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hokhani

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- Thread starter hokhani
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In summary, the question of which ball is more dangerous in hitting a person depends on the details of the collision, such as the elasticity and physical size of the balls. However, in terms of delivering the biggest force, the ball with the largest momentum will be more dangerous. On the other hand, in terms of compressing a spring, the ball with more energy will cause a greater compression. Overall, the answer to this question is complex and requires considering various factors.

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hokhani

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hutchphd

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The answer depends upon the details of the collision in ways that probably an ER physician is best equipped to answer. That being said the most obvious question is how "elastic' is the collision. If the balls bounce off elastically then all the energy is returned to the balls and presumably little irreversible damage is done. If the balls embed then the inelasticity implies permanent deformation. The demarcation between these regimes depends crucially on factors that include the physical size of the balls and the speeds involved.

So there is no simple answer.?

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hokhani

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Thanks. Suppose that the two balls stop after a millisecond of their strikes. I would like to know which factor is determining in damage; transfer of momentum or energy. In other words, the ball which transfers larger momentum is more dangerous or the ball which transfers larger energy?hutchphd said:This is a nicely phrased question.

So there is no simple answer.?

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jrmichler

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You can answer your own question: Think of some real world objects. How fast is a baseball? What would happen if one hit you? Calculate the kinetic energy and momentum. How fast is somebody running? What would happen if they ran into you? Calculate the kinetic energy and momentum. Repeat for other objects until you see a pattern.

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hutchphd

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Let me assume that the maximum force delivered is the destructive factor. ...that seems reasonable.hokhani said:Thanks. Suppose that the two balls stop after a millisecond of their strikes. I would like to know which factor is determining in damage; transfer of momentum or energy. In other words, the ball which transfers larger momentum is more dangerous or the ball which transfers larger energy?

Then if the balls stop over a fixed time the one with the largest momentum will deliver biggest force .

Notice if they stop over a fixed distance then the one with the largest energy will deliver the biggest force.

I think the second case sounds more realistic.

Other comments notwithstanding I find the question interesting.

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A.T.

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You can kill a person with minimal mechanical damage. For example, by rupturing a blood vessel at the brain through acceleration of the head. If you are interested in physics not biology, I suggest using a simpler body.hokhani said:Which ball is more dangerous in hitting a person.

Stop and remain at rest relative to the target like in a completely inelastic collision?hokhani said:Thanks. Suppose that the two balls stop after a millisecond of their strikes.

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hokhani

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Now, the situation becomes more interesting;

i) On one hand, we expect the ball (1) with greater momentum transfers greater force to the spring and so the spring becomes more compressed.

ii) On the other hand, the energy of the ball (1) is less than (2) and so we expect that the ball (1) compresses the spring less than the ball (2). It seems a discrepancy between the cases (i) and (ii)!

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jbriggs444

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"Force" is not something that is transferred. Momentum is transferred. However, you are correct that the ball with greater momentum will transfer more momentum to the spring. This makes sense since, all other things being equal, the ball with greater momentum (lower speed but higher mass) will spend morehokhani said:i) On one hand, we expect the ball (1) with greater momentum transfers greater force to the spring and so the spring becomes more compressed.

The conclusion is incorrect, however. 100% of the momentum transferred to the spring is transferred on out to its anchor point. None of it is retained. It is irrelevant to the compression of the spring.

Yes. This one is correct. The work done by the ball on the spring relates to the distance the spring is compressed. The energy that is transferred (the work done) is given by the integral of force overii) On the other hand, the energy of the ball (1) is less than (2) and so we expect that the ball (1) compresses the spring less than the ball (2). It seems a discrepancy between the cases (i) and (ii)!

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hokhani

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With your statements, we can infer that it is the energy (not the momentum) which determines the force exerted by the ball. So the more energy, the more is the exerted force. But I still don't have any intuitive picture of the momentum.jbriggs444 said:"Force" is not something that is transferred. Momentum is transferred. However, you are correct that the ball with greater momentum will transfer more momentum to the spring. This makes sense since, all other things being equal, the ball with greater momentum (lower speed but higher mass) will spend morecompressing the spring. The momentum that is transferred is the integral of force overtime.time

The conclusion is incorrect, however. 100% of the momentum transferred to the spring is transferred on out to its anchor point. None of it is retained. It is irrelevant to the compression of the spring.

Yes. This one is correct. The work done by the ball on the spring relates to the distance the spring is compressed. The energy that is transferred (the work done) is given by the integral of force over. More energy, more work, moredistance. This time no energy is transferred out the far end of the spring. The anchor point does not move. The distance moved is zero, so the work done is zero.distance

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jbriggs444

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More energy, more total displacement, more peak force. One could reason that way.hokhani said:With your statements, we can infer that it is the energy (not the momentum) which determines the force exerted by the ball. So the more energy, the more is the exerted force.

But "peak force" is not the be all and end all of characterizing an impact.

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vco

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Generally, energy does the damage. But the real world is more complicated than that.

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gleem

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Momentum is a measure of an object's motion. It is defined as the product of an object's mass and velocity. In simpler terms, it is the quantity of motion an object has.

Momentum and kinetic energy are closely related. Kinetic energy is the energy an object possesses due to its motion, and it is directly proportional to the square of an object's velocity. Momentum is also directly proportional to an object's velocity, so an increase in momentum will result in an increase in kinetic energy.

Yes, momentum can be negative. The direction of momentum is determined by the direction of an object's velocity. If an object is moving in the opposite direction of a chosen positive direction, its momentum will be negative.

In a closed system, where there is no external force acting on the system, the total momentum before and after an interaction remains constant. This is known as the law of conservation of momentum and is a fundamental principle in physics.

Momentum is used in various real-world applications, such as in sports, car safety, and rocket propulsion. In sports, athletes use their momentum to their advantage to increase their speed and power. In car safety, engineers design crumple zones to absorb the momentum of a moving car in the event of a crash. In rocket propulsion, the principle of conservation of momentum is used to propel the rocket forward by expelling gas in the opposite direction.

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