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4. A chunk of ice of mass m₁ is sliding with a horizontal velocity of magnitude v₁i on the floor of an ice- covered valley when it collides with and sticks to another chunk of ice of mass m2 that is initially at rest at the base of a hill. The two blocks stick together and move up the hill together. Since the valley and hill are icy, there is no friction between the chunks and the ground. a) Which conservation laws may be applied to understand the motion of the ice chunks in this problem? b) What is the maximum vertical distance H that the combined ice chunks will go up the hill after the collision? Write the answer in terms of the quantities given in the problem (m₁, V1i, and/or m₂) and, perhaps, constants (e.g., g, n, ½ ...). c) Calculate a numerical value for H if m₁ = 5.00 kg, m₂ = 7.50 kg, and v₁ = 12.0 m/s. {1.17 m} d) How much kinetic energy (if any) is lost due to the collision? H m2 m₁
3. Block A in the figure below has mass 1.50 kg, and block B has mass 3.00 kg . The blocks are forced together, compressing a spring S between them; then the system is released from rest on a level, frictionless surface. The spring, which has negligible mass, is not fastened to either block, and it drops to the surface after it has expanded and pushed on both blocks. Block B acquires a speed of 1.25 m/s. Note: you can think of this problem as an example of a one-dimensional explosion. a) What is the final speed of block A? {2.50 m/s} b) How much potential energy was stored in the compressed spring? {7.03 J} MA mB