TEST 2 Practice Problems Newton’s 2nd law 1. A pilot flies an airplane in a vertical circular loop at a constant speed υ = 160 m/s. If the pilot’s apparent weight at the top of the loop is one-third of his true weight when he is on the ground, find the radius R of the plane’s circular path. Ans: 1960 m 2. A small 8 Kg sphere is tied to two strings and spins horizontally around the vertical rod with θ = 36.87° as shown. If the frequency of the sphere’s circular motion is 1.2 rev/s, find the tension force in the horizontal string. Use cos36.87° = 0.8 and sin36.87° = 0.6. Ans: 77.6 N 3. A block is placed inside the spinning cone as shown. Given L = 0.5 m, μs = 0.3, and β = 36.87˚, find the minimum rotating frequency f of the cone that will keep the block from slipping. Use cos36.87° = 0.8 and sin36.87° = 0.6. Ans: 0.477 rev/s μs β L F 36.87° μk B B μk = 0.2 A μk = 0.25 36.87˚ 0.5 m f 4. The 10 Kg block slides on the horizontal floor as the pulling force F = 30 N is applied on the cable as shown. If the acceleration of the block is 7.2 m/s2, find the coefficient of friction μk between the block and the floor. Use cos36.87˚ = 0.8 and sin36.87˚ = 0.6. Ans: 0.15 5. Two blocks A (mA = 20 Kg) and B (mB = 15 Kg) are connected by a cable passing over a pulley, and a force F is applied pulling block B as shown. The coefficients of friction are μk = 0.25 between A and the ramp and μk = 0.2 between B and the horizontal floor. If block A slides up along the incline with an acceleration a = 0.56 m/s2, find the pulling force F. Use cos36.87° = 0.8 and sin36.87° = 0.6. Ans: 103 N θ F