Kinetic energy – problems and solutions

1. Two cars have the same mass, moving with different kinetic energy. The kinetic energy of the first car is 9 times the second car’s kinetic energy. The first car speed comparison with the second car is …..

__Known :__

Mass of car A (m_{A}) = m

Mass of car B (m_{B}) = m

The kinetic energy of car B (KE_{B}) = KE

The kinetic energy of car A (KE_{A}) = 9 KE

__Wanted:__ The first car speed comparison with the second car

__Solution :__

The equation of kinetic energy :

KE = 1/2 m v^{2}

2 KE = m v^{2}

v^{2 }= 2 KE / m

The speed of car A :

v^{2 }= 2 KE_{A} / m_{A }= 2 (9 KE) / m = 18 KE / m

The speed of car B :

v^{2 }= 2 KE_{B} / m_{B }= 2 KE / m = 2 KE / m

The comparison of the speed of car A and car B :

18 KE / m : 2 KE / m

18: 2

9 : 1 = 3^{2} : 1^{2}

2. The kinetic energy of the object at point B = 100 J. If the mass of the object is 2.5 kg, then determine the kinetic energy of the object when it strikes the ground at point C. Acceleration due to gravity is 10 m/s^{2}.

Solution

The kinetic energy of the object when it arrives at point B :

PE = m g h = (2.5)(10)(4) = 100 Joule

The kinetic energy of the object when it arrives at point C :

PE = m g h

PE = (2.5)(10)(4 + 6)

PE = (2.5)(10)(10)

PE = 250 Joule