9.4: Chapter 9 Homework Problems
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).
- 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?
- 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?
- 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?
- 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?
- Solution
-
\(d = 6.7 \, m\)
\(v = 2.12 \, m/s\)
\(W = 5464.92 \, J\)