(a) Suppose we have three masses, m₁ , m₂ and m₃,that initially are extremely (≈ infinitely) far apart from each other. The work needed to bring them to the positions shown in Fig. 8–50 is


W = - G ((m₁m₂/ r₁₂) + (m₁m₃/r₁₃) + (m₂m₃/r₂₃)) .


(c) Is W equal to the binding energy of the system—that is, is W equal to the energy required to separate the components by an infinite distance? Explain.


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A slingshot will shoot a 10-g pebble 22.0 m straight up. (a) How much potential energy is stored in the slingshot's rubber band?

A 100 g particle experiences the one-dimensional, conservative force Fx shown in FIGURE P10.60.a. Let the zero of potential energy be at x=0 m . What is the potential energy at x=1.0, 2.0, 3.0, and 4.0 m?Hint: Use the definition of potential energy and the geometric interpretation of work.

A particle moves from A to D in FIGURE EX10.36 while experiencing force F = (6i + 8j) N. How much work does the force do if the particle follows path. (b) ACD. Is this a conservative force? Explain.

A 100 g particle experiences the one-dimensional, conservative force Fx shown in FIGURE P10.60.b. Suppose the particle is shot to the right from x=1.0 m with a speed of 25 m/s. Where is its turning point?

The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV.c. What wavelengths appear in the atom’s absorption spectrum?

A slingshot will shoot a 10-g pebble 22.0 m straight up. (b) With the same potential energy stored in the rubber band, how high can the slingshot shoot a 25-g pebble? (c) What physical effects did you ignore in solving this problem?

Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 m that makes an angle of 45° with the vertical, steps off his tree limb, and swings down and then up to Jane's open arms. When he arrives, his vine makes an angle of 30° with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan's speed just before he reaches Jane. Ignore air resistance and the mass of the vine.

The maximum height a typical human can jump from a crouched start is about 60 cm. By how much does the gravitational potential energy increase for a 72-kg person in such a jump? Where does this energy come from?