8.1 Potential Energy of a System

In the example, what are the potential energies of the particle at $x = 1 \text{m}$ and $x = 2 \text{m}$ with respect to zero at $x = 1.5 \text{m}$? Verify that the difference of potential energy is still 7 J.

What are the values of the gravitational potential energy of the hiker at the base, summit, and sea level, with respect to a sea-level zero of potential energy?

When the length of the spring in the example changes from an initial value of 22.0 cm to a final value, the elastic potential energy it contributes changes by $−0.0800 \text{J} .$ Find the final length.

Suppose the mass in the equation is doubled while keeping the all other conditions the same. Would the maximum expansion of the spring increase, decrease, or remain the same? Would the speed at point B be larger, smaller, or the same compared to the original mass?

The kinetic energy of a system must always be positive or zero. Explain whether this is true for the potential energy of a system.

Describe the gravitational potential energy transfers and transformations for a javelin, starting from the point at which an athlete picks up the javelin and ending when the javelin is stuck into the ground after being thrown.

What is the dominant factor that affects the speed of an object that started from rest down a frictionless incline if the only work done on the object is from gravitational forces?

Using values from the table, how many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube? (These electrons were not dangerous in themselves, but they did create dangerous X-rays. Later-model tube TVs had shielding that absorbed X-rays before they escaped and exposed viewers.)

A camera weighing 10 N falls from a small drone hovering $20 \text{m}$ overhead and enters free fall. What is the gravitational potential energy change of the camera from the drone to the ground if you take a reference point of (a) the ground being zero gravitational potential energy? (b) The drone being zero gravitational potential energy? What is the gravitational potential energy of the camera (c) before i…

A cat’s crinkle ball toy of mass $15 \text{g}$ is thrown straight up with an initial speed of $3 \text{m}/\text{s}$. Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) How much work is done by the gravitational force during the ball’s rise to its peak? (c) What is the change in the gravitational potential energy of the ball during the rise to its peak? (d) If…