Frame S′ moves in the positive -direction with a constant speed relative to inertial…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

Frame S′ moves in the positive

x

-direction with a constant speed

u

relative to inertial frame S. An object of mass

m

travels with velocity

\mathbf{v}'

in frame S′ at a particular instant. All motion is confined to the

x

-axis. (a) Express the object’s velocity

\mathbf{v}

as measured in frame S in terms of

u

and

\mathbf{v}'

. (b) Write symbolic expressions for the translational kinetic energies

K

(measured in S) and

K'

(measured in S′). (c) Derive an expression for the difference

K-K'

in terms of

m

u

, and

v'

. Simplify your result as much as possible. (d) Identify the physical circumstances under which

K-K'

becomes zero, and interpret that special case in words.