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This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering.
001 (part 1 of 9) 10.0 points Firstly, we might want to know the times at which certain events occur, such as when the cart gets to the end of the track. One way to find this is by editing the condition of the while loop. Currently the condition is set to t < 10 s, but loop conditions are rather flexible. Change the loop condition so that it ends as soon as the cart gets to the end of the track. You can refer to the x, y, and z components of the cart’s position using cart.pos.x, cart.pos.y, and cart.pos.z, respectively. Note that the left and right ends of the track are located at the positions x=- and x=1, respectively. With an initial speed of 5 m/s, how many seconds does it take the cart to reach the end of the track? (We will use this same initial speed throughout the assignment.)
- 0.7s
- 0.3s
- 1.0s
- 0.4s correct
- 0.6s
- 1.7s
- 1.5s
- 0.1s
- 2.0s
- 0.8s
Explanation:
002 (part 2 of 9) 10.0 points Let us investigate the effect of a 10 N net force, F~ = 〈 10 , 0 , 0 〉. What could this force
represent, physically?
- A fan attached to the cart, blowing steadily correct
- Friction due to sliding on the track
- Gravity pulling down (-y direction) on the cart
- A kick given to the cart just as it begins to move
- A spring affixed to the left end of the track and the cart
- The normal force of the track on the cart
- Air resistance on the cart
Explanation:
003 (part 3 of 9) 10.0 points Change your code to use the above force. At what time (in seconds) will cart reach the end of the track?
- 0.56s
- 1.0s
- 0.31s correct
- 0.81s
- 0.24s
- 0.07s
- 0.13s
- 0.62s
- 0.36s
- 0.22s
Explanation:
004 (part 4 of 9) 10.0 points
Now try a 10 N force in the opposite direction, F^ ~ = 〈− 10 , 0 , 0 〉. Which of the following is a complete description of the cart’s behavior over time?
- The cart first moves to the right with a decreasing speed, turns around, then moves to the left with an increasing speed correct
- The cart moves to the right with an in- creasing speed
- The cart moves to the left with an in- creasing speed
- The cart moves to the left with a constant speed
- The cart first moves to the left with an increasing speed, turns around, then moves to the right with a decreasing speed
- The cart first moves to the left with a decreasing speed, turns around, then moves to the right with an increasing speed
- The cart moves to the right with a de- creasing speed
- The cart moves to the left with a decreas- ing speed
- The cart moves to the right with a con- stant speed
- The cart first moves to the right with an increasing speed, turns around, then moves to the left with an increasing speed
Explanation:
005 (part 5 of 9) 10.0 points How long (in seconds) does the cart take to return to its original position? (Hint: You will need to edit the condition of your while loop again.)
- 1.0s correct
- 0.07s
- 0.81s
- 0.24s
- 0.56s
- 0.13s
- 0.22s
- 0.36s
- 0.31s
- 0.62s
Explanation:
006 (part 6 of 9) 10.0 points Which force causes the cart to barely touch the end of track, turn around, and then return to the starting point?
- F~ = 〈− 12 , 0 , 0 〉
- F~ = 〈 2 , 0 , 0 〉
- F~ = 〈 8 , 0 , 0 〉
- F~ = 〈 6 , 0 , 0 〉
- F~ = 〈− 2 , 0 , 0 〉
- F~ = 〈− 8 , 0 , 0 〉
- F~ = 〈 10 , 0 , 0 〉
- F~ = 〈− 14 , 0 , 0 〉
- F~ = 〈− 6 , 0 , 0 〉 correct
- F~ = 〈 14 , 0 , 0 〉
Explanation:
007 (part 7 of 9) 10.0 points Now let us make the cart airborne. We need to change two things in the code to achieve this. First, go to the OBJECT S AN D IN IT IAL
Change your launch angle back to 45 degrees. Which of the following is observed?
- The cart continues to move in the +x direction with constant velocity
- The cart begins by moving in the +x and +y directions, then moves in the -x and +y directions at the time of impact
- The cart begins by moving in the +x and +y directions, then moves in the +x and -y directions at the time of impact
- The cart continues to move in the +y direction with constant velocity
- The cart begins by moving in the +x and +y directions, then moves in the +x and +y directions at the time of impact
- The cart begins by moving in the +x and +y directions, then moves in the -x and -y directions at the time of impact correct
- The cart’s speed is constant, but its di- rection changes
Explanation:
012 (part 3 of 6) 10.0 points At what angle (approximately) must the cart be launched so that pf x = 0?
- 33
- 73
- 82
- 53
- 66
- 16
- 59
- 26 correct
Explanation:
013 (part 4 of 6) 10.0 points Do you think there is any other angle between 0 and 90 degrees at which pf x = 0? (Hint: How does the angle affect flight time? How does flight time affect pf x?)
- Yes
- No correct Explanation:
014 (part 5 of 6) 10.0 points All of the above questions can also be worked out analytically because constant forces pro- duce relatively simple motion. However, it is easy to modify our program to produce trajectories that cannot be solved for analyt- ically, which is one of the main reasons we are interested in iterative computer model- ing. One very common day-to-day example of a non-constant force is air resistance, since it depends on the velocity at which an object is moving. In the ideal case, air resistance is proportional to v^2 and is directed opposite to the direction of motion. Let us assume for the time being that the constant of proportional- ity is 1. Thus, F~air is given by
F^ ~air = −|~v^2 |ˆv = −|~v|~v
In VPython, this statement reads
F air = −mag(cart.p/cart.m)∗cart.p/cart.m
Set your F net equal to the sum of F grav and F air (no fan force), then reset your launch angle to 45 degrees. Which of the following pairs of statements is true?
Is the resulting trajectory spatially symmetric like the parabola due to gravity alone? Ia. Yes
Ib. No
IIa. | p~f | > |p~i| IIb. | p~f | < |p~i| IIc. | p~f | = |p~i|
- Ia, IIb
- Ia, IIa
- Ib, IIc
- Ib, IIa
- Ib, IIb correct
- Ia, IIc
Explanation:
015 (part 6 of 6) 10.0 points We will now use our model to answer a subtle question. In introductory physics, it is often taught that if one bullet is shot horizontally from a gun and another bullet is dropped from the same height at the same instant, the two bullets will hit the ground at the same time. This is certainly true in the absence of air resistance, since the motion in the y direction is completely independent of the motion in the x direction. However, is this statement still true in the presence of air resistance? We can easily use our model to find out. In the OBJECT S AN D IN IT IAL V ALU ES section of your code, edit the cart’s position so that it starts at a height of 1 m. Its position should be pos = vector(− 1 , 1 , 0). Now set your initial velocity to 5 m/s at 0 degrees. Run the program and record the time taken to hit the ground. Finally, set your initial velocity to 0 m/s at 0 degrees and again record the time taken to hit the ground. What are the two times in seconds? [If you have time, you may want to remove Fair from the model to verify that the dropped and shot times are the same without air re- sistance; they will be. The explanation for the result you have deduced is that the mo- tion in the x and y directions are coupled.
In other words, they depend on one another. Therefore, the horizontal speed of the bullet affects the vertical air resistance force, leading to different times for the shot versus dropped bullets.]
- tshot = 0. 02 s, tdropped = 0. 35 s
- tshot = 0. 42 s, tdropped = 0. 42 s
- tshot = 0. 78 s, tdropped = 0. 94 s
- tshot = 0. 28 s, tdropped = 0. 11 s
- tshot = 0. 77 s, tdropped = 0. 15 s
- tshot = 0. 87 s, tdropped = 0. 87 s
- tshot = 0. 57 s, tdropped = 0. 53 s correct
- tshot = 0. 73 s, tdropped = 0. 73 s
- tshot = 0. 02 s, tdropped = 0. 47 s
- tshot = 0. 51 s, tdropped = 0. 55 s Explanation:
