Gravitational potential energy calculations

Question 1

A boy has a mass of 55 kg.
He climbs 12 m up a tree.
What is his gain in Gravitational Potential Energy (GPE)?

Answer 1

Change in GPE = mass × gravity × change in height

Change in GPE = 55 × 10 × 12
= 6600 J
= 6·6 kJ

Question 2

An astronaut has a total mass of 110 kg.
On the moon, he climbs into his spacecraft, 5 m up a ladder.
His GPE increases by 880J.
What is the strength of gravity on the moon?

Answer 2

Change in GPE = mass × gravity × change in height

880 = 110 × gravity × 5
8 = gravity × 5
gravity = 1.6 N/kg or m/s²

Question 3

A pear has a GPE of 14J and a mass of 275g. Calculate it’s height in m giving your answer to 2 decimal places. Take the value of g as 9.8 N/kg

Answer 3

Change in GPE = mass × gravity × change in height

GPE = mgh
h = GPE/mg
h = 14 / 0.275 x 9.8
h = 14 / 2.695
h = 5.19m (2 d.p)

Question 4

An apple has a GPE of 15J and is held at a height of h=225cm above the ground. Calculate the mass of the apple in g. Take the value of g as 9.8 N/kg

Answer 4

Change in GPE = mass × gravity × change in height

GPE = mgh
m = GPE / gh
m = ( 15 ) / 9.8 x 2.25
m = ( 15 ) / 22.05
m = 0.68kg
m = 680g

Question 5

A 5kg cat is lifted 2m into the air.

How much GPE does it gain?

Answer 5

Change in GPE = mass × gravity × change in height

GPE = mgh
GPE = 5 x 10 x 2
GPE = 100J

Question 6

A large block of stone is held at a height of 15m having gained 4500J of GPE. How much
does it weigh?

Answer 6

GPE = mgh
m = GPE / gh
m = 4500 / 10 x 15
m = 30kg

Question 7

A block of stone of weight 600kg gains 36000J of GPE. How high has
it been raised?

Answer 7

GPE = mgh
h = GPE / mg
h = 36000 / 600 x 10
h = 6m