Flying Pig Lab Report

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Physics

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Apr 3, 2024

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APC Flying Pigs! February 24 Purpose: The purpose of this lab is to investigate circular motion and the factors that affect it. Procedure: 1. An object suspended from a string that is rotating at a constant speed in a horizontal circle is known as a conical pendulum. Examples of conical pendulums include tether balls, amusement park swing rides, and toys like the Flying Pig. Observe the Flying Pig and record its mass (M) and the length of the string (L) in the data table. Q1: The diagram below shows the motion of the Flying Pig. Identify the forces acting on the pig. Fg (Force of Graivty) & T (Tension) Q2: Is there acceleration in the vertical (y) direction? No, the velocity in the vertical (y) direction is 0, therefore there is no acceleration. Is there acceleration in the horizontal (x) direction? Yes, there is centripetal acceleration in the horizontal (x) plane and direction because the velocity of the pig around the projected circle path of the pig is constant, therefore there is centripetal acceleration. Explain Q3: Draw a free body diagram of the Flying Pig at the instant shown in the diagram below. Do NOT draw on the diagram, make your own. Draw and label all the forces except for forces perpendicular to the page. q r Q4: Predict whether the tension in the string will be greater than, less than, or equal to the weight of the Flying Pig. Explain your answer. Greater, because T must supply enough force to equal out the weight and create a centripetal force. Q5: Write Newton’s Second Law (NSL) for the y direction and solve for the tension, T, in terms of m, g, and  . Does your equation verify your prediction in Q4? Explain. Fg (Force of Gravity)=Tcos(  ). Yes, because T itself is greater than Tcos(  ) therefore T is greater than Fg (force or gravity). Q6: What is the relationship between the acceleration of the pig (a C ), its speed (v) and the radius of the circle (r)? What is this acceleration called and what is its direction? a C =(v 2 )/r The acceleration is called centripetal, and its direction is around the projected circle path of the pig. Q7: Write N2L for the x direction and solve for v in terms of g, r, and  . Don’t forget the equation for T from Q5 and the equation for centripetal acceleration. Tsin(  )=(mv 2 )/r v= √𝑔𝑟𝑡𝑎𝑛 (  )

APC Flying Pigs! February 24 2. It is now time to fly the pig! Turn the pig on and give it a gentle push so it moves clockwise as seen from above. Let it reach equilibrium, then measure the period (T) the radius (r). Record your results in the data table below. Hint: measure the time for 10 complete revolutions of the pig and divide by 10 to get an accurate period. There are many ways to measure the radius of the circle. Brainstorm with your group to develop an accurate method. Turn your Flying Pig off once you have your measurements. Q8: Describe how your group measured the radius of the Flying Pig’s circle. Diagrams may be helpful. By placing a meterstick underneath the hook (where 0cm is located directly underneath the book) perpendicular to the pigs velocity when its above the meterstick and in periodic motion, by looking from above the meterstick we observe the radius. Q9: Knowing the length of the string and the radius you should be able to calculate  , the angle of the string from the vertical. Show your work and record your result in the data table. Lsin(  )=r 0.42/1.225=sin(  ) Sin -1 (0.42/1.225)=   =20.05 Q10: Using your equation from Q7, predict the speed (v) and centripetal acceleration (a C ) of the Flying Pig. Show your work and record your prediction in the data table. v= √𝑔𝑟𝑡𝑎𝑛  = √ 9 .8 × 0 .42 × tan ( 20 .05) v=1.226m/s a c =v 2 /r =(1.225) 2 /0.42 a c =3.577m/s 2 Q11: Determine the actual v and a C of the Flying Pig and record it in the data table. The speed is the change in distance divided by the change in time. The change in distance is the circumference of the circle that the Flying Pig was moving in. The change in time is the Period (T). Calculate the percent error of your predicted speed. Show your work and record your answer in the data table. v=d/t =2 π r/T =2 π (0.42)/2.233 =1.182m/s a c =v 2 /r =(1.182) 2 /0.42 =3.325m/s 2 v% error=|((v predicted)-(v actual))/(v predicted)|*100 =|(1.226-1.182)/1.226)|*100 =3.589%

APC Flying Pigs! February 24 M L T r  v predicted a C predicted v actual a C actual v % error (kg) (m) (s) (m) (degrees) (m/s) (m/s 2 ) (m/s) (m/s 2 ) (%) 0.156 1.225 2.233 0.42 20.05 1.226 3.577 1.182 3.325 3.589 Q12: Using your equation from Q5, calculate the tension in the string. Calculate the weight of the pig and compare it to the tension. How many times bigger is the tension than the weight of the pig? F g =Tcos(  ) mg=Tcos(  ) 0.156*9.8=Tcos(20.05) T=(0.156*9.8)/cos(20.05) T=1.63N mg=1.529N T=mg*x 1.63=1.529*x x=1.006 The tension is 1.006 times bigger than the weight of the pig. Q12: What caused the Flying Pig to move in a circle: the vertical component of the tension, the horizontal component of the tension, the weight, or a mysterious unknown thing called the centripetal force? The Flying Pig moved in a circle because of the horizontal component of tension, and “a mysterious unknown thing called the centripetal force”. The horizontal component of tension causes the pig to accelerate inward toward directly underneath the hook, but the velocity of the pig causes it to move forward. As the pig continues to move, the acceleration is constantly changing direction to keep the pig being pulled inward, while the velocity is remaining constant around the circle due to this acceleration. This causes the Pig to move in a circle. Q13: If the speed of the pig was increased, describe what would happen to the radius, angle, tension and period. If the speed of the pig was increased: The radius would increase. The radius of the circular path followed by the pig increases. This is because the centripetal force required to keep an object in circular motion is directly proportional to the square of the speed and inversely proportional to the radius of the circle. So, as the speed increases, the radius also increases to accommodate the higher speed. The angle would increase. As the speed increases, the angle between the rope and the vertical increases but never exceeds 90 because the angle is equal to the sin inverse of the radius divided by the length. As the radius increases, the angle also increases. The tension would increase. The tension would increase because it equals the weight of the pig divided by cos( ϴ ). Although the weight remains constant, as the angle between the rope and the vertical increases but not exceeding 90, cos( ϴ) decreases so the Tension would increase. The period would decrease. This is because the period of a conical pendulum depends on the radius and the gravitational acceleration, both of which remain constant. As the radius increases due to the increased speed, the time taken for one complete revolution decreases.

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APC Flying Pigs! February 24 Your lab “ report ” is to simply type up this document and with your answers/explanations/work/diagrams/etc. (Hint: check eClass for this document in digital form, then just add your answers/diagrams). One “report” per group.

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