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The Physics of Bowling

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Zoe Garbis

on 18 January 2013

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Transcript of The Physics of Bowling

The Physics of
Bowling Zoe Garbis • January 7th, 2013
Period 1 Physics • Physics of a Sport Motion 60 feet 60 feet Displacement A measurement of how far apart two things are
In bowling, the distance is how far the bowling ball travels until it gets to the end of the lane
Therefore, the distance that the bowling ball travels is usually around the length of the lane Distance Distance vs. Displacement Speed is the rapidity of a movement, or the rate at which distance is covered
In bowling, the speed of the bowling ball directly affects the momentum
The faster the speed of the rolling ball is, the more momentum there will be
Instantaneous speed: speed at any instant
Average speed: total distance covered ÷ time interval
The maximum speed of the bowling ball is at the point of release. After the ball is released, it slows down due to friction between the ball and the lane.
On average, 3 mph is lost during the time that the ball rolls. Speed Velocity is the speed of something in a given direction
To change velocity, change either speed or direction
Equations:
Velocity = displacement / time
Displacement = velocity *time
Time = displacement / velocity
Constant velocity: motion remains the same speed; motion in a straight line
Changing velocity results from speed or direction changing (or both)
Angular velocity is the rate of change of angular position
Indicates how fast the angle is changing Velocity Position-Time Graphs and
Velocity-Time Graphs Acceleration is the rate at which velocity changes
Change of velocity ÷ time interval (a = v ÷ t)
If speed or direction changes, velocity changes, object accelerates
Measured in speed per time interval , represented by letter g
As previously stated, the bowling ball actually decelerates while rolling, losing, on average, 3mph as it rolls down the 60 foot lane
In bowling, in order for the velocity to change, the ball must roll slower or faster, and since it decelerates, it rolls slower, as it loses speed due to friction Acceleration Vectors are arrows with direction and magnitude (velocity, speed, distance, displacement, force)
To add vectors, draw arrows in order (tip-to-tail), then figure out the displacement
To algebraically add vectors, draw in the horizontal components and the vertical components to make a right triangle and then figure out the hypotenuse
Ex: a child is bowling, using the bumpers on the side. The ball hits one, and (ignoring the spinning) continues Vectors Scalars are quantities that are fully described by a magnitude (or numerical value) alone.
Ex: 5 meters, 30 degrees, 50 seconds
Vectors are quantities that are fully described by both a magnitude and a direction.
Ex: 5 meters North, 30 degrees West
Bowling balls do indeed have a direction, and therefore follow the rules of vector quantities. Vector Quantities vs.
Scalar Quantities Forces Law is necessary for bowling; otherwise the ball would stop moving
Friction plays a part in bowling, and acts as an unbalanced force, but the lane is oiled down in order to reduce friction as much as possible An object in motion will stay in motion until acted on by an unbalanced force
An object at rest will stay at rest until acted upon by an unbalanced force
In bowling: a rolling bowling ball will continue to roll down the lane Newton’s 1st Law: Inertia Newton’s 2nd Law: f=m•a This law states that for every action, there is an equal and opposite reaction.
Whenever the bowling ball exerts a force (usually applied) on the pins, the pins exerts an equal and opposite force on the first. Newton’s 3rd Law Center of Gravity Types of Forces Unbalanced/Balanced Forces Free-Body Diagrams Momentum Angular Momentum vs.
Linear Momentum Conservation of Momentum Momentum Elastic and Inelastic Collisions Impulse Bibliography The distance between the starting and ending point
In bowling, since the lane is straight, the bowling ball has no way to travel but forward, so the displacement is the same as the distance Elastic Collision: a collision in which neither of the colliding objects become deformed, generate heat, or lose kinetic energy
Inelastic Collision: a collision in which the colliding objects become deformed, generate heat, or lose kinetic energy (that changes to another form) In bowling: as the bowling ball collides with the the pins, the kinetic energy of the ball is transferred to the pins. On this aspect, the collision is elastic. After multiple bowls, however, the pins deform, so in that aspect, the collision is inelastic. Angular momentum: moment of inertia times the angular velocity
Measuring an object's resistance to changes in its rotation rate or the angular velocity
L = w * i
Moment of Inertia: the angular counterpart to mass In collisions involving the bowling ball and the pins, momentum is conserved
The momentum in the bowling ball is transferred and conserved to the pins Momentum: a quantity that is the product of the object's mass and velocity
Represented as "p"
p = m * v Gravity: the force the pulls all objects on earth towards the core
The acceleration rate of gravity is -9.81 m/s^2
Gravity acts on all objects on Earth at the same rate regardless of mass
The reason for this is because in order for mass to be relevant when discuss Earth's gravitational force, there needs to be a mass that is similar or larger than the Earth, and since we are all so insignificantly light and small compared to our planet, the gravitational force acts the same on us
In bowling, the bowling ball stays on the lane as a result of gravity pulling downwards on it
Gravity is countered by normal force Friction Gravity The measure of the resistance an object has to changing its angular speed.
In bowling: the bowling ball rolling down the lane has angular momentum because the optimal path is for the ball to curve as it rolls Average speed of a bowling ball: 18mph
3 mph lost during rolling time
Lane: 60 feet long Oily Surface Normal Force Vector Addition Air Resistance Applied Friction: the resistance in contact between two surfaces
The rougher the surface, the more friction
The force of friction works against a sliding or rolling object
Bowling lanes are oiled in order to create smooth surfaces with less friction
The more oil that is laid down, the less friction there is between the ball and the lane surface, thus, the ball's speed will not be affected
Inside bowling balls, there is a weight block, but often these are unbalanced
When the weight block has more mass towards one end of the bowling ball (the left picture) the friction is even less because while the less heavily weighted side comes in contact with the floor, there is not as much weight affecting the amount of friction that will be applied to the ball With more symmetrical weight blocks (the right picture), this reduction of friction is less because the weight is distributed somewhat evenly towards the sides of the ball Normal: the force that pushes up away from the earth's core, opposing gravity
It pushes out at a 90 degree angle from the surface of the earth
Without normal force, we would pulled into the center of the earth due to gravity
Therefore, gravity and normal force on Earth are always balanced
Normal force keeps the bowling ball on the lane and prevents it from being pulled into Earth Air resistance plays a small role in physics, but should never be ignored
It is the friction of the air, and as an object moves, it collides with air molecules and is therefore slowed down
Air resistance does not affect the rolling bowling ball as much as friction, but still reduces the speed a little bit Applied: a force in which electrons refuse to mix with neutrons, creating a pushing force
This can be an engine, muscle, or machinery
The bowler initiate the applied force in this sport, when they swing their arm backwards, then use muscles in their arms to launch the ball forward
In the case below, when the bowler didn't let go, the applied force was so strong that he followed the bowling ball in its roll down the lane Force is measured in Newtons (N) To add forces towards the same direction, add
To add forces that go in opposite directions, subtract the smaller from the larger
To add forces going in perpendicular directions, use the Pythagorean Theorem to find the resultant The center of mass, in this case the same as the center of gravity, is the point in the object at which gravity acts; it is, essentially, the center of the object's mass
The center of mass in bowling balls is not in the exact center, due to the asymmetrical weight blocks located in the middle of the ball
These weight blocks do not have the same mass towards all ends of the ball, and therefore, the center of masses may be somewhere around where the red dots are placed. A free-body diagram shows the different forces acting on an object Therefore, the object is at rest, because friction negates applied force and normal force negates gravity. In this case, normal force is pushing up while gravity pulls down and applied force is pushing the the bowling ball east, while friction opposes that force, reducing the effect of the applied force In this free-body diagram, normal force negates gravity, and therefore the bowling ball is moving in neither of those directions.
However, by adding the vectors of friction and applied, you get 8N Eastwards. The ball is in motion. UNBALANCED BALANCED In this free-body diagram, normal force negates gravity, and therefore the bowling ball is moving in neither of those directions. Also, by adding the vectors of friction and applied, you find that they negate each other, and are therefore equal. The ball is at rest. This law states that the bowling ball's acceleration depends on net force acting on the object and its mass
If the force increases, the acceleration increases, but if the mass increases, the acceleration decreases The only time this is applicable is when the bowling ball goes from at rest, to accelerating due to the applied force from the bowler Impulse is a change in momentum, or a force multiplied by the time
These are always equal
Momentum-Impulse Theorem: change in p = m * v
Therefore, either the mass or the velocity (speed or direction) has to change
When the bowling ball hits the pins, a force is applied on the bowling ball for a certain amount of time that results in its mass undergoing a change in velocity
The force comes from the collision Equation for conservation of momentum:
Object 1: ball
Object 2: pin http://www.topendsports.com/sport/tenpin/physics.htm (January 14, 2013)
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Conceptual Physics Textbook (January 13, 2013) Content http://maozi.bubbleroom.se/2012/11
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http://www.enasco.com/product/PE02786E
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All other diagrams/shapes created using Shapes via Microsoft Office Images
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