1. The problem statement, all variables and given/known data A mass hangs on the end of a massless rope. The pendulum is held horizontal and released from rest. When the mass reaches the bottom of its path it is moving at a speed v = 2.7 m/s and the tension in the rope is T = 19.8 N. 1. How long is the rope? 2. What is the mass of the object? 2. Relevant equations 3. The attempt at a solution I found Q1 by the following method: ΔE = ΔU + ΔK ΔU = U2 - U1 ΔK = K2 - K1 At the initial postion, U1 = mgh and K1 = 0 At the 2nd position U2 = 0 and K2 = 1/2 MV2 ΔU = 0 - mgh ΔK = 1/2mv2 - 0 So ΔE = 1/2mv2 - mgh Since only conservative forces are doing work here, E1 = E2 and ΔE = 0 That means 0 = 1/2mv2 - mgh mgh = 1/2mv2 Canceling m: gh = 1/2v2 h = v2/2g h = 2.72 / (2 x 9.81) = 0.372 meters, which is correct. For Q2, I tried to find the mass the following way: T(tension) = Fc - mg Fc = mac ac = v2 / r So T = mv2/r - mg Then T = m(v2/r - g) Finally: m = T/[(v2/r) - g] m = 19.8/[(2.72/0.372) - 9.81] m = 2.02 kg But 2.02 kg is wrong and I don't know why. Using 2.02 kg in my equation T = Fc - mg gives me 19.769 N, which rounds to 19.8 N, which is what was given for tension.