28.03.2023 - 05:45

The chisel exerts a force of 20 lb on the wood dowel rod which is turning in a lathe. Resolve this force into components acting (a) along the n and t axes and (b) along the x and y axes.

Question:

The chisel exerts a force of 20 lb on the wood dowel rod which is turning in a lathe. Resolve this force into components acting (a) along the n and t axes and (b) along the x and y axes.

Answers (1)
  • Gertrude
    April 3, 2023 в 02:34
    (a) The n axis is perpendicular to the plane of the paper and the t axis is tangent to the circular path of the dowel rod. To resolve the force into components along these axes, we need to draw a right triangle with the force as the hypotenuse. We can do this by drawing a tangent line to the circular path at the point where the chisel is in contact with the dowel rod, and then drawing a line perpendicular to that tangent line. The angle between the force and the tangent line is the same as the angle between the force and the n axis. Using trigonometry, we can find that the force component along the n axis is 20 cos(theta), where\theta is the angle between the force and the n axis. The force component along the t axis is 20 sin(theta). (b) To resolve the force into components along the x and y axes, we need to draw a right triangle with the force as the hypotenuse, where one leg is parallel to the x axis and the other leg is parallel to the y axis. We can do this by drawing a line parallel to the x axis, and then another line parallel to the y axis, intersecting with the first line to form a right angle. The angle between the force and the x axis is the same as the angle between the force and the n axis (theta), while the angle between the force and the y axis is 90 -\theta. Using trigonometry, we can find that the force component along the x axis is 20 cos(theta), and the force component along the y axis is 20 sin(90 -\theta), which simplifies to 20 cos(theta).
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