# 9.4: Chapter 9 Homework Problems

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Exercise $$\PageIndex{1}$$

A car with a mass of 1100 kg locks up its brakes when it is traveling at 50 km/hr, stopping over a distance of 18 meters. If the same car were to lock up its brakes when traveling 80 km/hr, how far would you expect the car to slide before coming to a stop? (Hint: assume the same friction force in both cases). Figure $$\PageIndex{1}$$: A car with locked-up brakes, visibly skidding.
Solution

$$d = 46.06 \, m$$

Exercise $$\PageIndex{2}$$

A 2500-lb car traveling 60 mph (88 ft/s) impacts a highway crash barrier as shown below. If the barrier were designed to exert the following force over the 40-ft distance of the barrier, how far would you expect the car to travel after impacting the barrier? Figure $$\PageIndex{2}$$: problem diagram for Exercise $$\PageIndex{2}$$. A highway crash barrier and the graph of the force it exerts on an impacting car over the barrier's length.
Solution

$$d = 25.03 \, ft$$ (assuming no holes in the barrier)

Exercise $$\PageIndex{3}$$

The Duquesne Incline transports passengers up a 30.5 degree slope. If a fully loaded car has a mass of 5500 kg, what power is required to maintain an uphill speed of 10 km/hr? Figure $$\PageIndex{3}$$: The Duquesne Incline, a cable car that transports passengers up a steep hillside.
Solution

$$P = 76.13 \, kW$$

Exercise $$\PageIndex{4}$$

A bungee jumper with a weight of 150 lbs uses a bungee cord with an unstretched length of 60 feet.

• Assuming no air resistance, what will the jumper’s velocity be just before the bungee cord starts to stretch?
• If the bungee jumper falls a maximum distance of 150 feet, what is the spring constant of the bungee cord? Figure $$\PageIndex{4}$$: A man bungee-jumping above a lake.
Solution

$$v = 62.16 \, ft$$

$$k = 5.55 \, lb/ft$$

Exercise $$\PageIndex{5}$$

An 1100-kg truck is being used to raise a 100-kg box using the setup shown below. When the box is at a height of 3 meters, the box has a velocity of 1 m/s.

• How far did the truck travel to lift the box this high? (Hint: this is a dependent motion problem)
• What is the velocity of the truck at this time?
• What is the work that the truck has done over this time? Figure $$\PageIndex{5}$$: problem diagram for Exercise $$\PageIndex{5}$$. A cable attached at one end to a beam 4 feet above the ground passes through a pulley on a box on the ground and through another pulley on the beam, before being attached to the rear of a truck 5 feet away from the box. The truck drives away from the box to raise it from the ground.
Solution

$$d = 6.7 \, m$$

$$v = 2.12 \, m/s$$

$$W = 5464.92 \, J$$

This page titled 9.4: Chapter 9 Homework Problems is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jacob Moore & Contributors (Mechanics Map) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.