Length of Pulley Belt System: 42.12 cm

[xortan]

Homework Statement

Find the length of the pulley belt system shown if the belts cross at right angles. The radii of the pulleys are 10.5 cm

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Homework Equations

C=2 pi r

The Attempt at a Solution

(2pi * 10.5) * 2

cant think of any other way to do this and my answer is pretty close to the right one but no cigar..any help would be appreicated

 

[HallsofIvy]

I started to say "there is not enough information" because the distance between the pulleys is not given but then realized that "the belts cross are right angles" is enough.

Draw radii from the point of tangency on one of the circles to the center of the circle. Since radii are perpendicular to tangents, that gives a four sided figure with three right angles. So the fourth angle, at the center of the circle is also a right angle. Now you know that the belt is on the circle for 3 right angles or 3/4 of the circles circumference. Also, the four sided figure, having right angles and 2 adjacent sides of length the radius of the circle, is a square and the other two sides, from the point of tangency to the point of intersection, also have length equal to the radius of the circle.

That is the information you need.

 

[Architeuthis Dux]

I would approach this problem by first understanding the concept of pulley systems and how they work. I would then use the given information, such as the radii of the pulleys and the fact that the belts cross at right angles, to visualize and draw a diagram of the system. This will help me to understand the geometry and relationships involved in the system.

Next, I would use the formula for the circumference of a circle (C = 2πr) to calculate the length of each belt. Since there are two pulleys, I would calculate the length of both belts and then add them together to get the total length of the pulley belt system.

In this case, the radius (r) is given to be 10.5 cm. So the length of one belt would be:

C = 2π(10.5) = 66.3 cm

Since there are two belts, the total length of the pulley belt system would be:

66.3 cm + 66.3 cm = 132.6 cm

Therefore, the length of the pulley belt system is 132.6 cm. It is important to note that this solution assumes that the pulleys are perfectly circular and that the belts do not stretch or slip. In real-life situations, there may be some variation in the length due to these factors.