# Gravitational potential energy – problems and solutions

1. A 1-kg body free fall from rest, from a height of 10 m.

Determine :

(a) Work done by force of gravity

(b) The change in gravitational potential energy

Acceleration due to gravity (g) = 10 m/s^{2}

__Known :__

Mass (m) = 1 kg

Height (h) = 10 m

Acceleration due to gravity (g) = 10 m/s^{2}

Weight (w) = m g = (1 kg)(10 m/s^{2}) = 10 N

__Solution :__

(a)** Work done by force of gravity**

W = w h = m g h

W = (1)(10)(10) = 100 Joule

(b) **The change in gravitational potential energy**

The change in gravitational potential energy is equal to the work done by gravity.

ΔEP = 100 Joule

2. A 10 N object slides down on the smooth inclined plane along 2 meters. Determine work done by weight force!

__Known :__

weight (w) = 10 N

w_{x} = w sin θ = (10)(sin 30^{o}) = (10)(0.5) = 5 N

d = 2 m

Acceleration due to gravity (g) = 10 m/s

^{2}

__Wanted :__ work done by weight force

__Solution :__

W = F d = w_{x} d = (5)(2) = 10 Joule

**Alternative solution :**

Sin 30^{o} = h / d

0.5 = h / 2

h = (0.5)(2)

h = 1 m

Work done by weight force ;

W = F d = w h = (10 N)(1 m) = 10 N m = 10 Joule

3. A 1,500 gram object at 20 meters above the ground, free fall to the ground. What is the gravitational potential energy of the object. Acceleration due to gravity is 10 m/s^{2}.

__Known :__

Acceleration due to gravity (g) = 10 m/s^{2}

Mass (m) = 1500 gram = 1500/1000 kilogram = 1.5 kilogram

Height (h) = 20 meters

__Wanted :__ The gravitational potential energy

__Solution :
__

PE = m g h = (1.5 kg)(10 m/s^{2})(20 m) = 300 kg m^{2}/s^{2} = 300 Joule

4. Based on figure below, if mass of object 1 is 2 kg and mass of object 2 is 4 kg, comparison of potential energy of object 1 and object 2 is …..

__Known :__

Mass of object 1 (m_{1}) = 2 kilogram

Mass of object 2 (m_{2}) = 4 kilogram

Height 1 (h_{1}) = 12 meters

Height 2 (h_{2}) = 9 meters

__Wanted:__ Comparison of potential energy of object 1 and object 2

__Solution :__

PE = m g h

m = mass (its international unit is kilogram, abbreviated kg)

g = acceleration due to gravity (its international unit is meter per second squared, abbreviated m/s^{2})

h = height (its international unit is meter, abbreviated m)

PE = gravitational potential energy (its international unit is kg m^{2}/s^{2 }or Joule)

The gravitational potential energy of object 1 :

EP_{1 }= m_{1 }g h_{1}= (2)(g)(12) = 24 g

The gravitational potential energy of object 2 :

EP_{2 }= m_{2} g h_{2} = (4)(g)(9) = 36 g

Comparison of the potential energy of object 1 and object 2 :

PE_{1 }: PE_{2 }

24 g : 36 g

24 : 36

24/12 : 36/12

2 : 3

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