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Transcript
Centripetal Force Requirement Newton's first law of motion states that…An object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In what path do objects naturally travel? Straight lines. What is required for objects to move in circles? An unbalanced force. Newton's second law of motion says that… if acceleration is present then net force is present in the same direction. Does an object moving in a circle experience acceleration if it is moving around the perimeter of the circle with a constant speed? yes If so, then what does Newton’s Second Law imply about the net force? Net force is always present during circular motion, and points towards the center. What is a centripetal force? Any force pushing or pulling the object toward the center of the circular path. The word centripetal describes DIRECTION only. Is centripetal force a new type of force? NO! A centripetal force is either N, T, Ff, or w. Give three examples of centripetal force. 1. Weight of the earth towards the sun causes our orbit. 2. Banked turns provide normal force towards the center. 3. Motorcycles leaning in to the turns provide normal force. What are centrifugal forces? No such thing! (See www.physicsclassroom.com for more.) What are the relevant equations for centripetal force? Fc = mac What is the relationship between centripetal force and velocity? Since ac = v2/R, and Fc = mac, Fc = m v2/R. Therefore, Fc v2 493704771 Practice 1. If the speed of the object is halved (decreased by a factor of 2), the net force required is decreased by a factor of 4. 2. If the speed of the object is doubled, the net force required for that object's circular motion is 4x. 3. A girl fills a bucket with water, ties it to a strong rope, and spins it in a circle. She spins the bucket when it is half-full of water and when it is quarter-full of water. In which case is more force required to spin the bucket in a circle? Explain. Half full means double the mass, so double the Fc 4. A Lincoln Continental and a Yugo are making a turn. The Lincoln is four times more massive than the Yugo. If they make the turn at the same speed, then how do the centripetal forces acting upon the two cars compare? Explain. Since Fc m, then 4*m, means 4*Fc 5. The Cajun Cliffhanger at Great America is a ride in which occupants line the perimeter of a cylinder and spin in a circle at a high rate of turning. When the cylinder begins spinning very rapidly, the floor is removed from under the riders' feet. What effect does a doubling in speed have upon the centripetal force? Explain. Since Fc v2, then 2*v, means 4*Fc 6. If a 60-kg runner goes around a 20-m radius track at a rate of 2.5 m/s2, what is the centripetal force necessary? Fc = mac = 60* 2.5 = 150 N 7. A 3-kg wheel with a 12-cm radius rolls 0.75 m/s2. What is the centripetal force acting on the wheel? Fc = mac = 3* 0.75 = 2.25 N 8. A 3-kg wheel with a 12-cm radius rolls with a speed of 0.13 m/s. What is the centripetal force? Fc = m v2/R = 3 * 0.132/0.12 = 0.423 N 9. Determine the centripetal force acting upon a 40-kg child who makes 10 revolutions around the Cliffhanger in 29.3 seconds. The radius of the barrel is 2.90 meters. v = d/t = 2R/T = 2(2.9)/29.3 = 6 m/s Fc = m v2/R = 40*6.22/2.9 = 533 N 493704771