How Do You Calculate Kinetic and Potential Energy in Projectile Motion?

[falcon0311]

I understand that E = K1 + P1 = K2 + P2, BUT,

I'm not sure when what equals what for this problem, and I could use a push start.

Projectile (mass 2.40 kg) fired from a cliff 125 m high with Vo = 150 m/s, 41.0 degrees from the horizontal. What's the kinetic and potential energy just after firing?

I have K = 27,000 J. Is this right? How can I find the potential energy if it is not P = mgh?

Thanks for the help.

 

[Doc Al]

I have K = 27,000 J. Is this right?

Yes.

How can I find the potential energy if it is not P = mgh?

Who says it's not mgh? One thing to realize when calculating gravitational PE is that the reference point (where h = 0) is arbitrary. If you choose the ground as your reference point, then h = 125 m.

 

[cair0]

Yes.
Who says it's not mgh? One thing to realize when calculating gravitational PE is the the reference point (where h = 0) is arbitrary. If you choose the ground as your reference point, then h = 125 m.

yeah the problem SHOULD give you an origin if it is asking for the potential energy, since if it doesnt, you could set it anywhere and have pretty much any potential you wanted

 

[falcon0311]

Does it matter that the object is shot UP in the air when finding the potential energy just after being fired? Or is the potential energy equal to 0 since the object's flying?

 

[KingNothing]

It's equal to 0 because all of it's energy is kinetic at that point. Think of it this way. From the second it comes out of the cannon (if it is fired upwards at all), it begins to lose speed, and thus lose kinetic energy (and build up potential energy). If you are measuring it at the instant it is fired, it has not yet been given a chance to lose speed, and none of its KE has been converted to PE yet.

PE can be arbitrary, but it's almost always used in an experiment where the measurement stops, such as when the cannonball hits the ground. The PE of an object that has reached its top point...well, think of origin confusion like this: ask yourself: "will the object reach this point?" If yes, then say to yourself: since it is potential, its PE at this point will be its KE at that reference point.

Follow me?

 

[Doc Al]

Does it matter that the object is shot UP in the air when finding the potential energy just after being fired?

No, not a bit. PE depends only on position, not direction of motion.

Or is the potential energy equal to 0 since the object's flying?

No. Potential and kinetic energy are two separate things. PE has to do with position (height, in this case), KE with motion. It just so happens that the sum of KE and PE remains constant in this case. But if the object is at a height "h" above your reference point, then its gravitational PE is mgh regardless of its speed or direction of motion.

 

[falcon0311]

Okay, so I've got K = 27,000 J
U = 2940 J
and the velocity as the ball strikes the ground to be 270.8 m/s. He marked everything right, so I guess I'm just not confident when it comes to energy. Thanks for all the help.