A 1000kg roller coaster begins at 10m tall hill with initial velocity of 6m/s and travels down until a second hill. 1700J is transformed to thermal engird by friction. In order for rollercoaster to get up 2nd hill it must have velocity of 4.6m/s or less at the top. What is the maximum height the second hill could be

The maximum height could be 10.6 meters.

Explanation:

For this kind of exercise, we use the general principle for conservation of mechanical energy (E) that states:

(1)

That means the mechanical energy an object has on a point 2 should be equal to the mechanical energy on a point 1 plus the energy transformed into heat due friction denoted as Wf (It is negative because is lost). In our case point 1 is the point where the roller coaster begins and point 2 is at the second hill. Tola mechanical energy is the sum of potential gravitational energy and kinetic energy, so (1) is :

with K the kinetic energy and U the potential energy, remember potential energy is mgh and kinetic energy is with m the mass, v the velocity and h the height, then:

Solving for h_2:

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.