Question

Find the kinetic energy of the objects in the following scenarios: a) A cosmic pion of mass 140 MeV/c2 flies through outer space at a speed of 8.91 × 103 km/s. See the hint for help converting MeV/c2 to kg. b) A cheetah weighing 4.80 × 102 N chases a gazelle at a speed of 33.7 m/s. c) A truck weighing 2.84 short tons speeds down the road at 68.1 mph. d) An asteroid of mass 2.29 × 1017 kg buzzes the Earth at a speed of 15100 mph.

Answer 1

(a)

mass of cosmic pion m = 140 MeV /c²

1MeV = 1.6*10^(-13) J

c = 3*10^8 m/s

m = 140*1.6*10^(-13) / 9**10^16 = 24.88*10^(-29) kg

v = 8.91*10^3 km/s = 8.91*10^6 m/s

KE = 1/2*m*v^2

KE = 0.5*24.88*10^(-29) * (8.91*10^6)^2

KE = 9.87*10^(-15) J

(b)

weight of cheetah W = 4.80*10^2 N

g = 9.8 m/s^2

W = m*g

m = W/g = 4.80*10^2 / 9.8 = 48.97 kg

Energy of cheetah = 1/2*m*v^2

E = 0.5*48.97*(33.7)^2

E = 27812.81 J

(c)

mass of truck m = 2840 kg

velocity of truck v = 68.1 mph

1 mile = 1.6 km

v = 68.1*1.6*10^3 / 3600 = 30.26 m/s

E = 1/2*m*v^2

E = 0.5*2840*(30.26)^2

E = 1300.24 kJ

(d)

mass of asteroid m = 2.29*10^17 kg

v = 15100 mph

v = 15100*1600 / 3600

v = 6711.11 m/s

E = 1/2*m*v^2

E = 0.5*2.29*10^(17)*(6711.11)^2

E = 5.15 *10^(24) J