10. Conservation of Energy

A slingshot will shoot a $10$-g pebble $22.0$ m straight up. With the same potential energy stored in the rubber band, how high can the slingshot shoot a $25$-g pebble? 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?

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

A 100 g particle experiences the one-dimensional, conservative force F_x shown in FIGURE P10.60. 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 ACD. Is this a conservative force? Explain.

A 100 g particle experiences the one-dimensional, conservative force F_x shown in FIGURE P10.60. 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?

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)). 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.

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

The absorption spectrum of an atom consists of the wavelengths 200 nm, 300 nm, and 500 nm. b. What wavelengths are seen in the atom’s emission spectrum?

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

An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box?

The first three energy levels of the fictitious element X are shown in FIGURE P38.54. What wavelengths are observed in the absorption spectrum of element X? Express your answers in nm.

Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show the first five energy levels. Label each with the values of n and E_n.