PHYS 234 Quiz 3 Forces - quiz 3 PDF

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PHYS 234 Quiz 3 Feb. 16 2016

Name:

Forces cm

𝐹𝑐𝑒𝑛 = 𝑚

50

You are swinging a pendulum, making the pendulum bob move uniformly in a circular path. The length of your string is 50cm. The mass of the pendulum is 60 grams. If the pendulum travels on a circular path with 30cm radius, find the speed of the pendulum and the tension on the string. Make sure you draw a free body diagram.

30cm

𝑣2 𝑅

𝜃 = acos

3 = 53.1° 5

FT,y

Here is the free body diagram. The angle between tension and horizontal is given by geometry of the 3-4-5 triangle:

FT

Solution:

FT,x

From the y direction we have tension's component balancing gravity:

𝐹𝑇 =

Fg

𝐹𝑇,𝑦 − 𝐹𝑔 = 𝐹𝑇 sin 53.1° − 𝑚𝑔 = 𝐹𝑇 ∗ 0.8 − 0.06 ∗ 9.8 = 0 0.06 ∗ 9.8 = 0.735(𝑁) 0.8

From the x direction (towards the center of the circle), we have tension's x component providing centripetal force: 𝐹𝑇,𝑥 =

𝑚𝑣 2 𝑅

𝐹𝑇 cos 53.1° = 0.735 ∗ 0.6 = 0.441(𝑁) = 𝑣2 =

0.441 ∗ 0.3 = 2.21 0.06 𝑣 = 1.48 𝑚/𝑠

0.06 ∗ 𝑣 2 0.3...