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Chapter 6: Q. 107 (page 366)

Two pulleys, one with radius 2 inches and the other with radius 8 inches, are connected by a belt. (See the figure.) If the 2-inch pulley is caused to rotate at 3 revolutions per minute, determine the revolutions per minute of the 8-inch pulley.

Short Answer

Expert verified

The revolution per minute of 8-inch pulley is 0.75 rpm.

Step by step solution

01

Given

Radius of small pulley(r1)=2inch

Radius of large pulley(r2)=8inch

The 2-inch pulley is caused to rotate at 3 revolutions per minute.

02

Calculate the revolution per minute of large pulley.

The circumference of the small pulley is computed as,

C1=2蟺谤1=2脳3.14脳2=12.56inch

The circumference of the large pulley is computed as,

C2=2蟺谤2=2脳3.14脳8=50.24inch

Since the revolution per minute of the pulley is inversely proportional to its radius.

Therefore,

RpmofsmallpullyRpmoflargepulley=C2C13Rpmoflargepulley=50.2412.56Rpmoflargepulley=3脳12.5650.24Rpmoflargepulley=0.75

The revolution per minute of the 8-inch pulley is 0.75 rpm.

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