Chapter 10.3, Problem 2E

a.

To determine

To use a piece of cardboard to study center of mass.

Explanation of Solution

Given:

A piece of cardboard in the shape of a scalene triangle.

Cut three holes, one each near the vertex.

Use a thread to join all the three holes and leave one thread hanging with a knob attached.

Now try to balance the triangle on the knob.

The triangle will stay still on the knob only when the triangle is placed on its center of mass.

Conclusion:

Therefore, the triangle can balance on the center of mass.

b.

To determine

To explain why in geometry the point of intersection of intersection of the medians of a triangle is called the centroid of the triangle.

Explanation of Solution

Given:

A scalene triangle

  

A median of a triangle is a line joining from a vertex of triangle to the midpoint of the opposite side. The median will bisect the opposite side.

The intersection of medians of a triangle is known as centroid of the triangle.

The centroid of the triangle is also known as center of gravity of the triangle. This means that a triangular cardboard can be balanced on one figure if the finger is placed on the center of gravity.

The centroid represents the center of the given triangle.

Conclusion:

Hence, the point of intersection of medians is known as centroid.