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Chapter 6: Problem 58

A tractor tows a plane from its airport gate, doing 8.7 MJ of work. The link from the plane to the tractor makes a \(22^{\circ}\) angle with the plane's motion, and the tension in the link is \(0.41 \mathrm{MN}\). How far does the tractor move the plane?

Short Answer

Expert verified
To find the distance that the plane moves, plug in the given values into the rearranged formula from step 3. Ensure to convert the angle to radians before calculation. The result is the distance that the plane was moved by the tractor.

Step by step solution

01

Identify the known variables

First, identify the known values from the question. The work done (W) is given as 8.7 MJ or 8700000 J, the tension (T) is given as 0.41 MN or 410000 N, and the angle \(\theta\) is 22 degrees.
02

Apply Work-Energy Theorem

The work-done on an object by a net force is equal to the change in its kinetic energy. This is known as the work-energy theorem. In this case, the work done on the plane by the tractor is transformed into kinetic energy. When the force and the motion are in the same direction, work done is given by \(W = T \times d \times \cos(\theta)\), where d is the distance (which we intend to find), T is the tension and \(\theta\) is the angle between the force and direction of motion.
03

Solve for the distance

Re-arrange the formula to find the distance. So, \(d = \frac{W} {T \times \cos(\theta)}\). Substitute the known values into the equation to calculate the distance. Remember to convert the angle from degrees to radians first before the cosine operation.

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Most popular questions from this chapter

You're an engineer for a company that makes bungee-jump cords, and you're asked to develop a formula for the work involved in stretching cords to double their length. Your cords have force distance relations described by \(F=-\left(k x+b x^{2}+c x^{3}+d x^{4}\right)\) where \(k, b, c,\) and \(d\) are constants. (a) Given a cord with unstretched length \(L_{0},\) what's your formula? (b) Evaluate the work done in doubling the stretch of a 10 -m cord with \(k=420 \mathrm{N} / \mathrm{m}\) \(b=-86 \mathrm{N} / \mathrm{m}^{2}, c=12 \mathrm{N} / \mathrm{m}^{3},\) and \(d=-0.50 \mathrm{N} / \mathrm{m}^{4}\).

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