Motion Diagram

I Love Pi

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Hello! The problem and my solutions are attached below. The values I measured from my experiment are in blue to help keep track of the known data. I am to calculate 4 of the 5 variables.

I am uncertain about the values that I solved for. When I solved for delta t, I found initial time 1, final time 1, initial time 2, and final time 2, however I am uncertain if I solved for too many values of time. Similarly, I found initial velocity 1, final velocity 1, initial velocity 2, and final velocity 2, however I suspect I solved for too many values of velocity. At the same token, I am unsure how else to solve for delta t and the velocity because the motion of the toy car changes.

Also, I am 95% certain that I cannot solve for acceleration because there the toy car is moving at constant velocity. Please let me know if I can even solve for acceleration.

I struggled determining velocity final 2. Although velocity final 2 is at rest, I suspect the toy car still has momentum from the fall and therefore still has a velocity greater than 0. I am a bit confused.

I would really appreciate critiques to my attempt at solving this problem. Thank you SO much!
 

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topsquark

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Hello! The problem and my solutions are attached below. The values I measured from my experiment are in blue to help keep track of the known data. I am to calculate 4 of the 5 variables.

I am uncertain about the values that I solved for. When I solved for delta t, I found initial time 1, final time 1, initial time 2, and final time 2, however I am uncertain if I solved for too many values of time. Similarly, I found initial velocity 1, final velocity 1, initial velocity 2, and final velocity 2, however I suspect I solved for too many values of velocity. At the same token, I am unsure how else to solve for delta t and the velocity because the motion of the toy car changes.

Also, I am 95% certain that I cannot solve for acceleration because there the toy car is moving at constant velocity. Please let me know if I can even solve for acceleration.

I struggled determining velocity final 2. Although velocity final 2 is at rest, I suspect the toy car still has momentum from the fall and therefore still has a velocity greater than 0. I am a bit confused.

I would really appreciate critiques to my attempt at solving this problem. Thank you SO much!
I didn't check the numbers but, for the most part, it looks okay. A couple of comments:
1) Break the problem into two parts, the table and the fall. Don't worry about mixing times or speeds or accelerations between the two. They are motion under two different accelerations.

2) Overall, the x-component of the total displacement is 0.749 m. You didn't include the y portion of the displacement so you need to say that.

3) On the table: w = mg is the weight of an object. It does not matter what its acceleration is. The weight will always use g.

4) The acceleration in free fall is g downward. The x-component of this acceleration is 0 m/s^2 and the y-component is -9.8 m/s^2 (assuming +y upward.)

5) Free fall: Yes, since we only care about how long it's in free fall you subtract the two times.

6) Free fall: A common mistake students make about free fall is to take the final speed of the object to be 0 m/s if the object hits the ground. Yes, it's not moving. But that's after free fall is over with and you have had a collision. Collisions are another part of the problem. You care about the free fall motion so don't set vf = 0 m/s. You want the speed of the object just before it hits the ground.

7) Free fall: Similar to the displacement comment. The component of the final velocity in the y direction is -24.52 m/s. You need to say that because you have not included the x-component into this figure.

8) What are you trying to do on the last page? You already know that the x-component of the acceleration in free fall is 0 m/s^2 so you already know that the x-component of the final velocity is the same as the initial. (Again, do not set vf = 0 m/s. All you care about is while the object was in motion.)

-Dan
 

I Love Pi

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Okay, first of all, you are absolutely amazing! Thank you so much for your help!

1. I broke the problem into two parts. 👍 Thank you for the clarification.

2. On page two, I made my chart of the known data more elaborate. [The chart includes the (m), y portion of displacement (deltay), x portion of displacement on table (deltax1), x portion of displacement on ground (deltax2), total displacement (deltax1+deltax2=deltaxtotal), intial velocity 1 (vi1), initial time 1 (ti1), final time 1 (tf1), initial time 2 (ti2), and final time 2 (tf2)]. Two questions: a.) Is deltay= - 0.875 m because the toy car descends downward toward the ground? b.) Will I need to use the y portion of displacement for any of my other calculations?

3.👍 Thank you for the clarification. This makes sense.

4. 👍 Thank you for the clarification. This makes sense.

5. 👍 Thank you for the clarification. This makes sense.

6. 👍 Thank you for the clarification. So my value of Vf2=-24.52 m/s is the speed of the toy car just before it hits the ground.

7. a.) When you say “you have not included an x component”, are you referring to the fact that I did not draw a velocity vector in my free body diagram? b.) If I drew a velocity vector pointing right in my free body diagram of the toy car in free fall, would Vf2 be a positive value? c.) Would Vf1 and Vi2 which are both 25 m/s be positive or negative if Vf2 is negative? Is there a correlation between the two?

8. My apologies. That was work that I felt was irrelevant and accidentally included. I discarded of that.

9. a.) I am still confused on the x portion of my acceleration when the car is on the table, mainly because ax=2403.85 m/s^2 seems too large of a number to be a realistic acceleration of the toy car. b.) Concurrently, if the acceleration of 2403.85 m/s^2 is unrealistic, then my calculations for vf1, vi2, and Fa may be unrealistic as well.

Please feel free to critique my work!

I know this is a lot. Thank you so much for your patience with me! Your help is GREATLY appreciated!
 

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topsquark

Senior Member
Joined
Aug 27, 2012
Messages
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Okay, first of all, you are absolutely amazing! Thank you so much for your help!

1. I broke the problem into two parts. 👍 Thank you for the clarification.

2. On page two, I made my chart of the known data more elaborate. [The chart includes the (m), y portion of displacement (deltay), x portion of displacement on table (deltax1), x portion of displacement on ground (deltax2), total displacement (deltax1+deltax2=deltaxtotal), intial velocity 1 (vi1), initial time 1 (ti1), final time 1 (tf1), initial time 2 (ti2), and final time 2 (tf2)]. Two questions: a.) Is deltay= - 0.875 m because the toy car descends downward toward the ground? b.) Will I need to use the y portion of displacement for any of my other calculations?

3.👍 Thank you for the clarification. This makes sense.

4. 👍 Thank you for the clarification. This makes sense.

5. 👍 Thank you for the clarification. This makes sense.

6. 👍 Thank you for the clarification. So my value of Vf2=-24.52 m/s is the speed of the toy car just before it hits the ground.

7. a.) When you say “you have not included an x component”, are you referring to the fact that I did not draw a velocity vector in my free body diagram? b.) If I drew a velocity vector pointing right in my free body diagram of the toy car in free fall, would Vf2 be a positive value? c.) Would Vf1 and Vi2 which are both 25 m/s be positive or negative if Vf2 is negative? Is there a correlation between the two?

8. My apologies. That was work that I felt was irrelevant and accidentally included. I discarded of that.

9. a.) I am still confused on the x portion of my acceleration when the car is on the table, mainly because ax=2403.85 m/s^2 seems too large of a number to be a realistic acceleration of the toy car. b.) Concurrently, if the acceleration of 2403.85 m/s^2 is unrealistic, then my calculations for vf1, vi2, and Fa may be unrealistic as well.

Please feel free to critique my work!

I know this is a lot. Thank you so much for your patience with me! Your help is GREATLY appreciated!
Something I forgot to mention in my first reply. You have a force diagram for when the object is in free fall. What forces are on the object? Only one: the weight. We know that there can be no normal force because the object isn't sitting on anything! Notice that when you found your sum of forces in the y direction you said that it was not accelerating. But it is! It's accelerating downward at 9.8 m/s^2. Be sure that you understand this point.

1) I checked your numbers for the motion along the table. It looks like the "push" the object is given is more like a "slap." Your numbers are right.

2) Okay, basic vectors. The velocity of an object is how fast it is moving and in what direction. The magnitude of this quantity is called the speed. When you calculated the "speed" that the object is at just before it hits the floor you have calculated the y component of its velocity, not the speed. That component is negative because it is pointing downward. If you were to report the final speed you would have to vectorally add the x-component of the velocity to it. Displacement is also a vector. Please reveiw these topics to make sure you understand them.

3) You calculated the change in speed of the x-component of the velocity. Please note, once again, that you have no acceleration component in the x direction! You do not expect this component to change in value. There is no need to do this calculation. And you should have something very close to your initial component so something is wrong there. Check the numbers on that one. Experimentally you won't get exactly 25 m/s but it should be close.

4) Seeing as you have apparently defined the +x direction to be to the right, and the initial velocity component is pointing to the right, what sign should it have?

-Dan
 
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