Help with a potential energy question

[xregina12]

A 2kg ball is attached to a ceiling by a 3 m string. The height of the room is 5.4 meters. Acceleration due to gravity is: 9.8m/s^2. What is the gravitational potential energy relative to a point at the same elevation as the ball? Answer in units of J.
The way I set up the problem is:
y=-(5.4-3)=-2.4 meters
m=2kg
g=9.8m/s^2
PE=mgy=(2)(9.8)(-2.4)=-47.04 J.

however, i checked the answer in my book and it wasn't it. :(
anyone can help show me what I did or/understood wrong?

 

[G01]

Where is 0 potential energy defined to be? Normally, we say the ground (0m) is 0J in these type of problems. In that case the answer for the problem would be 47.04J, as you say. (The potential energy would be positive since it its 2.4 meters above the ground.)

The way they have the problem worded it seems they are asking for the potential energy of the ball if we say the ball's height is 0m (and the floor is at x=-2.4m). Is this what they are asking for?

Also, what is the answer they give? This may help figure out what they are asking for.

 

[xregina12]

Yes, I set 0 potential energy at the balls height.

 

[G01]

Yes, I set 0 potential energy at the balls height.

Then by definition the ball has 0J of potential energy. That is your answer.

i.e. The balls' position is y=0m

therefore, $$U=mgy=mg(0)=0$$

 

[xregina12]

oh i see! Thanks.

 

[G01]

Anytime.