The question
Name: ______________________ Date: ____________ Two blocks stick, then climb a ramp (10 points)
Diagram
Two blocks stick, then climb a ramp
Block A (mass m) slides at speed v₀ toward block B (mass 2m), which is at rest on a level, frictionless floor. Velcro on the facing sides makes the blocks stick together when they collide. The pair then slides up a frictionless curved ramp and reaches a greatest height h above the floor. Air resistance is negligible.
(a) On the axes, sketch the momentum of block A and the momentum of the two-block system as functions of time, from shortly before the collision until shortly after it (before the pair reaches the ramp). Label each line. Take the initial direction of A's motion as positive. [3 points]
(b) Derive an expression for the speed v_f of the blocks just after the collision, in terms of v₀. Begin your derivation by writing a fundamental physics principle or an equation from the reference information. [2 points]
(c) Derive an expression for h in terms of v₀ and physical constants, as appropriate. [2 points]
(d) Calculate h for v₀ = 6.0 m/s. Use g = 9.8 m/s². [1 point]
(e) A student says: "Block A starts with kinetic energy ½mv₀², and the pair ends with gravitational potential energy 3mgh, so ½mv₀² = 3mgh and h = v₀²/(6g)." Is the student correct? Justify your answer. [2 points]