# Newton's guide to putt-putt: discover how physics can help you sink golf putts like a professional.

DID YOU KNOW?

* In 1927, Garnet Carter patented the first miniature golf game, which he called "Tom Thumb Golf." He hoped his mini-golf course, located on Lookout Mountain in Tennessee, would attract people to his neighboring hotel and its full-length golf course. Turned out, his putt-putt course became more popular than his regulation-size golf course.

* Every year, professional mini-golf players putt away at the Masters of Pro Mini Golf. Rather than donning the trademark green jacket awarded in the PGA's Masters, the mini-golf champion sports a windbreaker.

CRITICAL THINKING:

* Each type of ball game requires a specially designed ball. Select a type of ball game. Then, describe how its ball's physical properties, such as its shape and material, help contribute to the game. For help, see: www.exploratorium.edu/sports/ball_bounces/index.html

CROSS-CURRICULAR CONNECTIONS:

ART: Divide the class into teams. Have each team design one section of a mini-golf course. Then, as a class, construct a model of the course. For ideas and examples, see: www.smm.org/sln/invent/golf/

RESOURCES

A carnival-like playground crisscrossed with "fairways" and rolling golf balls can get anyone into the competitive spirit. But before you hit the miniature golf course, study these lessons from physicist Sir Isaac Newton and learn how to sink putts with ease.

1. TEE TIME

Gazing at the green, you prepare for the first putt. For good aim, you visualize a path from your ball down the fairway's middle. Should you swing the putter with Tiger-Woods-like force? No way: Your ball would likely fly off the course. According to Newton's second law of motion, force equals mass multiplied by acceleration. "[In other words], the harder you hit the ball--giving it a bigger pushing force--the faster it will speed up, or accelerate," explains Paul Doherty, a physicist at the Exploratorium in California.

A moderate whack of your putter is all it takes to send the sphere rolling gently along the fairway.

2. ON A ROLL

Cross your fingers that the ball stops rolling before it strikes any obstacles. No luck--Ping!--your ball ricochets off a boat that juts into the middle of the fairway. "When the ball hits an obstacle, it exerts a force on [the obstacle]," says Doherty. "Because of action-reaction forces, [or Newton's third law of motion], the obstacle pushes back on the ball, causing the ball to change its direction." Also, your ball transfers some of its energy to the boat. With less energy, the ball's speed is reduced.

The biggest slowdown comes from the carpeted fairway. With each revolution, the dimpled orb presses down and deforms the turf, creating rolling friction. Eventually, this slowing force brings the ball to a halt ...

3. FEELING LOOPY?

... right in front of a teardrop-shaped loop. How should you hit the ball so it sticks to the ramp when traveling upside down? "As the ball moves around the loop, two forces act on it: a centrifugal force, which pushes the ball [outward] and against the ramp, and gravity, which pulls it down," says Raymond Penner, a physicist at Malaspina University-College in British Columbia. "If the centrifugal force is greater than gravity, the ball won't fall."

A faster-moving ball experiences a higher centrifugal force. So you give the ball a solid strike. It hurls up the steep ramp, over the loop, and then whizzes down the twister's backside.

4. GAME OVER

With the hole in sight, you imagine your ball zooming into the canister. But will the ball pop back out? To avoid this nerve-racking result, hit the ball lightly. Why? According to Doherty, if the ball reaches the cup at a high speed, it will drop in and hit the far rim of the canister with so much kinetic energy, or energy of motion, that it will overcome gravity's downward tug and bounce right out.

With a soft putt, and thanks to Sir Isaac, you score.

WEB EXTRA

Learn about Newton's laws of motion at: www.physics classroom.com/mmedia/newtlaws/newtlawsTOC.html

Directions: Fill in the blanks to complete the following sentences.

1. According to Newton's--law of--, force equals--multiplied by--. That means, the harder you hit an object, the faster it will speed up.

2. When a golf ball hits an obstacle, it exerts a force on the obstacle. Because of the--forces described by Newton's--law of--, the obstacle also pushes back on the ball, causing the ball to change its direction.

3. As a golf ball rolls down a carpeted mini-golf fairway, the ball presses down and deforms the turf. This creates a slowing force called -- --.

4. Consider a golf ball that is traveling through a tear-drop-shaped loop. As long as the ball's -- --, which pushes the ball outward and against the ramp, is greater than the pulling force of --, the ball won't fall off the ramp.

1. second, motion, mass, acceleration

2. action, reaction, third, motion

3. rolling friction

4. centrifugal force, gravity

GOLF GENIUS

In "Newton's Guide to Putt-Putt" (p. 16), you learned that physics can help you score in miniature golf. Now, use what you learned to calculate your way down the fairway. First, review "Newton's Numbers" (below). Then, use the formulas to help you answer the questions that follow.

Newton's Numbers

Force (newtons) = Mass (kilograms) x Acceleration (meters/[second.sup.2]), written as N = kgm/[s.sup.2]

Momentum (mkg/s) = Velocity (m/s) x Mass (kg)

Mass of a standard golf ball = 0.045 kg

1. You head to the first hole of the miniature golf course. With your putter, you whack the golf ball and watch as it rolls down the fairway with an acceleration of 3.5 m/[s.sup.2]. How much force, in newtons (kgm/[s.sup.2]), must your putter have applied to the golf ball? Round your answer to two decimal places.

2. Your ball stops at the foot of a steep slope. Today, the course managers are offering a free ice-cream cone to anyone who can putt the ball up and over the slope with just one stroke. Before you putt, the course managers offer you a choice: You can use either a standard golf ball or one with double the mass. Don't make any decisions yet! For now, calculate to find each ball's momentum, assuming a velocity of 3 m/s.

3. You really want a free ice-cream cone. So consider this: The greater the momentum of an object, the harder it is to stop the object. To increase the chance that your ball will climb up the slope in one stroke, do you choose the heavier golf ball or the standard one?

4. The ball sails up the slope and down the hill. Soon, it stops. If you chose the heavier ball in question 3, it's time to exchange it for the standard mass one to continue with the game. You make another hit, giving the ball a momentum of 1 mkg/s. Suppose you hit the ball with nail-on accuracy, how many seconds will it take for the ball to reach a ramp that's a whopping 22 meters away?

Hint: First, use the golf ball's mass to help you calculate the velocity. Then, if you know the meters traveled per second, you can determine how many seconds it takes to travel 22 meters.

5. Your ball is now within striking distance of the hole. Unfortunately, your aim is off. Your stroke sends your golf ball rolling with an acceleration of 2.5 m/[s.sup.2] before hitting a bolted-down Mr. Potato Head figure along the fairway. According to Newton's third law of motion, the obstacle and the ball will push on each other with equal and opposite forces. What is the force, in newtons, on the ball when it bounces off Mr. Potato Head? Round your answer to two decimal places.

6. Now your ball is perched on a small hill above the hole. In addition to the force from the face of your putter, what other force do you think will help push your ball down the hill and into the hole?

1.0.16 N

2. momentum of the standard golf ball: 0.135 mkg/s; momentum of the golf ball with double the mass: 0.27 mkg/s

3. You choose the heavier ball, because it will have a greater momentum.

4. it will take just under 1 second.

5. 0.11 N

6. gravity
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