Derive an Equation for Magnetic Force F12 The magnetic force F12 cannot be determined from Coulomb's...

   

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Derive an Equation for Magnetic Force F12 The magnetic force F12 cannot be determined from Coulomb's law because the pole strengths q* and q2* are not known. In the space below, derive an algebraic equation for F12 in terms of m, g, lo, and I, where m is the mass of the rider, g is the acceleration due to gravity (g = 9.80 m/s²), lo is the distance from the fulcrum of the lower magnet M, to its left pole, and / is the distance from the fulcrum to the notch on the right arm in which the rider is positioned. Show all your work. (Hint: use the fact that the torques due to F12 and the weight of the rider are equal when magnet M2 is balanced.) 2. Fel ing 94* F14 92* lo e F32 mg 93* F34 F12 F₁ In the Procedure Step 1, you derived an approximate expression for F12 by neglecting F34; call that result F12. Derivé a new expression for F12 taking F34 into account. Your new expression should be in terms of m, g, l, lo, o, q, and r12. (The phrase "in terms of means that only those variables listed are allowed in the final expression.) The result can and should be written without the use of trigonometric functions. (Hint: start as you did before with the fact that the sum of the torques on a system in equilibrium must be zero Exercise 2: Coulomb's Law 3. 4. Compare the expression you derived for Fiz in Question 2 to your derivation in Procedure Step 1 of Fis. Did neglecting F₁, in F2 cause you to overestimate or underestimate the force F₁2? Explain. Would the error in your calculation of "F12 due to neglecting F increase decrease with increasing r,2? Justify your answer mathematically and physically. (Hint: determine the sign of the first derivative of the magnitude of the error le-F1-Fiz) with respect to r12. [Why?] Use Mathematica to calculate the first derivative if you like.) Were you justified in calculating F12 neglecting F? Justify your answer quantitatively. (Hint: use your value for q' to calculate the percent difference between F12 and "Fiz for the worst-case data point. [Which is the worst-case data point and why??]) Derive an Equation for Magnetic Force F12 The magnetic force F12 cannot be determined from Coulomb's law because the pole strengths q* and q2* are not known. In the space below, derive an algebraic equation for F12 in terms of m, g, lo, and I, where m is the mass of the rider, g is the acceleration due to gravity (g = 9.80 m/s²), lo is the distance from the fulcrum of the lower magnet M, to its left pole, and / is the distance from the fulcrum to the notch on the right arm in which the rider is positioned. Show all your work. (Hint: use the fact that the torques due to F12 and the weight of the rider are equal when magnet M2 is balanced.) 2. Fel ing 94* F14 92* lo e F32 mg 93* F34 F12 F₁ In the Procedure Step 1, you derived an approximate expression for F12 by neglecting F34; call that result F12. Derivé a new expression for F12 taking F34 into account. Your new expression should be in terms of m, g, l, lo, o, q, and r12. (The phrase "in terms of means that only those variables listed are allowed in the final expression.) The result can and should be written without the use of trigonometric functions. (Hint: start as you did before with the fact that the sum of the torques on a system in equilibrium must be zero Exercise 2: Coulomb's Law 3. 4. Compare the expression you derived for Fiz in Question 2 to your derivation in Procedure Step 1 of Fis. Did neglecting F₁, in F2 cause you to overestimate or underestimate the force F₁2? Explain. Would the error in your calculation of "F12 due to neglecting F increase decrease with increasing r,2? Justify your answer mathematically and physically. (Hint: determine the sign of the first derivative of the magnitude of the error le-F1-Fiz) with respect to r12. [Why?] Use Mathematica to calculate the first derivative if you like.) Were you justified in calculating F12 neglecting F? Justify your answer quantitatively. (Hint: use your value for q' to calculate the percent difference between F12 and "Fiz for the worst-case data point. [Which is the worst-case data point and why??])