# A 1.98 kg ball is attached to a ceiling by a 2.1 m long string. The height of the room is 5.95 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.

Thte way you have worded this, the ball is below the ceiling, so the potential energy with respect to the ceiling is negative. PE = mgh, and since the zero position is the ceiling, the potential energy is 1.98x9.8x(-2.1) = -41 joules, correct to two significant digits.

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The formula for gravitational potential energy is

Ug = mgh   where m = mass, g = acceleration due to gravity and h + height

If I understand your question correctly, the ball is hanging 2.1 m from the ceiling, which means that its height is 3.85 m.

In that case, you will have the following equation

Ug = 1.98*9.8*3.85

When you multiply this, you come out with 74.7054 J

If I have misunderstood your question, you should still be able to do the math using the same formula.  For example, if the ball is meant to fall from the ceiling and be stopped by the string at 2.1 m from the ceiling, you just substitute 2.1 for 3.85.

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