1. A block slides down on smooth inclined plane without friction. What is block’s velocity when hits the ground. Acceleration due to gravity is 10 m/s2
Known :
Height (h) = 8 m
Acceleration due to gravity (g) = 10 m/s2
Wanted : velocity (v)
Solution :
Initial mechanical energy (MEo) = gravitational potential energy (PE)
MEo = PE = m g h = m (10)(8) = 80 m
Final mechanical energy (MEt) = kinetic energy (KE)
MEt = KE = ½ m v2
Principle of conservation of mechanical energy states that the initial mechanical energy = the final mechanical energy :
MEo = MEt
80 m = ½ m v2
80 = ½ v2
160 = v2
v = √160 = √(16)(10) = 4√10 m/s
2. A 1-kg object slides down along 8 meters. Determine kinetic energy after the object moves along 5 meters… Acceleration due to gravity g = 10 m/s2
Known :
Mass (m) = 0.2 kg
d = 5 meters
Acceleration due to gravity (g) = 10 m/s2
Wanted : kinetic energy (KE)
Solution :
sin 30o = h / d
0.5 = h / 5
h = (0.5)(5) = 2.5 meters
The change in height of the object is 2.5 meters.
The initial mechanical energy (MEo) = the gravitational potential energy (PE)
MEo = PE = m g h = (1)(10)(2.5) = 25 Joule
The final mechanical energy (MEt) = kinetic energy (KE)
MEt = KE
The principle of conservation of mechanical energy states that the initial mechanical energy = the final mechanical energy :
MEo = MEt
25 = KE
Kinetic energy = 25 Joule.
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