A 45.0-kg girl is standing on a plank that has a mass of 150...

A $45.0-\mathrm{kg}$ girl is standing on a plank that has a mass of 150 kg . The plank, originally at rest, is free to slide on a frozen lake that constitutes a flat, frictionless supporting surface. The girl begins to walk along the plank at a constant velocity of $1.50 \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}$ relative to the plank. (a) What is her velocity relative to the ice surface? (b) What is the velocity of the plank relative to the ice surface?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Center of Mass Analysis

The motion of the center of mass in an isolated system is unaffected by internal forces. Analyzing the system's center of mass helps in understanding how the individual motions of the components (the girl and the plank) contribute to the overall dynamics of the system.

Relative Motion

Relative motion involves describing the velocity of an object with respect to different reference frames. In this problem, the girl’s speed relative to the plank and the plank’s speed relative to the ice must be combined to determine the girl's speed relative to the ice sensation, requiring an understanding of how velocities add or subtract in different frames.

Conservation of Momentum

In an isolated system with no external forces, such as one on a frictionless surface, the total momentum remains constant. When the girl walks on the plank, she exerts an internal force, and the resulting momentum change of the girl is exactly balanced by a momentum change in the opposite direction for the plank.

Transcript

Please give Ace some feedback