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Haplosciences.com |
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UNIFORM CIRCULAR MOTION
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INTRODUCTION Acceleration is a vector. It has a magnitude and a direction. a = ∆V/∆T V is the velocity and is also a vector. If you change the direction of the velocity (without changing its magnitude), the object is accelerating. The speed is constant but the direction changes. Example: A car moves at a constant velocity of V1 = 10m/s @ North . It makes a turn and is now moving eastward at 10 m/s . V2 = 10m/s@East. The magnitude is constant but the direction changes. Did the car accelerate ? _______________ Trace V1 and V2 . Then trace (-V1) and (V2) . Then trace ∆V = V2 - V1 = V2 + (-V1) a = ∆V/∆T so the vector a has the same direction than ___________ If the time elapsed ∆T = 2s, trace the vector a |
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According to Newton’s second law, if an object accelerates (like the car), it means a force is acting on it. F = m a Force is a vector, so the force acting on the car has the same direction than the acceleration a. By turning the wheel, you force frictions between the road and the tires to act on the car to make it turn.
If m = 3kg (it is a toy car), can you trace F the force acting on the car ? F will produce a.
UNIFORM CIRCULAR MOTION
In a uniform circular motion, the magnitude of the velocity stays constant but not its direction.
In a circular motion, the acceleration points toward the center of the circle. If the object accelerates, a force is acting on it to cause the change in direction. This force is called the centripetal force. In the case of a motorcycle, the centripetal force is produced by the friction between the tires and the road. Can you trace the force ? The motion we are studying is called uniform because the magnitude of the velocity is constant. Only the direction of the motion is changing over time. It can be shown that the magnitude of the centripetal acceleration is: ac = V2 /r You can get to this results using geometry. Want to try ? answer
A centripetal force is any force or combination of forces that produces the centripetal acceleration for an object moving around a curve.
EXERCICES try without looking at the hints. 3) The moon orbits the Earth at a constant speed. What is the force acting on the Moon that keeps the Moon on orbit ? 4) A 0.25kg mass is attached to a 1.00 m length of string. The mass completes a horizontal circle in 0.42s. A) What is the speed of the mass ? Hint: speed = distance / t and distance = circumference of the circle = 2 Π r , t is given B) What is the centripetal force ? Hint: use the formula F =m V2 / r 5) A 2.0 kg mass is attached to a string 1.0m long and swings in a circle parallel to the horizontal. The mass goes around its path once each 0.80s. A) Find the speed of the mass. See 3A) B) Find the centripetal acceleration? Hints: ac = V2 / r with r = 1.0m C) What tension is in the string Hints: T the tension is the centripetal force. So T = m ac 6) It takes 6.00 102 kg racing car 10.0s to travel at a uniform speed around a circular race track of 50.0 miles radius. A) What average force must the car’s tires exert against the track to maintain its circular motion. Hints: first find the speed like for 2 and 3. Then find the centripetal force = average force. B) What is the acceleration of the car ? Hints: ac = Fc/m 7) An athlete whirls in a 7.00kg hammer tied to the end of a 1.3m chain in a horizontal circle. The hammer makes one revolution in 1.0s. A) What is the centripetal force of the hammer ? B) What is the centripetal acceleration of the hammer? 8) In a cyclotron, an electromagnet exerts a force of 7.50 10-13 N on beam of protons. Each proton has a mass of 1.67 10-27kg. The electromagnet causes the protons to travel in a circular path of radius 1.20m. What is the velocity of the proton beam? Hint: use Fc = m v2/r and solve for v 9) optional only. For Math/Physics lovers. An early major objection to the idea that the earth is spinning on its axis was that the earth would turn so fast (1600km/h) at the equator that people would be thrown off into space. Show the error in this logic by calculating: A) the weight of a 1.00 102 kg person B) The centripetal force needed to hold the same person in place at the equator. The radius of the Earth is about 6,400km. Conclusion ? Hint: convert km into and hr into seconds. Compare Fc and W. A) Find the Normal force of Earth on the person, that is, their person’s apparent weight. Hint: use third law. Action reaction. The earth push on us with the same force we push on the earth. 10) optional. A carnival ride has a 2.0m radius and rotates once 0.9s. A) Find the speed of a rider B) Find the centripetal acceleration of a rider C) What produces that acceleration? D) When the floor drops down, riders are held up by friction. Draw motion and free-body diagram of the situation. E) What coefficient of static friction is needed to keep the riders from slipping. Hint: frictional force = µs x Normal force. The normal force is the centripetal force. 11) optional A) Friction provides the force needed for a car to travel around a flat, circular race track. What is the maximum speed at which a car can safely travel if the radius of the track is 80.0m and the coefficient of friction is 0.40 ? Hint: friction = µs N 11) extra credits every one. See me to get the puzzle. Find the secret word. NO MATH ! 12) do this worksheet 13)
During our lab , a small mass was attached to the end of the string and
whirled around overhead in a horizontal circle path. The mass is 150g
and is traveling at 4.0 m/s. The string is 65cm long. How much is the
tension in the string to keep in a circle ? Sorry there is more, click here.
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A motorcycle is moving into a circle. Its speed is constant but not its direction. The vectors velocity V1 and V2 have the same magnitude but they don’t have the same direction. Since there is a change in velocity, there is an acceleration. The motorcycle is accelerating. Since a = ∆V / ∆T, a points in the same direction than a.
a (or ∆V ) is pointing toward the Center of the circle. |
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V is the magnitude of the velocity of the object moving in circle r is the radius of the circle ac is the magnitude of the centripetal acceleration |
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The tension in the string is the centripetal force that keeps the mass in a circular motion. Fc = m V2 /r If you cut the string, the mass will move in a straight line with a constant velocity because no force is acting on it. |
