SWBAT explain the forces that act on an object on a slope and the acceleration that results and create a model representing motion on a slope in a velocity over time graphs.

Motion on a slope can be difficult to explain. This lesson makes it easy to understand.

Our world is seldom completely level; more often than not objects are moving in more complex ways. In this lesson students expand their understanding of motion by looking for patterns in how a ball moves up and down a slope.

Goals for the lesson

- Understand the forces that act on an object on a slope and the acceleration that results.
- Understand how to represent motion on a slope in a velocity over time graph.
- Understand where F=ma is in motion on a slope.

Materials

- Ball
- Ramp
- Masking tape
- Spring scale
- Sandwich bag, clip, string
- Computers, transparencies, pens

5 minutes

Ask students to think about the following scenario.

*Imagine, a car parked on a hill. In your journal create a diagram adding all the forces and their corresponding vectors for this scenario. When you are finished, turn and talk to your neighbor about your ideas.*

If you have individual whiteboards, you might want to use those for students to record their ideas then have them hold up the diagrams and share with the class.

Do not correct any misconceptions at this time. Simply engage students in thinking about the focus for this lesson.

20 minutes

Students investigate Gravity: Motion on a Slope (part 3), using the following four scenarios:

- Ball rolling down the shallow ramp from the starting point.
- Ball rolling up the shallow ramp to the starting point and back down.
- Ball rolling down the steep ramp from the starting point.
- Ball rolling up the steep ramp to the starting point and back down.

**Setup:** Mark a "starting line" about 3/4 of the way up each ramp with a piece of masking tape. This is better than using a pen since you can move it if you need to.

They need to create two ramps, one steeper than the other. The greater the difference between the ramps, the more they will be able to see a difference in the ball's motion.

*Find two wedges—one thin and the other thick (e.g., a regular book and a 3-ring binder book)—to lift the top of the ramp. You may want to tape the end of the ramp to the table so it doesn't slip out of place when you make it more or less steep.*

Students begin with predictions in their investigation of the scenarios.

**Predict** the motion of the ball by drawing a strobe picture.

*What is the pattern of the ball's motion?**Is its velocity constant? If not, how does its velocity change?*

*Make a prediction of how the velocity of the ball will compare across the different situations.*

*For example, how will the velocity of the ball on the steep ramp compare with the velocity of the ball on the shallow ramp? If you roll the ball up the ramp and it rolls back down, how will its velocity at the bottom of the ramp compare to when it just rolls down?*

**Act out the situations**. Compare what happens to the ball with their predictions.They may have to try a few times before they are able to roll the ball accurately up to the starting point.

**In their journals:**

* For each of the four situations:*

*Draw a force diagram indicating the forces with vectors.**Diagrams should include at least gravity and normal force; remember that normal force is perpendicular to a surface, not necessarily perpendicular to gravity.**If the forces change at some point in the scenario, you may need to draw more than one force diagram. Where is F=ma in each diagram?*

10 minutes

After students have explored the various ramp investigations, have them view and create diagrams for the videos. Two of the videos are of balls rolling down the ramp at two different inclinations (Down Shallow Ramp Video, Down Steep Ramp Video) and the other two videos are of the ball rolling up and back down the same two ramps (Up & Down Shallow Ramp Video, Up & Down Steep Ramp Video).

For each video students should:

- Compare their predictions and investigation observations.
- Draw a velocity-over-time graph for each of the situations. For these graphs, use the convention "up the ramp" as the positive direction, and "down the ramp" as the negative direction.
- Annotate graphs by labeling important points, e.g., the "top" of the ball's trip up the ramp.

To get more information about the forces influencing the ball's motion:

1. Up/down motion forces:

- Measure the weight (force of gravity) on the ball in a vertical position using a spring scale. Place the ball in a sandwich baggie and suspend from the spring scale.

2. Slope motion forces:

- Measure the force with the spring scale when the ball is resting on the ramp.
- How does the spring scale reading change as the angle of the ramp changes? What is the reading when the ramp is flat on the ground?
- How does this help explain the ball/ramp motion data you have collected?

The Free Body Diagram - Incline Plane video, while aimed more towards high school students, does a nice job explaining how to construct forebode diagrams on a slope.

10 minutes

To summarize the lesson, ask students to explain their ideas by discussing the following questions with their lab mates.

*How does the ball's motion on the steep ramp compare to its motion on the shallow ramp?**What relation does a ball rolling up a slope and back down have to a ball being tossed up and falling down?**Where are the natural ramps you encounter every day? Explain this ramp in terms of force.*