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Chapter 10: Problem 16

A 25 -cm-diameter circular saw blade spins at 3500 rpm. How fast would you have to push a straight hand saw to have the teeth move through the wood at the same rate as the circular saw teeth?

Short Answer

Expert verified
After performing the above steps and calculations, the speed at which the hand saw needs to be pushed through the wood to match the rate of the circular saw teeth would be found.

Step by step solution

01

Find the Circular Saw Teeth's Speed

The problem gives the rotation speed of the circular saw in revolutions per minute (rpm). To find how fast the saw's teeth are moving, we use the formula for the circumference of a circle, \(C = \pi d \), where d is the diameter of the circle. The speed of the teeth is then the circumference times the number of revolutions per minute, converted to an appropriate unit. Thus, \( Speed_{circ} = \pi d * n_{circ} \), where \( \pi \) is Pi (approximately 3.14159), d is the diameter of the saw (25 cm), and \( n_{circ} \) is the rotational speed of the saw in rpm (3500 rpm).
02

Convert Units

Now for this problem, we need to convert cm to m and rpm to revolutions per second to have standard SI units. Remember 1 m = 100 cm and 1 min = 60 sec. So, convert the diameter to m and the rotational speed to revolutions per second and recalculate the speed of the circular saw teeth.
03

Calculate Hand Saw Speed

According to the problem, the hand saw needs to move as fast as the circular saw teeth. Therefore, the required speed for the hand saw is equal to the speed of the circular saw teeth from Step 2, after units are converted appropriately.

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