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298 HW01 (Questions 1-5)
Due in Lecture on 01/26/ NAME________________________________________________________ (please print)
- (i) What are the dimensions of the 3 fundamental observationally defined physical observables? What are the units in both imperial and SI scales? What are the conversions for each unit from one to the other? What are the dimensions and SI units for speed and acceleration? (2 points)
(ii) Suppose we create a funny system of units based on the velocity of light, c. IN this system of units, we want all velocities to be dimensionless. What are the dimensions of the two remaining observationally defined physical observables? What is the conversion from units of time to length in SI units? In Imperial units? (Note: c=3E8 m/s in SI units and 1
inch=2.54 cm.) Suppose we have a quantity that is defined by 2 2
T = 1 mv. What are the dimensions of this quantity and
what are the units in the funny system of units? (3 points)
- We will find that force has dimensions mass times acceleration. What is the dimension of force in terms of observationally defined physical observables? In SI units, the unit of force is called a Newton (abbreviated N). Using the unit conversions from question 1, derive the conversion from Newton to Pound (the Imperial unit of force is the familiar pound). ( points)
(iii) What is D
r written out in terms of unit vectors x ˆ^ and y ˆ? ( 1point)
- Let A = a 1 x ˆ^ + a 2 y ˆ+ a 3 z ˆ
r and B = b 1 x ˆ^ + b 2 y ˆ+ b 3 z ˆ
r . (i)Write each vector in polar form. (2 points)
(ii)Compute a vector C
r which is orthogonal to both A
r and B
r in component and polar form. (5 points)
(iii) Show explicitly using unit vectors and the dot product that C
r is orthogonal to A
r
. (3 points)
- Here assume that A ≠ 0
r and B ≠ 0
r
. Now show that if a (^) 3 = b 3 = 0 that the vector C
r orthogonal to both A
r and B
r is not
in the plane of A
r and B
r
. Also, show that C
r lies in the x-y plane with A
r and B
r given that B A
r r =. (Hint: You need only set B A
r r = and find C
r such that it is orthogonal to A
r !)
