Grade 6-7 1. A diver who climbs up to the 30 meter high dive
board gains 12000J of GPE. What is her mass?
2. A football kicked 11.5 meters in the air gains
63.25J of GPE. What is the mass of the football?
3. Explain, using calculations, why a pole vaulter
who competes on another planet wouldn't have
the same GPE as on Earth.

1. m  = 40 kg

2. m = 0.55 kg

3. Because of the different values of acceleration due to gravity, g, on the planet and the earth.

Explanation:

1. GPE = 12000 J

h = 30 meters

g = 10 m/

But,

GPE = mgh

where: m is the mass, g is the acceleration due to gravity, and h is the height.

12000 = m x 10 x 30

12000  = 300 m

m =

   = 40 kg

The mass of the diver is 40 kg.

2. GPE = 63.25 J

h = 11.5 meters

g = 10 m/

GPE = mgh

63.25 = m x 10 x 11.5

63.25 = 115 m

m =

   = 0.55 kg

The mass of the ball is 0.55 kg.

3. The pole vaulter's GPE on the earth would not be the same as that on another planet due to the variation in the value of the acceleration due to gravity on the two planets, even if he cover the same height.

Given that: m = 60 kg, h = 25 m, determine the GPE on the earth that has g = 10 m/, and another planet with g = 6.5 m/

Thus, on the earth;

GPE = mgh

       = 60 x 10 x 25

       = 15000

GPE = 15000 J

On the planet;

GPE = mgh

       = 60 x 6.5 x 25

       = 9750

GPE = 9750 J