Review. A steel guitar string with a diameter of 1.00 mm is stretched between supports 80.0 cm apart. The temperature is 0.08C. (a) Find the mass per unit length of this string. (Use the value 7.86 3 103 kg/m3 for the density.) (b) The fundamental frequency of transverse oscillations of the string is 200 Hz. What is the tension in the string? Next, the temperature is raised to 30.08C. Find the resulting values of (c) the tension and (d) the fundamental frequency. Assume both the Youngs modulus of 20.0 3 1010 N/m2 and the average coefficient of expansion a 5 11.0 3 1026 (8C)21 have constant values between 0.08C and 30.08C.

• Applications of basic vector Vector decomposition: ex) ex) • Applications of trig Deﬁnition: Insert proof from bb slide Std ids: • More vector apps 2 types of vector products: dot product(scalar): cross products(vector): Triangle abc:AB=ACcos =AC sin BC=ACsin =ACcos AD=ABcos =ABsin ABsin =ABcos Law of cosines a =B +c -2bccos b =a +c -2accos c =a +b -2abcos Circle area Sphere area Triangle area • Electricity: Electric potential- capacity of electric ﬁeld to do work on electric charge Electromagnets- electric currents generate magnetic ﬁelds,and changing magnetic ﬁelds generate electric currents Electric charges a