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
Known :
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
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
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
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 kilogram
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
[wpdm_package id=’1175′]
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- Work-kinetic energy problems and solutions
- Work-mechanical energy principle problems and solutions
- Gravitational potential energy problems and solutions
- The potential energy of elastic spring problems and solutions
- Power problems and solutions
- Application of conservation of mechanical energy for free fall motion
- Application of conservation of mechanical energy for up and down motion in free fall motion
- Application of conservation of mechanical energy for motion on a curved surface
- Application of conservation of mechanical energy for motion on an inclined plane
- Application of conservation of mechanical energy for projectile motion
