B1O Spiderweb Forces An orb-weaver spider sits in her web...

B1O Spiderweb Forces An orb-weaver spider sits in her web that is supported by three radial strands, as shown in FIGURE$6-47 .$ Assume that only the radial strands contribute to supporting the weight of the spider. If the mass of the spider is $5.2 \times 10^{-4} \mathrm{kg}$ , and the radial strands are all under the same tension, find the magnitude of the tension, $T .$

B1O Spiderweb Forces An orb-weaver spider sits in her web that is
supported by three radial strands, as shown in FIGURE$6-47 .$ Assume
that only the radial strands contribute to supporting the weight of
the spider. If the mass of the spider is $5.2 \times 10^{-4} \mathrm{kg}$ , and the radial
strands are all under the same tension, find the magnitude of the
tension, $T .$

Key Concepts

Static Equilibrium

Static equilibrium is a fundamental principle in mechanics where an object is at rest because the net force and net moment acting on it are zero. This concept is used to analyze forces acting on objects to ensure that the sum of forces in all directions balance, preventing any acceleration.

Force Resolution

Force resolution involves breaking a force vector into its component parts, usually along horizontal and vertical axes. This technique is critical in understanding how forces applied at an angle contribute to the overall net force in each direction, which is essential for solving equilibrium problems.

Tension

Tension is the force transmitted through a string, rope, or cable when it is pulled tight by forces acting at its ends. In problems involving multiple supports, like cables or strands, analyzing the tension helps determine how the applied load is distributed among them.

Gravitational Force

Gravitational force is the attractive force that the Earth exerts on objects, calculated by the product of the mass of the object and the acceleration due to gravity. This force represents the weight that must be balanced by other forces in static equilibrium situations.

Transcript

00:01 All right, question 30 has to deal with a spider and her web.

00:05 An orb weaver spider sits in her web that is supported by three radial strands.

00:10 So these radial strands are these red lines attached to three different points on, i believe, a wall.

00:16 Assume that the radial strands contribute to supporting the weight of the spider.

00:20 If the mass of the spider is 5 .2 times 10 to negative 4 kilograms and the radial strands are all under the same tension, find the magnitude of the tension t.

00:29 This is a representation of the diagram.

00:33 Perhaps the angles aren't necessarily to scale, but the scenario still holds true.

00:38 So we're given each of these angles.

00:40 So, for instance, for theta 1 to the top left, this arc line is what's given to be theta 1.

00:48 This arc line, top 2 is theta 2, which i'm calling these theta 1, 2, and 3, just for a little bit easier with each of their degrees.

00:59 And we see that.

01:00 The system is in equilibrium, so there's no force acting upward or downward or left or right.

01:08 So for this thing we should need to do, because we recognize this is a static problem, we'll need to look at the different forces in each direction.

01:17 So i'm going to label my axes x and y.

01:22 To this scenario, we know that if the gravity, sorry, the force acting on the spider will be completely down.

01:28 Again, that's given in the question.

01:29 So the weight of the spider is in the negative direction.

01:33 I'm going to going to look first to see the forces in the y direction and from there we'll look at if we need to look at the forces in the y in the x direction.

01:47 Right.

01:47 So if you look at actually, we'll get each of these different points connecting the spider in the wall.

01:53 So if this is our top left here, this is scenario one or the one top left.

01:59 So one is top left, two is top right, and three is bottom...

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