12 of 13 Items .... Course: PHYSICS
Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.
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The floor lamp casts a shadow.
Straight line AB is drawn on a wide, spacious floor. A lamp is at a height of 8m above point C, which is located on line AB. Line CD is perpendicular to line AB. A rectangular solid 5m by 3m by 4m is on the floor as shown. The box is 2m from line AB and a meters from line CD. Assume the lamp is a point source and will cast a perfect shadow. Given that the rectangular solid casts a shadow with area \(90m^2\), determine the distance a (in meters).
- Does the 2m distance from the wall matter to the shape of the shadow?
- How does the distance a change the area of the shadow?
- What shape is that shadow on the floor?
- Are the edges of the shadow guaranteed to parallel with the edges of the box?
- How far away is that box from the light?
.: [PHYSICS], [Five Triangles], [Understandings].
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Weights 1lb through 6lbs.
Where should we start?
.: [PHYSICS], [Erich Friedman], [Puzzle].
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Your teenage son has a fast car.
He knows that friction is determined by the weight of the car over the wheels, the "normal" force. He also knows that additional weight means that the car can't accelerate as fast, but he's also having problems with the rear tires spinning out. He's convinced that having Fat Eddie sit in the back will help his quarter-mile time.
Will the extra weight help him or hurt him?
.: [PHYSICS], [T.R.Milne], [The RealWorld].
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Would you rather ...
Which one is "easier"?
.: [PHYSICS], [internet], [Which Would You Choose?].
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Which skier would you rather be?
.: [PHYSICS], [Frank Noschese], [Which Would You Choose?].
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There are three scales.
The one on the right (navy shirt) indicates a 10 N force to the right ... +10 N.
The one on the left (green shirt) indicates a 10 N force to the left ... -10 N.
What will the scale in the middle read?
.: [PHYSICS], [Frank Noschese], [Notice, Wonder].
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A series of identical blocks.
A series of identical rectangular blocks is stacked out at their
balancing points from the top down. You can show with a simple center of mass calculation the total "stick-out" distance; that is, the horizontal distance from the back of the bottom block to the back of the top block is
\( \dfrac{1}{2}(1 + \dfrac{1}{2} +\dfrac{1}{3} +\dfrac{1}{4} + ... ) \)
.: [PHYSICS], [Frank Noschese], [Create a Problem].
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If the weights are all equal masses, is this in equilibrium?
3
If not, how would you change it?
Can this arrangement work if two of the masses are equal and the third is different?
.: [PHYSICS], [T.R.Milne], [The RealWorld].
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So ... is this possible? Or is it a well-done fake?
.: [PHYSICS], [internet], [Sensible?].
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Can you help Calvin understand this?
Do you know what a record looks like?
.: [PHYSICS], [internet], [Notice, Wonder].
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What questions could we ask about this graph of a weightlifter doing his thing?
Some ideas:
Why do the dotted lines seem to be the derivative of the solid ones?
Dotted or solid: which is height and which is velocity?
I like starting out vague - what's the same, what's different between the red and blue cases.
Then can ask about the work done, the average power delivered, the maximum instantaneous power delivered, reflection on how realistic the curve might be. ~Marco
.: [PHYSICS], [Marco], [Modeling].