1. A kicked football leaves the ground at an angle θ = 30o with the initial velocity of 10 m/s. Ball’s mass = 0.1 kg. Acceleration due to gravity is 10 m/s2. Determine (a) The gravitational potential energy at the highest point (b) The highest point or the maximum height
Known :
Mass (m) = 0.1 kg
The initial velocity (vo) = 10 m/s
Angle = 30o
Acceleration due to gravity (g) = 10 m/s2
Solution :
(a) The gravitational potential energy
Calculate the horizontal component (vox) and the vertical component (voy) of initial velocity.
vox = vo cos θ = (10)(cos 30o) = (10)(0.5√3) = 5√3 m/s
voy = vo sin θ = (10)(sin 30o) = (10)(0.5) = 5 m/s
The initial mechanical energy
The initial mechanical energy (MEo) = kinetic energy (KE)
MEo = KE = ½ m vo2 = ½ (0.1)(10)2 = ½ (0.1)(100) = ½ (10) = 5 Joule
The final mechanical energy
Kinetic energy at the highest point :
KE = ½ m vox2 = ½ (0.1)(5√3)2 = ½ (0.1)((25)(3)) = ½ (0.1)(75) = 3.75 Joule
Principle of conservation of mechanical energy
The initial mechanical energy (MEo) = the final mechanical energy (MEt)
KE = PE + KE
5 = EP + 3.75
PE = 5 – 3.75 = 1.25 Joule
The gravitational potential energy at the highest point is 1.25 Joule.
(b) The highest point or the maximum height
PE = m g h
1.25 = (0.1)(10) h
1.25 = h
The maximum height is 1.25 meters.
2. A 0.1-kg ball projected horizontally with initial velocity vo = 10 m/s from a building 10 meter high. Acceleration due to gravity is 10 m/s2. Determine ball’s kinetic energy when it hits the ground.
Known :
Mass (m) = 0.1 kg
Initial velocity (vo) = 10 m/s
Acceleration due to gravity (g) = 10 m/s2
The change in height (h) = 10 – 2 = 8 m
Wanted: kinetic energy at 2 meters above the ground
Solution :
The gravitational potential energy (PE) = m g h = (0.1)(10)(10) = 10 Joule
The initial kinetic energy (KE)= ½ m vo2 = ½ (0.1)(10)2 = ½ (0.1)(100) = ½ (10) = 5 Joule
The final kinetic energy = the initial gravitational potential energy + the initial kinetic energy = 10 + 5 = 15 Joule
[wpdm_package id=’1173′]
- Work done by force problems and solutions
- 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