Calculating Gravitational Potential Energy of a Hanging Ball

AI Thread Summary
To calculate the gravitational potential energy (PE) of a hanging ball, the formula PE = mgh is used, where m is mass, g is the acceleration due to gravity, and h is the height relative to a reference point. For the ball attached to the ceiling, the height is negative when measured from the ceiling, while it is positive when measured from the floor. The gravitational potential energy relative to the ceiling is zero, while it is positive when calculated from the floor. Understanding the reference point is crucial for accurate calculations, as it affects the sign of the height value. This approach clarifies how to determine gravitational potential energy in different contexts.
gansta344u
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Homework Statement


A 2.35 kg ball is attached to a ceiling by a
1.92 m long string. The height of the room is
5.92 m .
The acceleration of gravity is 9.8 m/s2 .
What is the gravitational potential energy
associated with the ball relative to the ceiling?
Answer in units of J

What is its gravitational potential energy rel-
ative to the floor? Answer in units of J.

What is its gravitational potential energy rel-
ative to a point at the same elevation as the
ball? Answer in units of J.

Homework Equations


PE=mgh

The Attempt at a Solution


I TRIED TO USE THE EQUATION BUT WHEN I PUT IT IN IT WAS WRONG MAYBE I AM CALCULATING WRONG PLEASE HELP MAYBE IF U CAN PROVIDE A MODIFIED EQUATION OR EVEN A SIMPLE ONE THAT WOULD HELP A LOT!
 
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gansta344u said:

Homework Equations


PE=mgh
Perhaps if you thought of the equation as PE = mgy, where y is the vertical position with respect to your reference point, you may understand it better.

For example, if you choose the ceiling as your reference, that means that y = 0 at the ceiling. What's the y value of the ball in that case?
 
Hint: Pay attention to the sign of your answer.
 
thanks a lot it helped a lot especially the last part, it worked.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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