How Does Energy Conversion Affect a Trolley's Movement on Different Elevations?

[access]

Homework Statement

**please check diagram i have attached**i have a few problems all relevant to this information
a trolley with mass of 4kg moves without friction. initially the trolley is on AB and moving to the right with a velocity of 10ms. DE is 2m above AB and C is 5m below C

a) what is total energy of trolley at C? (is this the same as potential energy so would be 4*9.8*5? or would the formula be different?

b) if the potential energy of the trolley is 274.4 Joules determine its kinetic energy as it moves along DE..
im confused on how to change potential energy to kinetic energy in this situtation or is this a trick question? as it has potential energy it doesn't have kinetic energy so the answer is 0?

 

[azureth]

(a)No,according to the law of conservation of mechanical energy(which is actually the total energy here),the total energy of it should be Ek+Ep wherever it is.

 

[access]

thankyou.. with b) is it that the KE must be the same as the PE?

 

[azureth]

Could you please restate question(b)?I am a little confused.Is it a question in your homework or that you came up with ?

 

[gneill]

thankyou..


with b) is it that the KE must be the same as the PE?

Not quite. Kinetic and potential energy get exchanged when the cart changes its height in the gravitational field. That is, the sum of kinetic and potential energy is a constant. In this problem the total amount of energy that we assign to the cart is determined at a location where we know both its velocity and height. That would be along the path AB.

Note that the problem doesn't ask anything about the cart when it's at point C on the diagram. Because the gravitational force is a conservative force, it doesn't matter if the cart goes down into the valley via point C before ending up on the plateau DE; all that matters, as far as the change in KE and PE of the cart is concerned in going from AB to DE, is the difference in elevation of AB and DE. That's 2 meters according to the diagram.

So, calculate the change in PE in going from AB to DE, and apply that change appropriately to the conservation of energy equation. PE + KE = constant, to find the new KE.

 

[access]

im sorry i don't really understand.. the PE of DE is relative to C as that is the 274.4 joules is what i thought.

Could you please restate question(b)?I am a little confused.Is it a question in your homework or that you came up with ?

sorry i missed some of the question "b) if the potential energy of the trolley AT LOCATION DE is 274.4 Joules, determine its kinetic energy as it moves along DE?" is the question from the homework.

 

[gneill]

You can set your reference height for PE anywhere you wish. Point C is a logical place, since it's the lowest point of the cart's trajectory. But no matter where your reference point is, the fact remains that the change in PE from the AB plateau to the DE plateau depends only upon the difference in height, 2m, between AB and DE. So the 274.4 Joule value that is given in (b) is really irrelevant -- it simply confirms that the reference point they used was point C. You still need to determine the kinetic energy using the initial KE on plateau AB and applying the change in PE that takes place in going from AB to DE.

 

[access]

so how do i plug this into a formula for KE? the only formula i have for KE is 1/2M*Vsquared.. how do i work out the velocity of the trolley at DE?
the difference in PE from AB to DE is 78.4 joules

 

[gneill]

so how do i plug this into a formula for KE? the only formula i have for KE is 1/2M*Vsquared.. how do i work out the velocity of the trolley at DE?
the difference in PE from AB to DE is 78.4 joules

First determine, using your formula, the KE of the cart when it is at AB. The KE of the cart when it's at DE will then be 78.4 Joules less than that...

 

[access]

thankyou heaps guys for your help..