BR Physics Chapter 1, Passage 5, Question 31 - effect of mass

[deleted388502]

All of the following statements about the kicking of the football and its flight are true EXCEPT.
A it is best if the football has a vertical velocity in the downward direction as it crosses the horizontal line.
B. The mass of the football does not affect its range.
C. The football changes direction throughout its flight.
D. The horizontal velocity of the ball is affected by air resistance.

So practically, I understand why B makes sense.

There are various other situations, however, such as other passages in the book where they ask about the effect of mass on range and it doesn't affect range.

Specifically, there's the question in Passage 1, Number 2 that asks:

If in trial A, Galileo threw a 2kg stone instead of the 1kg stone from the original experiment, the new stone's range would be:
A. Double
B: Half
C. Increased by a factor of sqrrt 2
D. The same

I got this right when I wrote the same, and I understand that the mass difference is negligible, so is this just a judgement call on when mass is affecting range and velocity?

Thanks!

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[ipmed]

Mass difference is not negligible. But when no air resitance mgh=mvsquared/2 so mass cancels and no mass in constant a formulas. however, air resitance is a force that depends on mass so mgh - air resitance = mvsquared/r

 

[SOOyC52H1Sof]

I think the idea is that in one case you are asked to use kinematic equations, and the mass does not show up, where as the second example used work/energy, and mass does show up in the equation.

 

[deleted388502]

Hmm, okay, so how would you recognize this as work/energy? Because I feel like it's posed as a kinematics problem - mass and range were the two words I saw, and I immediately just thought range equation and the fact that mass is not in it.

 

[DrknoSDN]

This is just a bad question. If you say you are kicking a football I would assume that the kickers force would be constant, and not the velocity of the ball when it launches. Give a kicker a 10 kg football and see if it goes the same distance.

Very difficult to assume all masses would have the same initial velocity in this scenario. On the other hand, the other options are even worse choices so that helps.

 

[Lunasly]

I'm hoping someone else can provide insight on this problem.

 

[DrknoSDN]

Sorry, I misread the question in the last response. Choice B is the untrue statement because the kickers force is constant (like I originally assumed), and thus equal forces on different mass balls would produce different trajectories and distances.


A. it is best if the football has a vertical velocity in the downward direction as it crosses the horizontal line.

• Book explanation:
  "The objective when kicking a field goal is to have the football clear a vertical
  height as far from the initial point as possible, so it is best to have the football with a downward vertical velocity as it clears
  the bar rather than an upward vertical velocity. Choice A is valid."

B. The mass of the football does not affect its range. (Not True)

• "We further assume that the kicker kicks with the same motion in each field goal attempt, so the football is assumed to have the same kinetic energy in each case. As
  the football gets heavier and the kinetic energy is kept constant, the initial velocity of the football must decrease."

C. The football changes direction throughout its flight.

• This is true, it's instantaneous velocity is in a direction tangent to it's position along it's flight path.

D. The horizontal velocity of the ball is affected by air resistance.

• True also because air resistance will produce a force in opposition to the direction of motion. The horizontal component of motion will also create a horizontal force in the opposite direction.

 

[Lunasly]

The answer makes sense, but why does mass matter in this case, but when we stop objects of different mass from free fall, then it doesn't matter?

 

[DrknoSDN]

The mass is significant because the kicker is having to put energy into the ball with the kick. If you put the same energy into two different masses they will experience different velocities due to inertia/momentum.

Mass does not influence dropped balls because technically you had to put more potential energy into the heavier ball to get it to the top of the cliff. A kicker can't put any more than his maximum energy into each ball so they are not equivalent examples. However if the kicker could put more energy into the heavier ball he could get it to go the same distance, (or farther)...

If a very light ball and an extremely heavy ball are launched into the air at 20 m/s... they hit the ground at the same time.
If a very light ball and an extremely heavy ball are thrown into the air by a small child, the heavy ball won't get as high, and will hit the ground first.

 

[Lunasly]

That makes sense, but I don't understand your last example. If you throw two balls of different masses in the air (and neglecting air resistance) at the same velocity, they should hit the ground at the same time. This is of course assuming that you increase the amount of kinetic energy you provide the heavier ball. However, if you supply the same KE to both balls, the heavier ball will launch at a slower initial velocity and will not reach the same max height as the other ball and will have a shorter time of flight (I.e., hit the ground first). Did I say that right?

So these examples and the example of dropping a ball from rest from a cliff is really a matter of where the energy comes from. The kinetic energy supplied to balls of different masses dropped from a cliff comes from the PE required to get each of those balls to the top of the cliff. Since they both have 0 PE at the bottom of the cliff and they both start with the same KE at the top of the cliff (zero, since dropped from rest), then their final KE's must be the same, allowing them to hit the ground at the same time and with the same amount of KE. So, technically, mass does play a role here, but it is with regard to PE (as you said, more energy required to bring heavier ball to top of cliff) and not KE (since they start from rest, speed is 0 so KE is 0, making mass irrelevant).

In the football example, we don't have PE to start off with and the KE comes from the kick. If we supply the same force to towards each kick (which is a poor assumption to make and is not mentioned in the passage), then the mass is relevant.

Hopefully my train of thought makes sense.

 

[DrknoSDN]

In the football example, we don't have PE to start off with and the KE comes from the kick. If we supply the same force to towards each kick (which is a poor assumption to make and is not mentioned in the passage), then the mass is relevant..

Yes. Exactly.

However, if you supply the same KE to both balls, the heavier ball will launch at a slower initial velocity and will not reach the same max height as the other ball and will have a shorter time of flight (I.e., hit the ground first). Did I say that right?.

Also yes, This is the premise of the OP question.

Since they both have 0 PE at the bottom of the cliff and they both start with the same KE at the top of the cliff (zero, since dropped from rest), then their final KE's must be the same, allowing them to hit the ground at the same time and with the same amount of KE.

No, not quite. If you drop two balls (different mass) from a cliff they have different PE at the top of the cliff, and by extension when all PE is converted to KE, they will also have different KE.
However objects with different kinetic energies and masses can still accelerate at the same rate, and therefore hit the ground at the same time.
The kinetic energy is determined by 1/2mv^2 and their final velocity will be the same because it is determined by acceleration from gravity. So the more massive object will have more kinetic energy. They both hit at the same time.

 

[Lunasly]

Ah OK, so they do end up with different KE's. What if the mass were the same, but they were shot from different angles? Would they hit the ground with the same amount of KE? Why? I can't understand that since KE is a state function that they would hit te ground with the same impact. However, doesn't the projectile that is shot at a higher angle reach a higher maximum height than the projectile launched at a smaller angle? If

So the time in which objects hit the ground from a given height depends really on then acceleration of gravity and the height that both objects are dropped from. If one reaches a higher maximum height, doesn't that one hit the ground with more KE?

 

[DrknoSDN]

Remember how maximum height is achieved. It is from subtracting the vertical component of KE from the objects total KE. Think of PE as borrowing energy from it's vertical motion.

What if the mass were the same, but they were shot from different angles? Would they hit the ground with the same amount of KE? Why? I can't understand that since KE is a state function that they would hit te ground with the same impact.

When they hit the ground (assuming height=zero) they both have the same KE, but the component in the downward direction will be different. The "impact" might not be the same because now your talking about inelastic collisions.
The projectile that had a greater velocity in the downward direction at impact (one that was launched more vertically), would cause more "damage" when striking the ground. That's essentially work=md*cos(theta). And the cos(theta) closer to 1 will produce more "work" on the ground when impacting. **[There is probably a better formula for relating this. Maybe F=mg*cos(theta)]

However, doesn't the projectile that is shot at a higher angle reach a higher maximum height than the projectile launched at a smaller angle? If
So the time in which objects hit the ground from a given height depends really on then acceleration of gravity and the height that both objects are dropped from. If one reaches a higher maximum height, doesn't that one hit the ground with more KE?

The height attained is determined by taking the upward component of KE and converting that to PE. So the higher object will have more KE converted to PE, but all the PE converts back to KE when it returns to the ground (zero potential energy)

Kinetic energy is not only down for projectiles. A projectile launched horizontally will have most of it's KE in the horizontal direction when it strikes the ground.
A related scenario is if you roll a ball, or launch a projectile that never leaves the ground, it never has any PE. Therefore when it "hits" the ground (time of launch), all of it's KE will be in the horizontal direction.

http://www.physicsclassroom.com/class/energy/Lesson-1/Kinetic-Energy
http://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy

 

[Lunasly]

I haven't read about energy yet, I am just basing this off of the kinematics chapter from TBR. One of the questions in the first passage in the book talks about projectiles launched from different angles with the same initial velocity. Upon impact, they all have the same KE, but their horizontal positions are different from one another. I was under the impression that you did not consider the components of kinetic energy given that its a state function.

Sorry for a of the trouble, but I think I'm more confused than I was before.

 

[syoung]

I try to consider this in extremes for your projectile at different angles. Assume zero air resistance

Let's say you're on a cliff 45 m high. 2 cases, vertical launch 10 m/s and horizontal launch 10 m/s of the SAME object 1 kg.

In the first case, the horizontal position would be 0. Your projectile lands in the same place. What was the KE when it landed? Still 1/2 mv^2 = 50 J. PE? 450 J. We are not at ground level.

In the second case, the horizontal position would be 30 m away. What was the KE when it landed? Still 1/2 mvr^2 = (r is the resultant velocity when it strikes, which would be found from the x and y components) 500 J. PE? 0 J

Overall the total energy of the system is conserved. Of course in a situation where you are on level ground and launching at different angles, yes the horizontal will change (intuition), but the KE will be the same as long as you use the same initial velocity and mass.

For the football question at hand, I wrote in a previous post. http://forums.studentdoctor.net/threads/ek-phys-1001-and-br-contradiction.988336/#post-15204529

Basically let's assume that the kicker uses his full energy 1000 J to kick the football, he cannot kick any harder (100% elastic collision). What happens if you now change the mass of the football to something heavier? Will that change the range? Yes, because the 1000 J now needs to move a heavier mass. Using conservation of energy, we can intuitively know that the range must be shorter for that heavier mass. Less of the 1000 J is changed to velocity.