It is common for a pitcher to throw a fastball that has a linear velocity of 100
ID: 1457239 • Letter: I
Question
It is common for a pitcher to throw a fastball that has a linear velocity of 100 mph and rotational velocity of 2000 revolutions per minute (rpm). A Major League baseball has a weight of five ounces and a circumference of nine inches. Be very careful with units in the following calculations!
PL1. What is the translational kinetic energy of a baseball that is thrown at 100 miles per hour? Give your answer in joules.
PL2. A baseball has a weight of five ounces and a circumference of 9 inches. Assuming it has a uniform density, what is the moment of inertia of a baseball? Give your answer in kgm^2.
PL3. What is the rotational kinetic energy of a baseball that is spinning at 2000 rpm? Give your answer in joules.
Explanation / Answer
It is common for a pitcher to throw a fastball that has a linear velocity of 100 mph and rotational velocity of 2000 revolutions per minute (rpm). A Major League baseball has a weight of five ounces and a circumference of nine inches.
100 mph = 44.69 m/sec
= 2PI/60*n = 0.10472*2000 = 209.4 rad/sec
m = 5*28.35 = 141.75 gr
r = 2.54*9/6.2832 = 3.64 cm
1. What is the translational kinetic energy Ekt (in joules) of a baseball that is thrown at 100 miles per hour?
Ekt = 1/2m*V^2 = (0.14175*44.69^2)/2 = 141.55 joule
2. A baseball has a weight of five ounces and a circumference of 9 inches. Assuming it has a uniform density, what is the moment of inertia J of a baseball? Give your answer in kgm^2.
J = 2/5m*r^2 = 0.14175*2/5*0.0364^2 = 7.51*10^-5 kgm^2
3. What is the rotational kinetic energy Ekr (in joules) of a baseball spinning at 2000 rpm?
Ekr = (7.51*10^-5*2.094^2*10^4)/2 = 1.65 joule
Total kinetic energy Ek = Ekr+Ekt = 1.65+141.55 = 143.20 joule
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