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

Define a design problem and weigh trade-offs

Grade 11 Science Worksheet - Challenge Me

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

1. 1.

   A barrier may slow a car at most 15 g (1 g = 9.8 m/s²). From 25 m/s, what is the shortest steady crush length, to 0.01 m, Ari?
2. 2.

   A barrier may slow a car at most 20 g (1 g = 9.8 m/s²). From 30 m/s, what is the shortest steady crush length, to 0.01 m, Bo?
3. 3.

   A barrier may slow a car at most 10 g (1 g = 9.8 m/s²). From 22 m/s, what is the shortest steady crush length, to 0.01 m, Esme?
4. 4.

   A 2,400 kg SUV hits the 2.5 m barrier at 25 m/s. Using the model's pattern, what changes, Jun?

   • Deceleration doubles to 25.6 g, and the force doubles to 300 kN
   • Deceleration stays near 12.8 g, but the force doubles to 300 kN
   • Deceleration stays near 12.8 g, but the force halves to 75 kN
   • Deceleration and force both stay at 12.8 g and 150 kN

5. Read this first

   Use this

   Motor model and bench test, 100 W output (example data). Columns: source, input power (W). model, 80% efficient, 125; bench run 1, 138; bench run 2, 141; bench run 3, 140.

6. 5.

   The model says 125 W in for 100 W out. Three bench runs read 138, 141 and 140 W. What do they show, Luz?

   • The real efficiency is about 60%, since it is 60 W below 200 W
   • The real efficiency is about 140%, since the input is bigger
   • The real efficiency is about 71%, below the model's 80%
   • The model is right, and the meter must be reading high

7. Materials for a bracket (example data) (example data)

   material	strength (MPa)	density (g/cm³)	cost ($/kg)
   steel	400	7.8	1
   aluminum	250	2.7	3

8. 6.

   Milo says an aluminum bracket costs 3 times a steel one, since aluminum is $3 per kg. For equal strength, agree or disagree?

   • Disagree: it needs half the mass, so it costs 1.5 times as much
   • Disagree: it needs 0.55 of the mass, so it costs about 1.7 times
   • Disagree: aluminum is lighter, so it costs less than steel does
   • Agree: the price per kg is 3 times, so the bracket costs 3 times as much
9. 7.

   Old motor: 83.5 to 84.5. New motor: 85.0 to 86.5. Noah says the new motor is more efficient than the old one. Do the six runs each support the claim?

   • No: six runs are too few to compare two motors with confidence
   • Yes: the new motor's top run, 86.5%, is above the old one's mean
   • No: the 1.8 point gap is too small to matter for a motor
   • Yes: the ranges do not overlap, and the gap beats both spreads
10. 8.

    Motor B (92%) costs $150 more than motor A (85%). Both give 2 kW for 3,000 h a year at 12¢ per kWh. About when does B repay its extra cost, Ren?

    • About 4.6 years
    • About 2.3 years
    • About 1.2 years
    • About 3 years
11. 9.

    A drone's hover power scales as mass^1.5. Carbon arms cut its mass from 1,000 g to 960 g for $30 more. By how much does flight time rise, Tala?

    • About 6%, since power falls to about 94% of before
    • About 2%, since a $30 part cannot change flight by much
    • About 4%, since mass falls by 4% and flight time follows it
    • About 13%, since power scales as the cube of the mass

12. 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)

13. 10.

    Which line best records the barrier decision in a design report, Zee?

    • B meets 3.0 m and 15 g for a 1,200 kg car; heavier ones are untested
    • B is safest because its 2.5 m crush zone is long and its cost is lowest
    • C is recommended, since its deceleration is lowest at 8 g, whatever the space
    • B meets the 15 g limit, so it is safe for any vehicle