# A2L Item 051

Goal: Reasoning about the vector nature of force.

Source: UMPERG

A rock sits on a hillside. The slope of the hillside is inclined to the
horizontal at approximately 30°. Which of the forces exerted on the rock is smallest in magnitude?

1. Friction force due to the ground
2. Gravitational force due to the Earth
3. Normal force due to the ground
4. The Friction, Gravitational and Normal force are equal in magnitude
5. Cannot be determined
6. None of the above

### Commentary:

(1). The smallest force is the friction force. The normal force
balances the component of gravity perpendicular to the hillside and the
friction force balance the component of gravity parallel to the
hillside. Since the hillside has a slope of 30°, the tangential
component of gravity is smaller.

#### Background

Many students fail to perceive that the static situation implies a
relationship between the forces. They may think that one requires
information such as the mass, and coefficient of friction to compute the
forces before the forces can be compared.

#### Questions to Reveal Student Reasoning

Can you determine the gravitational force? …normal force? …
friction force? Are there any relationships between these forces? If
so, what are they? Why doesn’t the rock slide down the hill?

#### Suggestions

Draw a free-body diagram.

Set up a demonstration using a block on a plane with adjustable angle.