Answer:
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/[tex]s^{2}[/tex]
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 = [tex]\frac{12000}{300}[/tex]
= 40 kg
The mass of the diver is 40 kg.
2. GPE = 63.25 J
h = 11.5 meters
g = 10 m/[tex]s^{2}[/tex]
GPE = mgh
63.25 = m x 10 x 11.5
63.25 = 115 m
m = [tex]\frac{63.25}{115}[/tex]
= 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/[tex]s^{2}[/tex], 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
