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Principle(s) Investigated: Centripetal acceleration, centripetal force, mass. List all principles that apply to this activity.
2b. Students know when an object is subject to two or more forces at once, the result is the cumulative effect of all the forces.
2e. Students know that when the forces on an object are unbalanced, the object will change its velocity (that is, it will speed up, slow down, or change direction)Past in the appropriate California content standards.
Materials:
- wood board about 81/2 x 5 x 1.
- rope about 2 feet long.
- plastic cup
- water.
- towel to clean up water if performing indoors
*the materials may be increased in size if the demonstrator wants a bigger demonstration.
Procedure: Give a detailed explanation of the procedure and include diagrams if possible.
- The teacher asks students what would happen if the cup were faced upside down (the water falls down).
- The teacher then explains the experiment. The cup will be placed on the wood board and swung in a circular motion by a student holding the rope.
- The teacher then chooses a student to hold onto the end of the rope and swing the board with the cup placed on it in a circular motion. The student must try not to drop the cup or the water inside.
- If time allows for it, another student may be chosen to swing the board.
- Ask the students why neither the cup nor the water fell down even though the objects were upside down.
- The teacher explains why neither the water nor the cup fell down.
Student prior knowledge: Students should know force, velocity, centripetal acceleration, and centripetal force.
Explanation:
When an object travels in a curved path it requires a force towards the center. The inward force is centripetal force, or "center seeking force". Centripetal force can be a number of different forces that are center seeking. Gravity, friction, and tension can all be a centripetal force. The equation for centripetal force is Fc = m(v^2/r). Centripetal force has direct relationship with mass, Fc=m. The greater the mass, then a greater centripetal force would be required to maintain it in a circular motion. The greater the velocity, the greater centripetal force would be required to maintain the object in a circular motion. Notice that velocity is squared, so the doubling of velocity would require four times the centripetal force Fc=v^2. Lastly, radius is inversely proportional to Centripetal Force Fc=1/r. The greater the radius, then the less force that is required to maintain the object in a circular motion.
Questions & Answers:
1. If you take a look at the loop of an amusement ride, you will see it is not a circle but more of tear drop shape. Why are the loops shaped like a tear drop?
The first clothoid loop was used at six flags magic mountain in Valencia, CA. A circular loop required a faster velocity going into the loop. The greater velocity increased the force felt by the riders. Engineers made a tear shaped loop to allow the ride just enough velocity to complete the loop without the riders feeling discomfort.
2. If the objects that were placed into the cup were more massive, would the student need to swing faster or slower?
If the object in the cup had more mass, then the student would not need to swing as fast. Centripetal force is mass multiplied by velocity. If mass is increased, then to achieve the same amount of centripetal force, the velocity would need to decrease. If the object had less mass, then it would require a greater velocity to generate the same centripetal force.
3. Why does the moon revolve around Earth and not crash into it?
The moon revolves around Earth because the gravity of Earth. As earth's gravity pulls the moon inward, providing the centripetal force, the moon's inertia keeps it in orbit. The moon wants to travel in a straight line, but Earth's gravity pulls it in, maintaining a circular motion.
Applications to Everyday Life:
1. When an amusement park ride completes a loop, centripetal force is what keeps the roller coaster train on the track and in a circular motion.
2. When a automobile hits a hard turn and the tires skid is another example. As the car hits the turn, the car is traveling in a circular motion. Friction provides the centripetal force required to keep the car in a circular motion and complete the turn.
3. When the sun revolves around the sun is yet another example. The Earth's initial velocity and inertia wants to keep going in the same direction, but the sun's gravity serves as the centripetal force that pulls the Earth inward maintaining it in orbit.
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