A 3.85 -kg object is attached to a vertical rod by two strings as shown in the f

Question

A 3.85-kg object is attached to a vertical rod by two strings as shown in the figure below. The object rotates in a horizontal circle at constant speed 7.50 m/s.

A 3.85-kg object is attached to a vertical rod by two strings as shown in the figure below. The object rotates in a horizontal circle at constant speed 7.50 m/s. Find the tension in the upper string. Your response is within 10% of the correct value. This may be due to round off error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize round off error. N Find the tension in the lower string. Your response differs from the correct answer by more than 10%. Double check your calculations. N

Explanation / Answer

let tension in upper string is T1 and that in lower string be T2. angle made by each string with the vertical, theta = cos^-1(1.5/2) = 41.41 degrees from vertical equilibrium of object; T1*cos(theta) = T2*cos(theta) + mg => T1*cos41.41 = T2*cos41.41 + 3.85*9.8 => 0.75*T1 = 0.75*T2 + 37.73 => T1 = T2 + 50.31 In horizontal direction; T1*sin41.41 + T2*sin41.41 = m*v^2/R => (T1 +T2)*0.66 = 3.85*7.5^2/[sqrt(2^2 -1.5^2)] => (2*T2 +50.31)*0.66 = 216.563/1.323 => T2 = 98.853 N T1 = T2 + 50.31 = 149.163 N a). 149.163 N b). 98.853 N

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