A crate on rollers is being pushed without frictional loss of energy across the

Question

A crate on rollers is being pushed without frictional loss of energy across the floor of a freight car (see the following figure). The car is moving to the right with a constant speed vo- If the crate starts at rest relative to the freight car, then from the work-energy theorem, Fd where d, the distance the crate moves, and v, the speed of the crate, are both measured relative to the freight car. (Assume the force is applied starting at t-o.) miv2 Vo and v-) (a) To an observer at rest beside the tracks, what distance d is the crate pushed when it moves the distance d in the car? (Use the following as necessary: d, t, (b) what are the crate's initial and final speeds v' and v' as measured by the observer beside the tracks? (Use the following as necessary; d, t, v, and vo.) (e) Show that Fdand, consequently, that work is equal to the change in kinetic energy in both reference systems. (Submit a file with a maximum size of 1 MB.)

Explanation / Answer

(a) distance of cart moved in car =d

let distance moved is d'

using work energy theorem for observer at rest

F*d'=0.5*m((v+Vo)^2-(Vo)^2=0.5*m(v^2*2v*Vo)

F*d'=0.5mv^2+0.5*m*2*v^2*Vo/v

we know

0.5mv^2=F*d

F*d'=F*d+F*d*2*Vo/v

d'=d+2d*Vo/v=d(1+2Vo/v)

(b)Vo'=Vo

v'=Vo+v

(c)Already proved in part (a)

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