# 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/s^2.a) What is the gravitational potential energy associated...

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/s^2.

a) What is the gravitational potential energy associated with the ball relative to the ceiling? Answer in units of J.

b)What is its gravitational potential energy relative to the floor? Answer in units of J.

c) What is its gravitational potential energy relative to a point at the same elevation as the ball? Answer in units of J.

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### 1 Answer

The gravitational potential energy (PE) is an energy relative to the position. Normally we say the ground isthe reference point where the PE taken tobe zero. A body of mass mass of m, at aheight h from the reference point has a PE equal to mgh joules,g being the gravitational attraction and is 9.8m/s^2.

a

Here mass m of the ball is 1.98 kg, g = 9.81. Height of the ceiling is 5.95m. height of the ball is 5.95=2.1m = 3.85m

Therefore, the gravtational PE of the ball with respect floor is

PE of ball at celing wrt floor = (1.98 kg )*9.8 m/s^2)*(5.95m) = 115.4538 J

a)

PE of ball wrt ceiling:

PE of ball at ceiling at the end of rope wrt floor =1.98*9.8*3.85J = 74.7054 J = -40.7484J implies the PE of the ball is less by 40.7484J than that at Ceiling. Or a work of 40.7484J has to be bone to raise the ball to the height of ceil

b)

PE of ball wrt floor =74.7054J

c)

PE of ball wrt a point at its own level.

The PE of ball at h1 and h2 from the ground is mgh1 and mgh2 and therefore, the PE of the ball at h2 wrt a point at h1 height = mgh2-mgh1 =mg(h2-h1). Therefore, h1=h2 equal to h, the PE of the ball at h1 wrt h2 is mg(H2-h1)=mg(h-h) = 0. So, the ball has zero gravitational PE wrt apoint at its own level.