The website, Real World Physics Problems (Links to an external site.), has an ex
ID: 1423516 • Letter: T
Question
The website, Real World Physics Problems (Links to an external site.), has an example of the Physics Of Bowling (Links to an external site.) and it describes the physics of a bowling ball that help us understand the factors that influence how a bowling ball curves, and how one can make the best possible shot when striking the pins. Assuming a larger hook to the left (for a right-handed person) increases a chance of a strike, provide your reasoning of the physical parameters that can improve a chance of a strike.
http://www.real-world-physics-problems.com/physics-of-bowling.html
Explanation / Answer
Bowling Ball Motion
The optimal trajectory of a bowling ball is a curved path where it strikes the pins at an angle. Striking the pins at an angle improves the chances that there will be a "strike" in which all the pins are knocked down.
The main influence on ball motion is friction between the ball and the lane, whether it's due to friction influenced by ball precession, or natural lane conditions (e.g. oiled vs. non-oiled).
Thus, we wish to look at three different cases of friction, in order to observe its effect on ball motion.
Let's assume that the initial angular velocity of the ball wo = 30 rad/s, and the initial linear velocity of the ball Vo = 8 m/s. This is a reasonable estimate for the typical bowler who averages 200 (ref: What Makes Bowling Balls Hook?, Cliff Frohlich, American Association of Physics Teachers, 2004).
Let's assume wo is pointing 15° to the left of the Y-axis, so that it has components wX = -30xsin 15° = -7.76 rad/s, and wY = 30xcos15° = 28.98 rad/s.
And let's assume that Vo is pointing in the positive X-direction.
The beginning of the bowling balls trajectory is at X = 0.
The following additional input values are used with regards to the initial orientation, and properties of the bowling ball:
• The distance between the center of the bowling ball C and the center of mass G is 1 mm (0.001 m). The point CG is pointing in the positive Y-direction.
• The bowling ball has a symmetric weight block with the pin pointing in the positive Y-direction.
• The radius of the bowling ball is 10.85 cm.
• The mass of the bowling ball is 7 kg.
• The minimum principal moment of inertia is 0.031 kg-m2. This is the moment of inertia about an axis passing through the center of mass of the bowling ball G and the pin.
• The maximum principal moment of inertia is 0.033 kg-m2. This is the moment of inertia about any axis which passes through the center of mass of the bowling ball G and which is perpendicular to the axis corresponding to the minimum principal moment of inertia.
Lastly, the input value for the acceleration due to gravity (on earth's surface) is 9.8 m/s2.
The above input values will be held constant for the following three friction cases to be considered. In all three cases the static friction will be assumed sufficient enough to maintain pure rolling once pure rolling begins.
Friction Case 1
The coefficient of kinetic (sliding) friction is equal to 0.12. This value of kinetic friction will be taken as constant over the entire length of the lane, as illustrated below.
Simulation Results
The bowling ball slides 9 m before pure rolling begins.
The ball hooks to the left = 68 cm.
The impact angle is 3.6°
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