Can kinetic energy and potential energy both increase?

In summary, the conversation discusses the energy changes that occur when a helicopter accelerates straight up from the roof of a hospital. It is determined that both potential and kinetic energy increase as the helicopter gains altitude and velocity. The work-energy theorem is also mentioned as a way to calculate the work done by external forces on the system.
  • #1
thepegmeister
4
0

Homework Statement



A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. (a) What type(s) of energy is (are) changing? Is each type increasing or decreasing? Why?


Homework Equations



Power=Work/Time
Work=Change in KE

The Attempt at a Solution



a) I would think that potential and kinetic energy are both changing; both increase because the helicopter gains altitude (increasing PE) and increases velocity (increasing KE). Is this correct? I know that in a situation where energy is conserved, one must decrease as the other one increases. I'm not sure whether this qualifies as an energy-conservative situation, though.

b) The work-energy theorem. The work done by gravity + work done by helicopter = change in KE. Is this correct?

Many thanks!
 
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  • #2
Your answer to a) is correct. Energy is conserved when there are no external forces do work on the system. In this case, the system is the helicopter, and the external force is the air is pushing it up. (Gravity doesn't count as an external force because you're already taking it into account with the potential energy.) That's why both types of energy can increase.

You're also correct about the work-energy theorem.
 
  • #3
Thank you, Vela! I really appreciate it.
 

1. Can kinetic energy and potential energy both increase?

Yes, kinetic energy and potential energy can both increase. Kinetic energy is the energy an object possesses due to its motion, while potential energy is the energy an object has due to its position or state. Both forms of energy can increase simultaneously.

2. How does an increase in kinetic energy affect potential energy?

An increase in kinetic energy typically results in a decrease in potential energy, and vice versa. This is because as an object gains kinetic energy and begins to move, it loses some of its potential energy due to changes in position or state.

3. Can an object have more potential energy than kinetic energy?

Yes, an object can have more potential energy than kinetic energy. This can occur when an object is at rest or is moving slowly. In these cases, the object may have a higher potential energy due to its position or state, but a lower kinetic energy due to its lack of motion.

4. What are some examples of situations where both kinetic and potential energy increase?

One example is a roller coaster. As the roller coaster car moves up the first hill, it gains potential energy. As it goes down the hill and gains speed, it also gains kinetic energy. Another example is a pendulum. At the highest point of its swing, the pendulum has the most potential energy. As it swings down and picks up speed, it also gains kinetic energy.

5. Is there a limit to how much kinetic and potential energy an object can have?

Yes, there is a limit to how much kinetic and potential energy an object can have. According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or transformed. Therefore, the total amount of energy an object has cannot exceed the initial amount of energy it had to begin with.

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