## Rolling Uphill

Author(s): Jim Mauch and Jen Klipfel
Discrepant Event - Teacher's Guide
SED 695B; Fall 2005

Detailed Explanation of Discrepant Event

Principles ilustrated

• Center of Mass
• Gravitational force
• Newtonian Physics

A conical object placed on a ramp made of two rails will not roll in the direction anticipated. (see video above). Although the rails slope downward, they also taper to a point. The conical shape of the object makes it necessary for the object to rise in order to roll 'down' the rail.

On the other hand, Starting on the downhill side of the rails, the object will roll toward the 'uphill' end. As the rails widen, the funnel is actually lowering as it rolls toward the 'top' of the ramp.

The key here is the center of mass. This object is 'falling' as long as its center of mass is moving toward the Earths' center of mass. In this case, the object must roll up the ramp in order for this to happen.

Standards
1. Newton's laws predict the motion of most objects. As a basis for understanding this concept:

 c. Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton's second law). e. Students know the relationship between the universal law of gravitation and the effect of gravity on an object at the surface of the Earth.

Practical Applications:

Our perception can sometimes make it appear that we are moving uphill when we are actually moving down hill. Look at the links below to see a huge number of areas on Earth that seem to defy gravity. the so called 'gravity hill' in Santa Paula, California is a popular spot where cars seeminly will defy the laws of gravity.

Questioning Script

Prior knowledge & experience:

• objects are pulled toward the Earth
• A rolling object will roll along a ramp in a direction that brings it closer to the Earth

Root question:

• Why does this object roll uphill?

Target response:

• Close examination reveals that it is not actually rolling uphill. Due to the arrangement of the two rails, the center of mass actually is moving downward as the object rolls.

Common Misconceptions:

• The object will move in a direction parallel to the ramp regardless of the shape of the object. If it appears to be going uphill, it is going uphill.

The ramp is obviously lower to the left than it is to the right.
the object placed at the 'uphill' end will not roll.
A view of our cost saving apparatus using readily available materials.
This model can be constructed easily with materials readily available in the lab. Two plastic rulers and a cardboard box were used as the ramp. Two glass funnels carefully taped together with transparent packing tape composed the rolling object.
The conical shape of the object allows the center of mass to drop as the object appears to roll 'up' the ramp.
Gravitational force is divided into two forces. the force perendicular to the path taken by the center of mass (equal in magnitude and opposite in direction to the normal force) and a force parallel to the path taken by the center of mass. the sum of all forces cancel except for this parallel force. So the object accelerates.