Question

Vector PreLab

Prelab questions This Prelab should be submitted before the start of the lab. Follow your TA instructions on how to turn in the assignments. Note: you will need to read the lab manual to answer the questions.

1. Consider vectors ?⃗ and ?⃗⃗, where A=120 N, thetaA=0 ± 1°, and B=130 N, thetaB=140 ± 1°. Assume that ?? and ??, the uncertainty in forces A and B, are zero. a) Find Ax, Ay, and their uncertainties. Refer to Equations 1, 5 and 6. Use radians for the ?? values in Equations 5 and 6.

b) Find Bx, By, and their uncertainties. c) If ?⃗ + ?⃗⃗ + ?⃗⃗ = 0, calculate Ex, Ey, and their uncertainties. The absolute uncertainty in a sum is the sum of absolute uncertainties in quadrature: ????? = √∑?? 2 .

d) Find the magnitude (length) of ?⃗⃗ and the angle theta E (See Equations 2 and 3; don’t calculate the uncertainties).

Answer 1

a)

,  

( )

  

and

with uncertainity is  

  

and

with uncertainity is  

-----------------------

b) ,

  

and

with uncertainity is  

  

and

with uncertainity is  

----------------------

c)

  

  

with uncertainity is  

  

  

with uncertainity is  

-----------------

d) Magnitude of E is

direction counter clockwise from +ve X-axis.