4. When installing a Red Carpet for the Oscars, workers found that if they push the carpet roll in the direction to unroll, it will keep unrolling by itself. However, if they push it to roll it up, it will move some distance and then stop. Why is this happening if the surface is flat and the friction is negligible? Calculate the distance the roll will move if it is initially given a push of velocity v₀ = 1 m/s to roll it up. The carpet is 1 in thick, 60 m long, and half-rolled up prior to being pushed. (Hint: Use energy conservation.)