In a straight-line motion experiment four reference frames are defined: • Frame A – a…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

In a straight-line motion experiment four reference frames are defined: • Frame A – a small robot moving on the floor of a boxcar • Frame B – the boxcar itself • Frame C – a flatbed railcar that the boxcar rests upon • Frame G – the ground (Earth) All frames move only along the

+x

axis with constant velocities. The symbol

v_{X/Y}

denotes the velocity of frame

X

measured in frame

Y

. (1) Starting from the definition of relative velocity, write an equation that relates

v_{A/G}

v_{A/B}

and

v_{B/G}

. State the sign convention you use and justify each term in your expression. (2) Introduce the intermediate frame C and derive an explicit expression for

v_{A/G}

that contains

v_{A/B}

v_{B/C}

, and

v_{C/G}

. Show each algebraic step clearly. (3) Demonstrate algebraically that your result from part (b) is unchanged whether you group the terms as

(v_{A/B}+v_{B/C})+v_{C/G}

or as

v_{A/B}+(v_{B/C}+v_{C/G})

. Explain the physical significance of this property when dealing with successive inertial frames.

Related theory

Browse the problem library