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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

Casting of molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis, as in Figure P7.62. Molten metal is poured into the rotating cylinder and then cooled, forming the finished product. Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bubbles are displaced toward the axis so that unwanted voids will not be present in the casting. Suppose a copper sleeve of inner radius 2.10 cm and outer radius 2.20 cm is to be cast. To eliminate bubbles and give high structural integrity, the centripetal acceleration of each bit of metal should be 100g. What rate of rotation is required? State the answer in revolutions per minute.

images

Figure P7.62

To determine
The required rate of rotation to acquire a centripetal acceleration of 100g .

Explanation

Given info: Inner radius of the cupper sleeve is 2.10cm . The outer radius of the cupper sleeve is 2.20cm . The required centripetal acceleration to eliminate the bubbles and give high structural integrity is 100g .

Explanation:

The centripetal acceleration of a particle is given by,

ac=rω2

  • ω is the angular speed
  • r is the radius
  • g is the acceleration due to gravity

On re-arrangement for the angular velocity will be,

ω=acr

As r decreases the required rotation rate increases. Use the minimum value of the r to determine the required angular speed.

ω=acrmin

Substitute 100g for ac , 9.80ms-2 for g , 2.10cm for rmin to determine the angular speed,

ω=100g2

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