Question

1. the diagram below shows the path of a roller coaster cart.

if there is no friction, which statement about the cart must be true?
f the cart has used up all of its energy at point s.
g the cart has half as much total energy at point v as at point u.
h the cart has more total energy at point q than at any other point.
i the cart has the same amount of total energy at every point shown.

1. which scenario best demonstrates an increase in potential energy?

a a cyclist pedaling on a flat road
b a hot air balloon rising into the sky
c a ball bouncing down a flight of stairs
d a snowball rolling down a mountainside

Explanation:

For question 6:
According to the Law of Conservation of Energy, in the absence of non - conservative forces like friction, the total mechanical energy (sum of potential and kinetic energy) of a system remains constant.
For question 7:
Potential energy \(U = mgh\) (where \(m\) is mass, \(g\) is acceleration due to gravity, and \(h\) is height). When a hot air balloon rises (\(h\) increases), its potential energy increases. A cyclist on a flat road has no significant change in height (\(h\) is constant), a ball bouncing down stairs has a decrease in height (so potential energy decreases), and a snowball rolling down a mountainside has a decrease in height (potential energy decreases).

Answer:

1. ① The cart has the same amount of total energy at every point shown.
2. B. a hot air balloon rising into the sky