Question

A smooth cube of mass m and edge length r slides with speed v on a horizontal surface with negligible friction. The cube then moves up a smooth incline that makes an angle theta with the horizontal. A cylinder of mass m and radius r rolls without slipping with its center of mass moving with speed v and encounters an incline of the same angle of inclination but with sufficient friction that the cylinder continues to roll without slipping. Which object will go the greater distance up the incline? cylinder cube Find the difference between the maximum distances the objects travel up the incline. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration of gravity.) d = Explain what accounts for this difference in distances traveled.

Just need part b please and thank you

Answer 1

Given mass = m length r speed = v let us consider for cube. By conservation of energy 1/2 mv^2 = mgh. Therefore h = v^2/2g = s sin theta let for cylinder. Delta E = 0. 1/2 mv^2 + 1/2 I w^2 - mgh^2 = 0 v = rw^2 Therefore 1/2 mv^2 + 1/2 (1/2 mr^2) (v/r)^2 - mgh^1 = 0 Therefore h^1 = 3/4 v^2/g = s' sin theta Therefore s = s^1 - s = (3/4 v^2/9 - 1/2 v^2/9) 1/sin theta Delta s = 1/4 v^2/9 (sin theta)