(Solved): In the figure below, a block slides along a track from one level to a higher level after passing th ...

In the figure below, a block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictiontess until the block reaches the higher level. There a frictional force stops the block in a distance \( d \). The block's initial speed is \( v_{0} \); the height difference is \( h \) and the coefficient of kinetic friction is \( \mu_{k} \). Find \( d \). (Use any variable or symbol stated above along with the following as necessary: \( g \) for the acceleration of gravity.) \[ d= \] A single conservative force \( \vec{F}=(7.0 x-12) \hat{i} \mathrm{~N} \) where \( x \) is in meters, acts on a particle moving along an \( x \) axis. The potential energy \( U \) associated with this force is assigned a value of 263 at \( x=0 \). (a) Write an expression for \( U \) as a function of \( x \), with \( U \) in joules and \( x \) in meters. \( U(x)= \) (b) What is the maximum positive potential energy? J. (c) At what negative value of \( x \) is the potential energy equal to zero? \( m \) (d) At what positive value of \( x \) is the potential energy equal to zero? \( \mathrm{m} \)