# UNIVERSITY-OF-THE-DISTRICT-OF-COLUMBIA-Division-of-Mathematics

UNIVERSITY OF THE DISTRICT OF COLUMBIA Division of Biology, Chemistry, Mathematics, and Physics University Physics I Summer Session 1 -2017 SAMPLE TEST # 3

NOTE: ANSER ALL QUESTIONS (100 POINTS) 1. a. Provide a mathematical definition of work. b. What is the unit of work in the MKS system of units? c. The vectors A and B are given by: A = 2i + 3j and B = â€“2i + 2j. Determine the vector cross product A x B. d. The vectors A and B are given by: A = 2i + 1j and B = â€“2i + 4j. Determine the scalar dot product A . B. Find the angle between A and B.

e. Two Connected Objects when Friction is Present: Determine the magnitude of the acceleration of the two objects shown to the right.

2.
a. Provide mathematical definitions of K.E., P.E. and give their units in the MKS system of units. b. Provide a mathematical definition of torque, and give its unit in the MKS system of units. c. Considering m1 = 3 kg, m2 = 7 kg, and ðœƒ = 50o. (a) Draw the freebody diagram of both objects, (b) find the magnitude of the acceleration, (c) find the tension in the string, (d) find the speed of each object after 2 seconds.

d. The force on a particle is Fx = (9x â€“ 18), where F is the force in newtons and x is in meters. Find the net work done by this force on the particle as it moves from x = 0 to x = 4 m.

3.
a. Derive an equation for the velocity in terms of the terminal velocity of a falling object when the air friction is proportional to the velocity of the falling object. b. Calculate the moment of inertia of a uniform rigid ro