TBR Physics Chapter 1 Problem 24

[RocketSurgeon]

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Hi!

I kinda stumbled chapter 1 problem 24 in TBR. Would really appreciate any insight and a clearer explanation. I think I'm missing something. This is a d

24. While an air cart is moving up and then down an inclined air track the magnitude of the acceleration:

1. the cart experiences on the way up is only half as much as the magnitude of the acceleration it experiences on the way down.
2. on the way up is necessarily different than the magnitude of the acceleration on the way down.
3. has the numerical value of the magnitude of the acceleration due to gravity, g.
4. on the way up is the same as the magnitude of the acceleration on the way down.

The answer according to TBR is D. At first glance I agreed but the more I think about it it does not make sense. Their logic is that the acceleration is constant since the only acceleration is due to gravity.

But the only way the cart would oscillate is if the cart has some force pushing it up. Otherwise, it should just roll down right?. Okay, so this force has to be greater on the way up because you are fighting gravity i.e. acceleration up is really = (acceleration due to the force by the cart) - (acceleration due to gravity). However, acceleration on the way down is really = (acceleration due to the force by the cart) + (acceleration due to gravity). So the force is different in both directions. But this is only because the essentially the internal force of the cart wanted it to be that way. If the force in the up and down direction were the same the cart would move up by y and down by y+epsilon where epsilon is the extra distance covered by the cart because the acc. in the downwards direction is slightly larger than the acc. in the up direction.

Maybe my engineering brain has overcomplicated this problem! Help appreciated. :/

 

[brood910]

Hi!

I kinda stumbled chapter 1 problem 24 in TBR. Would really appreciate any insight and a clearer explanation. I think I'm missing something. This is a d

24. While an air cart is moving up and then down an inclined air track the magnitude of the acceleration:

1. the cart experiences on the way up is only half as much as the magnitude of the acceleration it experiences on the way down.
2. on the way up is necessarily different than the magnitude of the acceleration on the way down.
3. has the numerical value of the magnitude of the acceleration due to gravity, g.
4. on the way up is the same as the magnitude of the acceleration on the way down.

The answer according to TBR is D. At first glance I agreed but the more I think about it it does not make sense. Their logic is that the acceleration is constant since the only acceleration is due to gravity.

But the only way the cart would oscillate is if the cart has some force pushing it up. Otherwise, it should just roll down right?. Okay, so this force has to be greater on the way up because you are fighting gravity i.e. acceleration up is really = (acceleration due to the force by the cart) - (acceleration due to gravity). However, acceleration on the way down is really = (acceleration due to the force by the cart) + (acceleration due to gravity). So the force is different in both directions. But this is only because the essentially the internal force of the cart wanted it to be that way. If the force in the up and down direction were the same the cart would move up by y and down by y+epsilon where epsilon is the extra distance covered by the cart because the acc. in the downwards direction is slightly larger than the acc. in the up direction.

Maybe my engineering brain has overcomplicated this problem! Help appreciated. :/

A constant force must be applied to make what you are saying true.

They are talking about acceleration AFTER the force is applied.
After that, only force on the cart is the gravitational force.

 

[RocketSurgeon]

Thanks @brood910

Okay so the bit I am still confused about this. Let's make this problem a bit simpler the cart is now only moving in the y direction. Let the oscillation point be x. The cart oscillates between x+h and x-h. For the object to go up to height x+h the force upwards F_up (this is ma) has to be greater than force downwards F_down (this is mg). Similarly, on the way down F_down > F_up should hold true.

F_up = ma
F_down = mg

So this means on the way up

F_up > F_down
=> ma > mg

So this means on the way down

F_down > F_up
=> mg > ma
(note the two a values cannot be the same lets call them a_1 and a_2)

Since the object is oscillating. There is no net acceleration |ma_1-mg| == |ma_2-mg|. So at this point I buy that the magnitude of the a_1 ad a_2 is the same but this has nothing to do with gravity since 'a' could hold any value and the relationship above would hold.

 

[brood910]

You are overthinking this.

Think about kinematics.
After you throw a ball upward, what acceleration do you use to solve for flight time, etc? gravity.

 

[RocketSurgeon]

Yup haha I'm def over thinking this! I'm going to move on I need to study orgo!