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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

Keratinocytes are the most common cells in the skin’s outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body diameter of 1.00 × 10−5 m (10 μm), what minimum angular speed would be required to produce the observed linear speed of 1.67 × 10−7 m/s (10 μm/min)? (b) How many complete revolutions would be required for the cell to roll a distance of 5.00 × 10−3 m? (Because of slipping as the cells roll, averages of observed angular speeds and the number of complete revolutions are about three times these minimum values.)

(a)

To determine
The minimum angular speed required to produce linear speed of 1.67×107ms1 .

Explanation

Given info: The diameter of the cell body is 1.00×105m . The required linear speed is 1.67×107ms1 .

Explanation:

The linear speed of the cell is given by,

v=rω

  • v is the linear velocity
  • r is the radius of the cell
  • ω is the angular velocity

On re-arrangement for the angular velocity,

ω=vr

In terms of the diameter of the cell body,

ω=2vd

  • d is the diameter

Substitute 1.67×107ms1 for v and 1

(b)

To determine
The number of complete revolution required for the cell to cover a linear distance of 5.00×103m .

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