[Once again, there’s way too much I want to do here, and will need to think about how to scale back]
Constant Force Warm-Up?
Students have warm-up with a “square” force vs. time pulse (constant over a time interval). Given initial velocity, they have to calculate final velocity using Newton’s Laws and Kinematics.
Edit: I may split groups into two warms up… different width / height pulses with same impulse. Why did these two force scenarios result in same change in velocity?
Introduce Jump off the Force Sensor:
Orient students to how shape of graph (being constant) force allowed us to assume the acceleration was constant. Tell them I want to show them a force vs. time graph for a real world situation– me jumping off the force sensor. I want to ask them about what they notice about the graph, but before hand I want them to think about what they might expect to see.
I will show them the jump first without the force sensor data (it will be a shallow knee bend and then jump), and ask them to draw a motion diagram and free-body diagram for three stages.
Edit: well Ss work on this, I will encourage them to do jumps and talk about it.
- At Rest on the sensor (before attempting to jump)
- Jumping but still in Contact with the
- In the air, before hitting the floor.
Then I will show them the Force vs. Time Graph. Question will be, “What do you notice about the shape of the graph?” Lot’s to notice and talk about here.
Edit: why did value start where it did? Why did the value go up? Why did the value drop to zero?
Brief Direct Instruction: Impulsive Forces
Introduce concept of impulsive forces with a few examples, and some features of impulsive forces:
- Often involve relatively large contact forces between two objects
- Magnitude of the forces rises and then falls
- Often occur over short periods of time
- Maximum force often occurs at maximum compression
- Shape of the graph is non-constant and can be complicated.
I have a few clicker questions about to apply these ideas to the jump if I feel it’s needed:
- Where on the graph did I lose contact with the scale?
- Where on the graph did maximum compression of scale occur?
- Where on the graph might I have been at my highest point?
Deep Knee Jump Discussion:
Students are going to be asked how the force vs. time graph might be different for a deep knee jump. Once again, show them without the reading. I could ask them to free-hand sketch, which I think, but I will use a clicker question to say, “Which of these does your graph best resemble?).
We will discuss and then observe. Key idea for discussion after is, “How did I jump higher with the deep knee bend even though the maximum force was less?” Key in on the idea of time.
Brief direct instruction to show how force vs. time graph allows us to see two things at once, how much force and for how much time.
Apply Idea of Force vs. Time to Landing on the Scale:
This time I’m going to jump down onto the scale from same height. Once by doing a heal landing with no knee bending, and another by doing a toe landing with knees bending. Students will be asked to whiteboard important features of how the graphs will be similar and different. Students discuss and then we observe.
Direct Instruction: Representing and Interpreting Impulse
I will either lecture or students will do a close reading of a section on impulse as the area under a curve, followed by some direct instruction to clarify. A big goal I have here is how the impulse takes into account both the of variables that matter (how much force and for how long), but then also scaffold how to interpret the impulse number.
I want to show them that the area under both jumps was the same. That makes sense since the same job had to be accomplished — either way, I fell from same height with same speed, so the job that had to be done was stopping my fall. I will have to guide here strongly, but the idea is that number is how much force would be needed over 1.0 s to get the same result. That another way of stopping me would be to exert a constant force throughout 1.0s = to impulse number in N.
Short Practice Exercise (Hand Calculation):
Students will then have a triangle pulse to calculate the impulse for, to interpret the number, and then draw a different shape graph that was same impulse delivered over half the time.
Short Practice (Logger Pro Calculation):
Students will crash a cart into wall with a stiff bumper and squishy bumper, and calculate impulse delivered to cart. Guiding question will ask them to predict how shape of the force vs. time graphs will be similar / different? [Photogates are not for careful measurement now, but for making sure incoming velocity is same across trials).
What effect to impulse have? Jumping Animals and Marshmallow Blow Guns
From the reading, they talk about how animals that are good jumpers have long legs. Help them relate this to “extending the amount of time”. Just the idea that if you want to deliver a lot of impulse, sometimes it’s easier to extend the time rather than increase the force. But increasing the force is always an option as well.
Show the Marshmallow blow gun. Remind them how with projectile motion we often just assumed that projectiles “started” with some initial velocity. We ignored how they got that initial velocity. Watch I use this blow gun to deliver an impulse to the Marshmallow so it projectiles off with some initial velocity.
Ask students: What could I change about the blow dart gun so that the marshmallow shoots at a higher velocity? Ask why, but also how is consistent with what we’ve learned today about impulse? (Blow harder to increase force, or make a longer tube to increase the time). Let students play for a bit.
Is it possible to use a weak force and a hard force and get the same velocity? How?
Now ask students: What do you think will be different if I deliver the same impulse to a marshmallow that is twice as heavy (two in the gun)… Let them go observe.
We need to draw out two big ideas here:
There are many different ways to deliver the same impulse, and have same end result (if object is same).
The same impulse delivered to a more massive object, however, results in less change to velocity:
I will either have them do a careful reading or brief lecture on Impulse-Momentum Theorem. Key here is to connect lecture and /or reading to our activities.
Clicker Questions to Practice Applying Idea:
One problem that shows force vs. time graph… ask about change in momentum. Then ask, how much velocity that would translate into for 1.0 kg object, 2.0 kg, 0.5 kg?
One problem that shows a cart rebound off a wall, ask how much impulse was delivered? This will be very similar to quick lab exploration they did, so may do as a demo as well.
Problem-Solving (New Skill in Isolation):
Impulse delivered to a baseball hit off end of the bat? Draw possible force vs. time graph
Impulse delivered to a passenger colliding into a wall: Draw force vs. time graph for hitting dash vs. hitting the air bags. How similar / different?
Challenge Problem for Next Time (New Skill Integrated into Broader Skill Set):
Launch marshmallow gun horizontally and mark the landing location. Work backwards to find the impulse delivered!