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

Given

Radius of small pulley $(r_{1}) = 2 inch$

Radius of large pulley $(r_{2}) = 8 inch$

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

Calculate the revolution per minute of large pulley.

The circumference of the small pulley is computed as,

$C_{1} = 2 {πr}_{1} = 2 \times 3.14 \times 2 = 12.56 inch$

The circumference of the large pulley is computed as,

$C_{2} = 2 {πr}_{2} = 2 \times 3.14 \times 8 = 50.24 inch$

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

Therefore,

$\frac{Rpm of small pully}{Rpm of large pulley} = \frac{C_{2}}{C_{1}} \frac{3}{Rpm of large pulley} = \frac{50.24}{12.56} Rpm of large pulley = 3 \times \frac{12.56}{50.24} Rpm of large pulley = 0.75$

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

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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

Step by step solution

Given

Calculate the revolution per minute of large pulley.

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