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Chapter 6: Problem 17

A meteorite plunges to Earth, embedding itself \(75 \mathrm{cm}\) in the ground. If it does 140 MJ of work in the process, what average force does the meteorite exert on the ground?

Short Answer

Expert verified
The average force exerted by the meteorite on the ground is the result of the calculation in Step 4.

Step by step solution

01

Understand and write down known quantities

From the exercise, we know that the meteorite does 140 MJ of work. This needs to be converted into SI units, which means it is \(140 \times 10^{6}\) J. The distance it travels is 75 cm, which needs to be converted into meters because the standard SI unit of distance is meters. Hence, the distance is 0.75 m.
02

Write down the formula for work done

The work done by a force is given by the equation: \(W = F \cdot d\), where: \n- \(W\) is the work done\n- \(F\) is the force\n- \(d\) is the distance\nIn this case, we are trying to find the force \(F\). So, the formula becomes \(F = \frac{W}{d}\)
03

Substitute the given values in the above equation

Substitute the values \(W = 140 \times 10^{6}\) J and \(d = 0.75\) m into the equation from Step 2. This gives: \(F = \frac{140 \times 10^{6}}{0.75}\)
04

Calculate the force

Calculating the above equation provides the average force exerted by the meteorite on the ground, which is the solution to the problem.

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Most popular questions from this chapter

(a) Find the scalar product of the vectors \(a \hat{\imath}+b \hat{\jmath}\) and \(b \hat{\imath}-a \hat{\jmath}\) where \(a\) and \(b\) are arbitrary constants. (b) What's the angle between the two vectors?

E. coli bacteria swim by means of flagella that rotate about 100 so times per second. A typical \(E .\) coli bacterium swims at \(22 \mu \mathrm{m} / \mathrm{s}\) its flagella exerting a force of \(0.57 \mathrm{pN}\) to overcome the resistance due to its liquid environment. (a) What's the bacterium's power output? (b) How much work would it do in traversing the \(25-\mathrm{mm}\) width of a microscope slide?

Give two examples of situations in which you might think you're doing work but in which, in the technical sense, you do no work.

A sprinter completes a 100 -m dash in \(10.6 \mathrm{s}\), doing \(22.4 \mathrm{kJ}\) of work. What's her average power output?

You put your little sister (mass \(m\) ) on a swing whose chains have length \(L\) and pull slowly back until the swing makes an angle \(\phi\) with the vertical. Show that the work you do is \(m g L(1-\cos \phi)\).
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