Learning object #2
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A coin suspended from a 0.5m string is oscillating as a simple pendulum. The net tangential force on the coin is measured to be 20N, and the tension in the string is 10N. Using these measurements and the equations for a simple pendulum, the mass of the coin is calculated to be 2.29kg. The displacement of the coin at the time of measurement is calculated to be 0.56m. The frequency of oscillation is calculated to be 0.71Hz, and the angular frequency is calculated to be 4.46rad/s.
Learning object #2
- 1. LO: Simple Pendulum You are swinging a coin suspended from a string of length 0.5m from side to side (on a 2-‐dimensional plane). You are in a lab and measure with some instruments that the net tangential force at a certain point in time is 20N and the tension force in the string at that point in time is 10N. Before you do anything else, Joss “The Boss” Ives (your Physics 101 professor) jumps in to help you measure the mass of the coin, but manages to tip over a water-‐filled graduated cylinder and break the scale. He quickly apologizes, but you don’t worry because you know how to find the mass using the whiz-‐kid physics powers Joss taught you in your lectures (which you happen to attend with the greatest enthusiasm!). Part a) Find the mass of the coin that was suspended from the string. Part b) Out of curiosity, you also want to find the displacement at that point. In other words, find s (hint: arc distance). Part c) Find the frequency and the angular frequency of oscillation of the pendulum. Length = 0.5m s = ? m = ? T = 10N Fnet,t = 20N
- 2. Solution: Given Information: FT = 10N Fnet,t = 20N Relevant Equations: T = mgcos θ Fnet,t = -‐mgsin θ s = Lθ f = ω/2π = (1/2π)*sqrt(g/L) Part a) | 𝐹!"#,! 𝑇 | = | −mgsin 𝜃 mgcos 𝜃 | = | − sin 𝜃 cos 𝜃 | = tan 𝜃 𝜃 = tan!! 𝐹!"#,! 𝑇 𝐹!"#,! = −𝑚𝑔 sin 𝜃 𝑚 = − 𝐹!"#,! 𝑔 sin 𝜃 𝜃 = tan!! 20𝑁 10𝑁 ≅ 1.11° 𝑚 = 20𝑁 (9.8)(sin 1.11°) ≅ 2.29𝑘𝑔 Part b) 𝑠 = 𝐿𝜃 𝑠 = 0.5𝑚 1.11° ≅ 0.56𝑚 Part c) 𝑓 = 1 2𝜋 𝑔 𝐿 = 1 2𝜋 9.8 0.5𝑚 ≅ 0.71 𝐻𝑧 𝜔 = 2𝜋𝑓 ≅ 4.46 𝑟𝑎𝑑 𝑠