Answer to Question #212487 in Physics for CARLOS

Question

Use the picture of a cart of mass m moving on a roller coaster as well

as the accompanying information to answer the following question.The

section of track displayed is frictionless and composed entirely of

semicircular pieces of radius r.The letters A through E refer to

specific locations along the track. if r=12 meters,and if the cart's

velocity at point A is 3 meter per second,what is the cart's velocity

at point D? Round off your answer to nearest tenth of a meter per

second.

Answer 1

Find the total initial energy. The initial energy consists of kinetic and potential energy. The potential energy can be counted from the ground level, i.e., we only consider the height difference between A and D, which is 12 m.

$$E_i=E_K+E_P,\\ E_i=\frac12 mv^2+mgr.$$

According to conservation of energy, this initial energy fully converts into final (only kinetic) energy:

$$E_f=\frac12mu^2,\\\space\\ E_i=E_f,\\\space\\ \frac12 mv^2+mgr=\frac12 mu^2,\\\space\\ u=\sqrt{v^2+2gr}=15.6\text{ m/s}.$$