11th grade Define a design problem and weigh trade-offs worksheet

Define a design problem and weigh trade-offs

Grade 11 Science Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   A motor lifts a 120 kg load at 0.5 m/s and is 75% efficient. With g = 9.8 m/s², how much power does it draw, Bo?
2. 2.

   A motor lifts a 30 kg load at 1.5 m/s and is 60% efficient. With g = 9.8 m/s², how much power does it draw, Esme?

3. Read this first

   Crash-barrier designs for a 1,200 kg car at 25 m/s (example data)

   design	crush length (m)	cost ($ thousand)
   A	1.5	40
   B	2.5	55
   C	4	80

   Limits: crush length at most 3.0 m and deceleration at most 15 g, where g is 9.8 m/s². Constant deceleration is v² ÷ (2d)

4. 3.

   Using the table, which is the cheapest barrier design that meets both limits, Jun?

   • C, since its 78 m/s² is the lowest deceleration of the three
   • B, since its 125 m/s² is under 147 and its 2.5 m fits
   • No design, since no crush length can meet both of the limits together
   • A, the cheapest, since its 1.5 m crush zone fits easily in the space

5. Motors rated for the same job (example data) (example data)

   motor	efficiency (%)	mass (kg)	cost ($)
   P	88	1.2	120
   Q	88	1.5	140
   R	82	0.9	100

6. 4.

   Using the table, which motor can be dropped whatever the weights, Luz?

   • R, since its efficiency is the lowest of the three motors
   • Q, since P matches its efficiency with less mass and lower cost
   • P, since it does not top the table on each column at once
   • No motor, since any motor can win under some choice of the weights
7. 5.

   A pump needs 500 W of output. Motor B (80%, 0.5 kg) replaces motor A (90%, 1.0 kg). What does B trade away, Milo?

   • About 7 W more input power, to save 0.5 kg of mass
   • About 50 W more input power, to save 0.5 kg of mass
   • About 69 W more input power, to save 0.5 kg of mass
   • About 10 W more input power, to save 0.5 kg of mass

8. Crash-barrier designs for a 1,200 kg car at 25 m/s (example data)

   design	crush length (m)	cost ($ thousand)
   A	1.5	40
   B	2.5	55
   C	4	80

   Limits: crush length at most 3.0 m and deceleration at most 15 g, where g is 9.8 m/s². Constant deceleration is v² ÷ (2d)

9. 6.

   A team says barrier B is safe because it stops a 1,200 kg car in 2.5 m. B's average force is 150 kN. What is the flaw, Noah?

   • It was tested at one mass; at 150 kN a 3,000 kg SUV needs 6.25 m
   • Nothing is missing, since 2.5 m is under the 3.0 m limit for space
   • The speed of 25 m/s was not given, so the test says little
   • It should have used a lighter car, since light cars crush more
10. 7.

    A designer doubles a barrier's crush length from 1.5 m to 3.0 m. What changes, Pia?

    • Deceleration stays the same, but cost doubles
    • Deceleration falls to a quarter, with the same road space
    • Deceleration falls by a third, but it needs half the space
    • Deceleration halves, but it needs twice the road space

11. Stopping distance of a car on two tire compounds, five trials each (m) (example data)

    trial	compound X	compound Y
    1	24.1	23.2
    2	23.8	24.9
    3	24.5	22.8
    4	24	24.6
    5	24.3	23.5

    Mean X is 24.14 m with a spread of 0.7 m. Mean Y is 23.8 m with a spread of 2.1 m.

12. 8.

    Ren claims compound Y stops the car in a shorter distance. Does the table support that claim?

    • No: X's trials vary less, so X must be the better compound
    • Yes: five trials are enough to show any difference
    • Yes: Y's mean is shorter and it holds the single shortest stop
    • No: the 0.34 m gap is smaller than Y's 2.1 m spread

13. First test of a barrier with a 2.0 m crush zone (1,200 kg car at 25 m/s) (example data)

    measure	result	limit
    crush length (m)	2	at most 3.0
    deceleration (g)	15.9	at most 15

14. 9.

    A 2.0 m crush zone gave 15.9 g, over the 15 g limit. Which single next change should Tala test?

    • Change the zone length and the car's mass together
    • Shorten the zone to save road space and rerun the same test
    • Raise the limit to 16 g so that the first test passes
    • Lengthen the zone to about 2.5 m and rerun the same test
15. 10.

    The spec says at least 80%. The mean is 80.8% and the spread is 7 points. The spec says the motor is at least 80% efficient. Does the table clearly support it, Zee?

    • Yes: its top run reached 84%, which is well above the 80% spec
    • Not clearly: two runs fall under 80% and the spread is 7 points
    • No: two runs fell below 80%, so the motor fails the spec outright
    • Yes: the mean of 80.8% is above the 80% that the spec asks for