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Chapter 6: Problem 37

You are on the Moon and would like to send a probe into space so that it does not fall back to the surface of the Moon. What launch speed do you need?

Short Answer

Expert verified
Answer: The minimum launch speed required is 3.122 × 10^5 m/s.

Step by step solution

01

Identify the variables

Identify the variables given in the problem. The mass of the Moon (M_moon) is 7.342 × 10^22 kg, the radius of the Moon (R_moon) is 1.737 × 10^6 m, and the gravitational constant (G) is 6.674 × 10^-11 N m²/kg².
02

Write down the escape velocity formula

Write down the escape velocity formula to find the minimum launch speed: v_escape = sqrt((2*G*M_moon) / R_moon)
03

Insert the given values

Insert the given values into the escape velocity formula: v_escape = sqrt((2*6.674×10^-11 N m²/kg²*7.342×10^22 kg) / 1.737×10^6 m)
04

Perform the calculations

Perform the calculations to find the escape velocity: v_escape = sqrt((2*6.674×10^-11 * 7.342×10^22) / 1.737×10^6) = sqrt(9.738×10^11) = 3.122 × 10^5 m/s
05

Find the required launch speed

The required launch speed to send a probe into space so that it does not fall back to the surface of the Moon is 3.122 × 10^5 m/s.

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Most popular questions from this chapter

(a) If forces of magnitude \(5.0 \mathrm{N}\) applied to each end of a spring cause the spring to stretch \(3.5 \mathrm{cm}\) from its relaxed length, how far do forces of magnitude \(7.0 \mathrm{N}\) cause the same spring to stretch? (b) What is the spring constant of this spring? (c) How much work is done by the applied forces in stretching the spring \(3.5 \mathrm{cm}\) from its relaxed length?
The bungee jumper of Example 6.4 made a jump into the Gorge du Verdon in southern France from a platform \(182 \mathrm{m}\) above the bottom of the gorge. The jumper weighed \(780 \mathrm{N}\) and came within \(68 \mathrm{m}\) of the bottom of the gorge. The cord's unstretched length is \(30.0 \mathrm{m}\) (a) Assuming that the bungee cord follows Hooke's law when it stretches, find its spring constant. [Hint: The cord does not begin to stretch until the jumper has fallen \(30.0 \mathrm{m} .]\) (b) At what speed is the jumper falling when he reaches a height of \(92 \mathrm{m}\) above the bottom of the gorge?
Sam pushes a \(10.0-\mathrm{kg}\) sack of bread flour on a frictionless horizontal surface with a constant horizontal force of \(2.0 \mathrm{N}\) starting from rest. (a) What is the kinetic energy of the sack after Sam has pushed it a distance of \(35 \mathrm{cm} ?\) (b) What is the speed of the sack after Sam has pushed it a distance of \(35 \mathrm{cm} ?\)
The forces required to extend a spring to various lengths are measured. The results are shown in the following table. Using the data in the table, plot a graph that helps you to answer the following two questions: (a) What is the spring constant? (b) What is the relaxed length of the spring? $$\begin{array}{llllll} \hline \text { Force (N) } & 1.00 & 2.00 & 3.00 & 4.00 & 5.00 \\\ \text { Spring length (cm) } & 14.5 & 18.0 & 21.5 & 25.0 & 28.5 \\\ \hline \end{array}$$
A block (mass \(m\) ) hangs from a spring (spring constant k). The block is released from rest a distance \(d\) above its equilibrium position. (a) What is the speed of the block as it passes through the equilibrium point? (b) What is the maximum distance below the equilibrium point that the block will reach?
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