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...

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.