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04:10A spring of equilibrium length L₁ and spring constant k₁ hangs from the ceiling. Mass m₁ is suspended from its lower end. Then a second spring, with equilibrium length L₂ and spring constant k₂, is hung from the bottom of m₁. Mass m₂ is suspended from this second spring. How far is m₂ below the ceiling?
A horizontal spring with spring constant 250 N/m is compressed by 12 cm and then used to launch a 250 g box across the floor. The coefficient of kinetic friction between the box and the floor is 0.23. What is the box's launch speed?
How much work does tension do to pull the mass from the bottom of the hill (θ = 0) to the top at constant speed? To answer this question, write an expression for the work done when the mass moves through a very small distance ds while it has angle θ, replace ds with an equivalent expression involving R and dθ, then integrate.
The gravitational attraction between two objects with masses mA and mB, separated by distance 𝓍, is F = GmAmB/𝓍², where G is the gravitational constant. If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a 1.5 x 1013 kg comet is passing the orbit of Mars, heading straight for the sun at a speed of 3.5 x 104 m/s. What will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and G = 6.67 x 10-11 Nm²/kg².
A red ball has a mass of 250 g. A constant force pushes the red ball horizontally and launches it at a speed of 15 m/s. The same force pushes a green ball through the same distance, launching it at 25 m/s. What is the mass of the green ball?
A 30 g mass is attached to one end of a 10-cm-long spring. The other end of the spring is connected to a frictionless pivot on a frictionless, horizontal surface. Spinning the mass around in a circle at 90 rpm causes the spring to stretch to a length of 12 cm. What is the value of the spring constant?
