Question

While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

Name: Problem 68, Chapter 3: Conceptual Physics
Uploaded: 2021-08-26T00:30:42-08:00
Duration: 1 min 46 s
Channel: Surendra Kumar
Description: While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

   While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

Conceptual Physics

Paul G. Hewitt 12th Edition

Chapter 3, Problem 68

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Solved by Expert Surendra Kumar

08/26/2021

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Galileo is rolling a ball down an inclined plane and he observes that the ball rolls 1 cubit as he counts to 10. We are asked to find out how far the ball will have rolled from its starting point when he has counted to 20. Show more…

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While rolling balls down an inclined plane, Galileo observes that the ball rolls 1 cubit (the distance from elbow to fingertip) as he counts to 10. How far will the ball have rolled from its starting point when he has counted to 20?

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Key Concepts

Uniformly Accelerated Motion

This concept describes motion where an object experiences constant acceleration. In such cases, the distance traveled is proportional to the square of the time elapsed, a principle that emerged from early studies of objects on inclined planes.

Quadratic Time-Displacement Relationship

Under uniform acceleration, the distance an object travels is not directly proportional to time but to the square of the time. This means that if the elapsed time is doubled, the distance increases by a factor of four, illustrating a quadratic dependency.

Scaling Laws in Physics

Scaling laws help in understanding how physical quantities change with scaling factors. Here, the quadrupling of distance when time is doubled is a direct application of scaling, showing how changes in one variable (time) affect another (displacement) under constant acceleration.

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