how long the object would take to travel its own length.
The phone is moving at 5. Inserting the given numbers, we obtain. What if we had assumed the phone did bounce on impact? Would this have increased the force on the iPhone, decreased it, or made no difference?
In Example 9. In words, the average force applied to an object is equal to the change of the momentum that the force causes, divided by the time interval over which this change of momentum occurs. Car crashes, punting a football, or collisions of subatomic particles would meet this criterion. For a continuously changing momentum—due to a continuously changing force—this becomes a powerful conceptual tool. If the driver or passenger should hit the dashboard, then the force and time required to stop their momentum is exerted by the dashboard.
Padded dashboards provide some give in such a collision and serve to extend the time duration of the impact, thus minimizing the effect of the force. This same principle of padding a potential impact area can be observed in gymnasiums underneath the basketball hoops , in pole-vaulting pits, in baseball gloves and goalie mitts, on the fist of a boxer, inside the helmet of a football player, and on gymnastic mats.
Fans of boxing frequently observe this same principle of minimizing the effect of a force by extending the time of collision. When a boxer recognizes that he will be hit in the head by his opponent, the boxer often relaxes his neck and allows his head to move backwards upon impact. In the boxing world, this is known as riding the punch. A boxer rides the punch in order to extend the time of impact of the glove with their head.
Extending the time results in decreasing the force and thus minimizing the effect of the force in the collision. Merely increasing the collision time by a factor of ten would result in a tenfold decrease in the force.
Nylon ropes are used in the sport of rock-climbing for the same reason. Rock climbers attach themselves to the steep cliffs by means of nylon ropes.
If a rock climber should lose her grip on the rock, she will begin to fall. In such a situation, her momentum will ultimately be halted by means of the rope, thus preventing a disastrous fall to the ground below. The ropes are made of nylon or similar material because of its ability to stretch.
If the rope is capable of stretching upon being pulled taut by the falling climber's mass, then it will apply a force upon the climber over a longer time period. Extending the time over which the climber's momentum is broken results in reducing the force exerted on the falling climber.
For certain, the rock climber can appreciate minimizing the effect of the force through the use of a longer time of impact. In racket and bat sports, hitters are often encouraged to follow-through when striking a ball. This increase in time must result in a change in some other variable in the impulse-momentum change theorem. Surprisingly, the variable that is dependent upon the time in such a situation is not the force. The force in hitting is dependent upon how hard the hitter swings the bat or racket, not the time of impact.
Instead, the follow-through increases the time of collision and subsequently contributes to an increase in the velocity change of the ball. By following through, a hitter can hit the ball in such a way that it leaves the bat or racket with more velocity i. In tennis, baseball, racket ball, etc.
You undoubtedly recall other illustrations of this principle. A common physics demonstration involves the catching of water balloons of varying speed and varying mass. A water balloon is thrown high into the air and successfully caught i. The key to the success of the demonstration is to contact the balloon with outstretched arms and carry the balloon for a meter or more before finally stopping its momentum.
The effect of this strategy is to extend the time over which the collision occurred and so reduce the force. This same strategy is used by lacrosse players when catching the ball. The ball is "cradled" when caught; i. The effect of this strategy is to lengthen the time over which the collision occurs and so reduce the force on the lacrosse ball.
Another common physics demonstration involves throwing an egg into a bed sheet. The bed sheet is typically held by two trustworthy students and a volunteer is used to toss the egg at full speed into the bed sheet.
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