A pendulum is made of a ( 251.3 ± 0.1) g mass and a string that is ( 1.3±0.005)m

Question

A pendulum is made of a ( 251.3 ± 0.1) g mass and a string that is ( 1.3±0.005)m long. If the mass has a speed of (1.3± 0.1) m/s at the bottom of the swing:
A) Calculate the centripetal acceleration of the mass ( with uncertainty).
B) use Newton's second law of motion to obtain the equation needed to solve for the tension. Note the free body diagram must be included.
C) Calculate the tension in the string ( with uncertainty).
D) Determine the centripetal force acting on the mass ( with uncertainty)

Explanation / Answer

A) we have that a=v^2/r=1.3(m/s2). we have ?a/a=2*?v/v + ?r/r. so ?a/a = 2*0.1/1.3+0.005/1.3=0.154 so ?a=0.2 so a=1.3+-0.2 B) tension F=m*v^2/r + mg. C) F=mv^2/r +mg = 2.79(N). we have that F=m*(v^2/r+g) so dF/F=dm/m + d(v^2/r+g)/(v^2/r+g) = 0.0184 so dF=0.5 so F=2.8+-0.5

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