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/s2

Gravitational potential energy – problems and solutions 1Known :

Mass (m) = 1 kg

Height (h) = 10 m

Acceleration due to gravity (g) = 10 m/s2

Weight (w) = m g = (1 kg)(10 m/s2) = 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

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

Gravitational potential energy – problems and solutions 2Known :

weight (w) = 10 N

wx = w sin θ = (10)(sin 30o) = (10)(0.5) = 5 N

d = 2 m

Acceleration due to gravity (g) = 10 m/s2

Wanted : work done by weight force

Solution :

W = F d = wx d = (5)(2) = 10 Joule

Alternative solution :

Sin 30o = 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

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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/s2.

Known :

Acceleration due to gravity (g) = 10 m/s2

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/s2)(20 m) = 300 kg m2/s2 = 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 (m1) = 2 kilogramGravitational potential energy – problems and solutions 5

Mass of object 2 (m2) = 4 kilogram

Height 1 (h1) = 12 meters

Height 2 (h2) = 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/s2)

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

PE = gravitational potential energy (its international unit is kg m2/s2 or Joule)

The gravitational potential energy of object 1 :

EP1 = m1 g h1= (2)(g)(12) = 24 g

The gravitational potential energy of object 2 :

EP2 = m2 g h2 = (4)(g)(9) = 36 g

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

PE1 : PE2

24 g : 36 g

24 : 36

24/12 : 36/12

2 : 3

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