1. A 1-kg block slides down on the smooth curved surface. Determine the kinetic energy and the velocity of the block at the lowest surface. Acceleration due to gravity is 10 m/s2.
Known :
Mass (m) = 1 kg
The change in height (h) = 5 m
Acceleration due to gravity (g) = 10 m/s2
Wanted: Kinetic energy (KE) and the velocity of the block.
Solution :
(a) Kinetic energy
The initial mechanical energy = gravitational potential energy
MEo = PE = m g h = (1)(10)(5) = 50 Joule
The final mechanical energy = kinetic energy
MEt = KE = ½ m vt2
Principle of conservation of mechanical energy states that the initial mechanical energy = the final mechanical energy :
MEo = MEt
PE = KE
50 = KE
Kinetic energy (KE) = 50 Joule.
(b) Block’s velocity
The principle of conservation of mechanical energy :
The initial mechanical energy (MEo) = the final mechanical energy (MEt)
The gravitational potential energy (PE) = kinetic energy (KE)
50 = ½ m v2
2(50) / m = v2
100 / 1 = v2
100 = v2
v = √100
v = 10 m/s
2. A 2-kg object slides down without friction. What is the kinetic energy and the velocity of the object at 2 meters above the ground. Acceleration due to gravity is 10 m/s2
Known :
Mass (m) = 2 kg
The change in height (h) = 10 – 2 = 8 m
Acceleration due to gravity (g) = 10 m/s2
Wanted : kinetic energy (KE) and velocity (v) at 2 meters above the ground.
Solution :
(a) Kinetic energy at 2 meters above the ground
The initial mechanical energy = the gravitational potential energy
MEo = PE = m g h = (2)(10)(8) = 160 Joule
The final mechanical energy = kinetic energy
MEt = KE = ½ m vt2
The principle of conservation of mechanical energy states that the initial mechanical energy = the final mechanical energy :
MEo = MEt
PE = KE
160 = KE
Kinetic energy (KE) at 2 meters above the ground is 160 Joule.
(b) Object’s velocity at the lowest surface
Principle of conservation of mechanical energy :
The initial mechanical energy (MEo) = the final mechanical energy (EMt)
The gravitational potential energy (PE) = kinetic energy (KE)
160 = ½ m v2
160 = ½ (2) v2
160 = v2
v = √160 = √(16)(10) = 4√10 m/s
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