Work, power, energy, physics question

Question

A 3.0 kg model plane flies horizontally at 20 m/s 

 

A) The plane goes into a dive and levels off at 8.0 m closer to the ground. How much potential energy did it lose during the dive? 

B) How much kinetic energy did it gain during the dive?

 

I have so much trouble setting up the equation in order to solve problems like these! 

Answer 1

Hi Rebecca,

 

The equation for figuring out gravitational potential energy (I'll abreviate it PE for potential energy) is:

 

PE = mgh where m is the mass in kg, g = 9.8 m / s² is the constant acceleration due to the Earth's gravity field, and h is the height in m. The final unit of PE will be a Joule, abbreviated J which is equivalent to kg m² / s².

 

The equation for kinetic energy (abbreviated KE) is:

 

KE = ¹/₂ mv² where m is the mass in kg again and v is the velocity in m / s. Notice again that since the v is squared, the units on the right side combine to form kg m² / s² which is a Joule ( J ), the unit for energy).

 

A) PE = 3.0 kg * 9.8 m / s² * -8.0m = -235.2 J

You put in a negative 8.0m because the plane LOST that much height, you see that the amount of energy came out negative and so that is how much energy the plane LOST during the dive.

 

B) Assuming all of the potential energy lost was fully converted into kinetic energy (it has to go somewhere so assuming we can neglect any heating effects due to friction or any rotational effects that are created, it means it would all have to have  been converted to linear motion), it means that the plane gained the exact same amount of kinetic energy as it lost potential energy so the answer is 235.2 J.

 

If you were asked to also calculate the new velocity of the plane you could use the equation for kinetic energy I included above. Hope this helps, let me know if you need any clarifications.