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What do you think your students should know about Newton’s second law? How will they learn it? How will you assess them? Make sure that your assessment addresses typical student difficulties

• What do you think your students should know about Newton’s second law?

• How will they learn it?

1. Qualitative Cycle

2. Quantitative Cycle

Equipment: rollerblades, backpack, lots of books, very light weight elastic tubing, a medicine ball, beanbags.

Note: For the following experiments, the teacher will be in roller blades.

Experiment 1: Attach one end of the tubing to a sturdy object that is about waist height (ex: a door knob). The teacher will be holding on to something that will not move. A student stretches the tubing and hands it to the teacher. Part 1: The teacher lets go. And the students watch the tube pulling her until the line goes slack and she costs at constant speed. Ask students to describe the motion. They should say that Part 2: Repeat the experiment with two or three elastic tubes. Now ask the students to compare her motion with that in part 1. The students should say that when there were more tubes pulling on her, she speed up faster and traveled at a greater constant speed when the lines went slack.

''Experiment 2:'' Now instead of the elastic cords we will use a medicine ball. Part 1: The teacher is pushed by one student and goes at a constant speed. A second student throws the ball lightly at the teacher. Ask the students how the teacher’s motion changed when she caught the ball. They should describe both the motion of the ball and the teacher. The ball changed direction. The teacher slowed down as she caught the ball and then traveled at a constant speed. Ask the students what applied a force to what (i.e. why did the teacher’s or ball’s motion change?). Part 2: Repeat part 1 with the ball being thrown harder. Ask the students how the teacher’s and ball’s motion differed from part 1. They should say the she slowed down more and the ball did not go as fast in the opposite direction.

Explanation: Two ways: First Way: For each experiment have the students work in groups of two to drawl free body diagrams and motion diagrams. For experiment one a diagram should be drawn for the period when the tubing was taut and one for when it was loose. For the medicine ball experiment, a free body diagrams should be drawn for the moment the ball is caught and for the period after the ball is caught. For each experiment ask “What was the direction of motion?”, “What was the direction of delta v?” and “Was there acceleration?”. If the students say there is no acceleration remind them of the previous lesson on the equations of motion. Otherwise ask “In what direction was the acceleration?”, and “What affects the acceleration and how does it affect acceleration?”. The students will work in groups to answer the first 3 questions and then discuss them with the teacher. Then the students will answer the last two questions in groups. The students should realize that as the net force increases the acceleration increases and visa versa. If they do not realize that it is the net force, have them take a look at their free body diagrams and ask if there is only one object acting on the teacher. Second Way: Ask the students to work in groups to create an explanation. Ask the following questions, “What affects the acceleration of the teacher or ball?”, and “How does it affect the motion of the teacher or ball?” The students should get that the rubber tubing and the ball apply force to the teacher, and the teacher applies force to the ball. From this they will deduce that force is proportional to acceleration. This however is not correct. Have the students draw free body diagrams for each experiment in the same manner as described in “way 1”. Ask if there is only one object acting on the teacher. The students should change their explanation to account for multiple forces. Explanation: The acceleration increases as the net force increases and visa versa. (Note force and acceleration are vectors that point in the same direction.) Acceleration is in the direction of the net force. Testing Experiment: This experiment requires three bobs each of different mass. Call them m1, m2 and m3. You will also need a cord and a suspended pulley. The idea is to have two bobs hanging over the pulley. Have the students weigh m1, m2, and m3 to find the force the earth exerts on the bobs. Make sure m2>m1 and m3<m1. The students will use their explanation to predict which way m1 will accelerate when it is paired with m2 and when it is paired with m3. Will it accelerate faster for m2 or m3? The students should work in groups and draw free body diagrams to help them figure out the net force. Run the experiment to see if the predictions are true.

[[ Observation Experiments:]]

Experiment 3: Repeat experiment 1 with a few modifications. Instead of varying the number of tubes, vary the weight of the backpack that the teacher wears. Students should notice that the teacher does not speed up as fast when the backpack is heavier.

Experiment 4: Repeat experiment 2, but do not vary how hard the medicine ball is thrown. Instead vary the weight of the back pack. Students should notice that the teacher moves slower after catching the ball when the back pack is heavier.

Explanation: Ask the student to work in groups to determine which quantities are changing and how the change in one affects the other. They should say that as the mass increases the acceleration decreases and visa versa. Testing Experiment: As with the last testing experiment, we will work with bobs hanging from a pulley. This time however, the students will add mass to one side of the system. That is if m1, and m2 are hanging from the pulley for the first drop, then for the second run m1[[ and m3 will hang from the one side and m2 from the other. Have students predict the outcome.

Quantitative Cycle:]]

Experiment 1: Video of cart, spring scale and hanging bob. Have your students record data in groups of two. They need to record the position, clock reading and scale reading. Students will use this data to find a relationship between net force and acceleration.

Experiment 2: Video of cart with fan and various masses. Have the students record the weight of the mass, the clock reading and position. Each group may pick one of the three masses to save time.

Explanation: Before the students can create an explanation, they need to do some calculations. For experiment 1, the mass of the cart was constant and the force was varied. In order to find the relationship between force and acceleration, students need to calculate the acceleration and determine the net force. To calculate the acceleration students will use the graphical approach. That is they will find the velocity for 1s time intervals and then plot v vs. clock reading. They will then find the slope which is the acceleration. If students do not remember the steps involved in finding acceleration this way, then remind them of the lessons on deriving the equations of motion. Their answers can be checked using the equations of motion. How is acceleration related to force? Have students compare the acceleration and force for all of the different hanging bobs. Ask students to recall their observations form the qualitative experiments above. Students should notice that acceleration equals a constant times the force. For experiment 2, students follow the same process as they did for experiment 1 for finding acceleration. Now the students however are comparing mass to acceleration. Students should notice that as the mass increases, the acceleration decreases. Have the students work in groups to figure out that acceleration is proportional to 1/m. Explanation: Have the students put the results of the analyses of experiments 1 and 2 together. They should get the following: a = net force/ mass.

Testing Experiment: Use a cart with a spring scale attached to either side. Attach a hanging bob to each spring scale. (Bobs should not have the same mass.) Knowing the force that each mass exhorts on the cart and the mass of the cart, have students predict the acceleration. Have the students collect the clock reading and position readings foe the experiment so they can calculate the acceleration. Does this match the predicted acceleration?

Represent and Reason: Part 1: (a) Write a description: A 1000kg elevator is moving down ward and slowing down. (b) Sketch the situation; the system object is circled: (c) Draw a free body diagram with perpendicular axes; label the forces if needed. (d) Draw the direction of the acceleration and of the net force. Are they consistent? (e) Write Newton’s law in component form.

Solution: x: 0/ 1000kg = ax Y: if the down direction is positive (9.8 m/s^2)*1000kg – Fc on el = 1000kg*ay ; ay <0 Part 2: (a) Write a description: A 1000kg car is being pulled out of a dry lake by the mechanical crank. The bank of the lake makes a 30 degree angle with the horizon. Assume no friction. (b) Sketch the situation; the system object is circled: (c) Draw a free body diagram with perpendicular axes; label the forces if needed. (d) Draw the direction of the acceleration and of the net force. Are they consistent? (e) Write Newton’s law in component form. Solution: X: (F crank on car)*cos30 – (F ground on car)*sin30 = 100kg* ax

```              Y: - Fe on car +(F crank on car)*sin30 +(F ground on car)*cos30 = 0
```

Equation Jeopardy: Part 1: (a) Mathematical description. x: (10N – 22N)/0.5kg = ax y: (9.2N – 9.8N) / 0.5kg= ay (b) Sketch a situation the equation might describe. (c) Write a problem for which the equation is a solution.

Solution: You are- fishing and you catch a fish. The fish swims away from you. The fish applies 22N of force to the lore. The maximum force that your reel can exert on the lore is 10N. How fast is your lore accelerating away from you? Part 2: (a) Mathematical description. X: (20N*(cos45) – 0)/7kg = ax Y: 9.8(m/s)*7kg- 20N*sin45 – Fy on o = 7kg*(0 m/s^2) (b) Sketch a situation the equation might describe. (c) Write a problem for which the equation is a solution.

Solution: A 7 kg sled is dragged through the snow. The child pulling the sled exerts 20N of force on the sled at an angle of 45 degrees above the horizon. How fast is the sled accelerating? How hard is the ground pushing up on the sled? Evaluate the Solution: Exercise 3.4.9 in the Active Learning Guide: This exercise was chosen because it tests the student’s understanding that an object’s acceleration is due to the net force. It also tests the student’s knowledge of the relationship between the direction of net force and acceleration. • Typical Student Difficulties:

Students may think that only moving objects induce force. That is things like the earth do not induce force and they do not consider friction to be a force.

Students often think that forces always influence an objects motion.

Students may also believe that force is a quantity that is carried by an object and keeps the object moving until it is used up. Hence if there is no force on an object then it has to be at rest.

Students confuse velocity, acceleration and distances.

Students focus on the object that is applying force, and so miss some of the forces on the object in question For the cart experiments, the students may think that the scale reads the weight of the hanging bob.

Students have difficulty determining what is in a system and what is not. Difficulties include using an appropriate coordinate system, placing the tips of force arrows at the origin (makes it difficult to determining Fnet), identifying forces and identifying components of forces. F=ma Students think weight is a property of an object.

Students may have difficulty with free body diagrams.