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Chapter 5: Problem 48
A car of mass 942.4 kg accelerates from rest with a constant power output of 140.5 hp. Neglecting air resistance, what is the speed of the car after 4.55 s?
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A flatbed truck is loaded with a stack of sacks of cement whose combined mass is \(1143.5 \mathrm{~kg}\). The coefficient of static friction between the bed of the truck and the bottom sack in the stack is \(0.372,\) and the sacks are not tied down but held in place by the force of friction between the bed and the bottom sack. The truck accelerates uniformly from rest to \(56.6 \mathrm{mph}\) in \(22.9 \mathrm{~s}\). The stack of sacks is \(1 \mathrm{~m}\) from the end of the truck bed. Does the stack slide on the truck bed? The coefficient of kinetic friction between the bottom sack and the truck bed is \(0.257 .\) What is the work done on the stack by the force of friction between the stack and the bed of the truck?
A car of mass \(m\) accelerates from rest along a level straight track, not at constant acceleration but with constant engine power, \(P\). Assume that air resistance is negligible. a) Find the car's velocity as a function of time. b) A second car starts from rest alongside the first car on the same track, but maintains a constant acceleration. Which car takes the initial lead? Does the other car overtake it? If yes, write a formula for the distance from the starting point at which this happens. c) You are in a drag race, on a straight level track, with an opponent whose car maintains a constant acceleration of \(12.0 \mathrm{~m} / \mathrm{s}^{2} .\) Both cars have identical masses of \(1000 . \mathrm{kg} .\) The cars start together from rest. Air resistance is assumed to be negligible. Calculate the minimum power your engine needs for you to win the race, assuming the power output is constant and the distance to the finish line is \(0.250 \mathrm{mi}\)
Two cars are moving. The first car has twice the mass of the second car but only half as much kinetic energy. When both cars increase their speed by \(5.0 \mathrm{~m} / \mathrm{s}\), they then have the same kinetic energy, Calculate the original speeds of the two cars.
A father pulls his son, whose mass is \(25.0 \mathrm{~kg}\) and who is sitting on a swing with ropes of length \(3.00 \mathrm{~m}\), backward until the ropes make an angle of \(33.6^{\circ}\) with respect to the vertical. He then releases his son from rest. What is the speed of the son at the bottom of the swinging motion?
A force has the dependence \(F_{x}(x)=-k x^{4}\) on the displacement \(x\), where the constant \(k=20.3 \mathrm{~N} / \mathrm{m}^{4}\). How much work does it take to change the displacement from \(0.73 \mathrm{~m}\) to \(1.35 \mathrm{~m} ?\)
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