Centripetal Force

Centripetal Force

Description

The apparatus and set up used demonstrates the magnitude and direction of centripetal forces.

Possible Incorporated Topics

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centripetal force

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spring force

Theory

An object moving in a circle at a constant speed is said to be undergoing "uniform circular motion". Though the speed of the object is not changing, the direction of motion is which implies the object is experiencing acceleration. To cause this acceleration, there must be a force on the object. This force is directed toward the centre of the circle, so it is called a "centripetal force". The machine used in this demonstration (Fig.1) can be used to show some properties of centripetal force. It consists of a mass (M) hanging by a string from a bar on a rotating post (A). The vertical post (B) and the mass are joined by a spring (S), which is responsible for exerting the centripetal force that keeps the mass moving in a circle. Watching the video, one can see not only that the centripetal force is directed toward the centre of the circle, but also that it is possible to calculate the magnitude of the centripetal force using this set-up. As the mass rotates faster and faster, it stretches the spring and moves in a circle with a larger and larger radius. Once the circle is large enough, the mass strikes a flexible post (P). Since the spring is exerting the centripetal force, the magnitude of the spring force is equal to the centripetal force. Calculating the spring force at this radius will therefore give the magnitude of the centripetal force. Apparatus

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three metal rods; two that can interlock to form a "T" shape; -one rod must hold a mass and the other must have a spring connected to it (see A and B in diagram)

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various hanging masses

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mass hanger

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spring (S)

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flexible metal rod (P)

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string which connects to mass M and the mass hanger

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pulley attached to a metal rod

(see Fig. 1 for diagram of set-up).

Fig.1: Set-up of apparatus. Procedure 1. Refer to Fig.1 for set up. Make sure everything is securely attached since the apparatus may end up being spun fairly quickly! (In the filmed demo. the entire apparatus is clamped to the table to eliminate wobbling). 2. Spin the rotating post faster and faster until the mass, M, just touches the flexible vertical post (P). (This demonstrates the direction of centripetal motion) To calculate the magnitude of the centripetal force at the radius of the post:

3. Attach a string to the side of the mass facing the pulley and place it over the pulley. Attach a mass hanger to the other end of the string. 4. Place hanging masses onto the mass hanger until the spring is stretched enough that the mass, M, touches the vertical post. 5. The spring force (and therefore the centripetal force) is then the total mass added to the mass hanger times the acceleration due to gravity, i.e.: Fcentripetal = mg

SAFETY WARNINGS!

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Ensure the mass attached to post A is screwed on tight; otherwise it will fly off when spinning.

Spinning Ball

Description

The use of a simple apparatus demonstrates one aspect of Newton’s first law of motion: An object in motion will continue with the same speed and direction unless acted on by some external force.

Possible Incorporated Topics

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Theory

centripetal motion and forces

Newton’s first law of motion says that a moving object will continue moving in a straight line unless it is acted on by a force. For example, if you threw a football, it would keep flying forever if the force of gravity were not pulling it down to Earth; a curling rock would slide forever if the ice it was sliding on was frictionless. In this demonstration, a steel ball is given a push and rolls around on the inside of a plastic cylinder. If an object moves in a circle like this, it is obviously not moving in a straight line, and therefore it must have a force acting on it. The force present is the normal force from the ball's contact with the inside of the cylinder (see Fig.1).

Fig.1: Normal force acting on the ball If the ball loses contact with the cylinder (like when it encounters the hole in the cylinder’s side), it no longer has the normal force acting on it. It will then continue to roll in a straight line tangential to the direction it was traveling before encountering the hole since the only force acting on it is the force of the push that was initially given to it (see Fig. 2).

Fig. 2: Motion of ball in notched cylinder. Apparatus - small steel ball - plastic cylinder with a notch cut out of the circumference of one of the cylinder’s faces Procedure 1. Place the cylinder on a flat surface with the notched side up. 2. Place the steel ball against the inside of the cylinder and push it, observing the ball’s motion around the cylinder’s circumference. 3. Flip the cylinder so that the notched side is against the surface. 4. Push the ball as in step 2 and observe its motion when it encounters the hole in the cylinder.

SAFETY WARNINGS! -

push the ball at a safe speed and make sure the demonstrator is ready to catch it when it reaches the notched part of the cylinder.

Double Ball Drop PIRA #: 3N30.60 setup time: 1 minute

Description: Dropping two balls, one on top of the other, causes one of the balls to bounce super high!

Theory: This demonstration shows one of the effects of the conservation of momentum. Two rubber balls (a tennis ball and a basketball) are dropped from about chest height. As they fall, they build up speed. When the basketball strikes the floor, it rebounds and collides with the tennis ball. Just before the balls collide, they both are moving at the same speed, but the basketball has a larger mass (and therefore more momentum). It turns out that the basketball transfers most of its momentum to the lightweight tennis ball, with the result being that the tennis ball bounces very high, and the basketball barely rises off the ground.

Apparatus: • • •

basketball tennis ball ping-pong ball (optional)

Procedure: First take the basketball and tennis ball and hold them with the tennis ball on top. Drop both balls at the same time. The same trick can be done with three balls. Hold the tennis ball on top of the basketball as before, but also place the ping-pong ball above the tennis ball, and drop the balls together.

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Don't do this demo around the good crystal glasses - they'll probably get knocked over.

Electrical Fleas Start your own electric flea circus! You're probably familiar with some of the effects of static electricity: Static electricity makes the sparks when you comb your hair on a cold day, and it makes balloons stick to the wall at a birthday party. In this Snack, static electricity makes electric "fleas" jump up and down. • • • • •

A sheet of acrylic plastic or other clear plastic (about 1 foot [30 cm] square and 1/s inch [3 mm] thick). A piece of wool cloth or fur. 4 supports about 1 to 2 inches (2.5 to 5 cm) high (tuna cans work nicely). A large piece of white paper, 11 x 17 inches (28 x 43 cm). Tiny bits of "stuff." Aluminized ceiling glitter works well, as do grains of rice, puffed rice cereal, spices (dill weed, basil, ground cloves, or nutmeg), or bits of Styrofoam.

(5 minutes or less)Put the piece of paper on the table. Place the supports on the paper beneath the four corners of the plastic, and scatter the tiny bits of Styrofoam, spices, ceiling glitter, or rice under the plastic. (You can set this assembly up on any tabletop.)

(15 minutes or more)Charge the plastic by rubbing it vigorously with the piece of wool cloth or fur. Watch the "fleas" dance! Try different types of material for charging the plastic, including your hand, and experiment with other materials for fleas. Also, try the plastic at different heights.

Both the plastic and the fleas start out electrically neutral. That is, they have an equal number of positive and negative charges. When you rub the plastic with the wool cloth, the cloth transfers negative charges to the plastic. These negative charges polarize the fleas, attracting the positive charges to the tops of the fleas and pushing the negative charges to the bottoms of the fleas. The attraction between the negative plastic and the positive charge concentrated on the top of the fleas makes the fleas jump up to the underside of the plastic. When a flea actually touches the plastic, some of the plastic's negative charge flows to the flea. The top of the flea becomes electrically neutral. But since the whole flea was originally neutral, the flea now has some excess negative charge. The negatively charged flea and the negatively charged plastic repel each other strongly, which causes the flea to jump quickly back to the table. As the flea's excess negative charge slowly drains away to the tabletop, or to the air, the flea again becomes neutral and is ready to jump up to the plastic once more.

While the fleas are dancing, put your ear on the plastic plate. Listen to the tapping of the fleas as they hit the plastic. The tapping rate slowly decreases as the charge on the plastic is depleted. The dance of the fleas sounds like the clicking of a Geiger counter measuring a radioactive source that is decaying.

Electroscope What's your (electrical) sign? A commonly available brand of plastic tape can gain or lose negatively charged electrons when you stick it to a surface and rip it off. By suspending pieces of tape from a straw, you can build an electroscope, a device that detects electrical charge. A plastic comb will enable you to identify whether the pieces of tape are positively or negatively charged. • • • •

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4 plastic drinking straws with flexible ends. 2 plastic 35 mm film cans. Enough modeling clay to fill the film cans halfway. A roll of 3-M Scotch Magic™ Tape, 3/4 inch (2 cm) width. (Don't substitute other brands of tape the first time you try this Snack. Once you know what to expect, you can experiment with other tapes.) A plastic comb and hair or a piece of wool cloth.

(5 minutes or less)Press enough modeling clay into both film cans to fill them halfway to the top. Press the inflexible ends of two drinking straws into the clay in each can, and bend the flexible ends to form horizontal arms that extend in opposite directions. The heights of the straws should be the same. (15 minutes or more)Tear off two, 4 inch (10 cm) pieces of tape. Press each piece firmly to a tabletop or other flat surface, leaving one end of each tape sticking up as a handle. Quickly pull the tapes from the table and stick one piece on an arm of a straw in one film can, and the other piece on an arm of a straw in the other film can. Move the cans so that the two tapes are face to face, about 6 inches (15 cm) apart. Then move the cans closer together. Notice that the two tapes repel each other. Tear off two more pieces of tape and press the sticky side of one against the smooth side of the other, leaving one end of each tape sticking out as a handle. Quickly pull the tapes apart and stick them to the two remaining arms. Bring the arms close together. Notice that these two tapes attract each other. Run the comb through your hair, or rub the comb with the wool cloth. Then hold the comb near the dangling tapes. Notice that the comb repels the piece of tape whose smooth side was in the middle of the "sandwich" and attracts the tape whose sticky side was in the middle. When you

hold the comb near the tapes pulled from the flat surface, the comb will repel both tapes if they were pulled from a Formica™ surface; the comb may attract tapes pulled from other surfaces. Try pulling other kinds of tape from various surfaces, or rubbing various objects together, and then bringing the tape or objects near the tapes on the arms. Bring your hand near the tapes and notice what happens.

When you rip the two pieces of tape off the table, there is a tug-of-war for electric charges between each tape and the table. The tape either steals negative charges (electrons) from the table or leaves some of its own negative charges behind, depending on what the table is made of (a positive charge doesn't move in this situation). In any case, both pieces of tape end up with the same kind of charge, either positive or negative. Since like charges repel, the pieces of tape repel each other. When the tape sandwich is pulled apart, one piece rips negative charges from the other. One piece of tape therefore has extra negative charges. The other piece, which has lost some negative charges, now has an overall positive charge. Since opposite charges attract, the two tapes attract each other. When you run a plastic comb through your hair, the comb becomes negatively charged. Tapes repelled by the comb have net negative charge, and tapes attracted by the comb either have net positive charge or are uncharged. You may have found that your hand attracts both positively and negatively charged tapes. Your body is usually uncharged, unless you have acquired a charge -- by walking across a carpet, for example. An uncharged object attracts charged objects. When you hold your hand near a positively charged tape, the tape attracts electrons in your body. The part of your body nearest the tape becomes negatively charged, while a positive charge remains behind on the rest of your body. The positive tape is attracted to the nearby negative charges more strongly than it is repelled by the more distant positive charges, and the tape moves toward your hand.

Since some table surfaces will not charge the tape, be sure to test your surfaces before trying this Snack with an audience. Charge leaks slowly off the tape into the air or along the surface of the tape, so you may have to recharge your tapes after a few minutes of use. You can use your electroscope to test whether an object is electrically charged. First use the comb to determine the charge on a piece of tape, and then see whether an object whose charge is unknown repels the tape. If the tape is negatively charged and an object repels it, then the object is negatively charged. Don't use attraction to judge whether an object is charged: A charged object may attract an uncharged one. If tape is attracted to an object, the tape and the object may

have opposite charges, or the tape may be charged and the object uncharged, or the object may be charged and the tape uncharged. But if the tape is repelled by the object, the tape and the object must have the same charge. The only way that tape and an object will neither repel nor attract is if both are uncharged.