Intro to Energy Types Practice Problems

An adult grasshopper can jump to a height of about 50 cm. i) What is the increase in the gravitational potential energy for a 0.25 g grasshopper in such a situation and ii) what is the origin of this energy?

A 2.5 g ball is fired upward using a spring-loaded toy gun. The ball goes only 5 m above its initial position. How high can a 10 g ball be launched by a toy gun having the same potential energy as the spring? 

A 5-g ping pong is fired straight up using the elastic energy that has been stored in the rubber band of a slingshot. At a height of 10 meters above the release position, the speed of the ball is zero. How much potential energy is contained in the rubber band?

A Cirque artist needs to swing across a river using a 15-meter rope attached to a bridge. Initially, the rope makes an angle of 60° with the vertical, and the artist swings down before rising to meet a colleague on the bank of the river. When he reaches the other bank, his rope makes a 25° angle with the vertical. Calculate the artist's speed just before he releases the rope and is caught by his colleague.

Suppose a car is traveling from point P to point R along the path PQR, and it's experiencing a force F = (12i + 6j) N. Determine the work done by the force on the car following path PQR  based on the figure shown below. Can we classify this force as conservative or non-conservative?  

Understanding the potential energy changes along the path can provide valuable insights into the energy state of the system. Suppose a one-dimensional system (m = 400 g) is being acted upon by a conservative force F_x, with the potential energy set to zero at a reference point x = x₀. Calculate the system's potential energy at various points along the path: (i) x = x₀ + 2.0 m, (ii) x = x₀ + 4.0 m, (iii) x = x₀ + 6.0 m, and (iv) x = x₀ + 8.0 m, where x₀ = 0 m.

A small ball of mass 50 g experiences a conservative force F_x in one dimension. If the ball is initially at x = 2.0 m and given a velocity of 15 m/s to the left. Determine the position of the ball's turning point.

Hint: To determine the position of the turning point, you need to find the point where the kinetic energy of the ball is zero, and the potential energy is at a maximum.

Consider a theoretical atom with distinct energy levels measured at 0.00 eV, 1.80 eV, and 7.20 eV. Determine the precise wavelengths that would be observed in the emission spectrum of this atom.

Determine what wavelengths are present in the absorption spectrum of a hydrogen-like atom with distinct energy levels at 0.00 eV, 3.50 eV, and 5.50 eV.

In a one-dimensional box, a subatomic particle having the same mass as an electron undergoes a quantum transition from the n=3 energy level to the n=1 energy level and emits a photon with a wavelength of 400 nm. Determine the length of the box.

The energy level diagram of a hypothetical ion is shown below. The energy levels are labeled as E₁, E₂, and E₃. Determine the wavelengths of radiation required to excite the ion from the ground state, E₁, to the 2^nd and 3^rd states.

Draw an energy level diagram for Li²⁺, showing the numerical values of n and E_n for the first four values of n.

A stream of electrons causes an emission at λ = 122 nm on He ⁺ ions due to the transition from the 4^th to 2^nd energy level. Determine the electric potential used to accelerate the electrons. Assume He⁺ ions do not gain additional electrons in the process.

Consider three planets, $P_1$ , $P_2$ , and $P_3$ , each with masses $m_1$ , $m_2$ , and $m_3$, initially positioned infinitely far apart. The work required to bring them into a stable equilateral triangular configuration around their common center of mass, where each side of the triangle has the same distance r, is given by:

$W=-G\left(\frac{m_1m_2}{r}+\frac{m_1m_3}{r}+\frac{m_2m_3}{r}\right)$

Does this work W correspond to the gravitational binding energy of the planetary system? Explain.

Consider an atom that absorbs radiation at wavelengths of 165 nm, 320 nm, and 510 nm from the ground state. What other wavelengths can be emitted? Take the ground state energy to be 0 eV.