9.4: Chapter 9 Homework Problems

Last updated
Save as PDF

Page ID: 54729

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

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).

A car whose brakes have locked up. — 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?

A graph of the force in pounds exerted by a highway crash barrier on a car, vs. distance along the barrier's length. From a distance of 0 to 20 ft the force is a constant 10,000 lbs; from a distance of 20 ft to 40 ft the force is a constant 20,000 lbs. — 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?

A cable car filled with passengers travels up a steep hillside. — 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?

A man bungee jumping above a lake. — 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?

A 100-kg box with a pulley attached to its top rests on the ground. A horizontal beam is held 4 meters above the ground by a vertical post. The right end of a cable is attached to the horizontal beam; the left end passes through the pulley on the box, then passes through another pulley mounted on the underside of the beam, and then is attached to the rear bumper of a truck that is 5 feet to the left of the box. — 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

\(d = 6.7 \, m\)

\(v = 2.12 \, m/s\)

\(W = 5464.92 \, J\)