Consider the situations shown below with masses sliding down ictionless surfaces. All masses start from rest and all the springs have same uncompressed lengths and same spring constants. 5kg 5kg A B 5kg 5kg . 5m 5111 0.5m 2m C D \"'3 15 kg 5 in F E Rank these situations, on the basis of the initial gravitational potential energy, from least to greatest. Least Gravitational PE Greatest Gravitational PE 1. 2. 3. 4. 5. 6. Rank these situations in order from least to greatest the final kinetic energies of the sliding masses the instant before they compress the spring. Least KE Greatest KB 1. 2. 3. 4. 5. 6. Rank these situations, on the basis of the elastic potential energy, from least to greatest. Least Elastic PE Greatest Elastic PE 1. 2. 3. 4. 5. 6. If the incline is not a frictionless surface, which of the above rankings would change? Now let's consider a hoop with mass 3.0 kg and radius 2.0 cm rolling down an incline. Calculate the following quantities for case A. Gravitational Potential Energy: Kinetic Energy: Speed of the hoop at the end of the incline: Elastic Potential Energy of the spring: How would the values of the above quantities change if a cylinder with same mass and radius roll down the incline? Try the following problems: Two air-track gliders of similar mass are at rest as shown in the figure below. One of them is being pushed towards the other with speed 2 m/s. M = 200 g (V1x)i = 2 m/s (Vzx)i = 0 M M 1. The visual overview after the collision is given below: Vif V2f a. What is the final velocity of each of the gliders? b. What are the total momenta before and after the collision? Is the momentum conserved? c. What are the total mechanical energies before and after the collision? Is the mechanical energy conserved? 2. The visual overview after the collision is given below: Vf a. What is the final velocity of the glider with mass 2M? b. What are the total momenta before and after the collision? Is the momentum conserved?c. What are the total mechanical energies before and after the collision? Is the mechanical energy conserved? 3. In case the mechanical energy not conserved in the above cases, how much energy is transformed into other form during the collision? 4. An atom is bombarded by a neutron. The atom then explodes into two parts, and each part goes in different direction as shown below: Before: M v - = 0 (le)i ( 2x)1 After: m1 30 x 6 m2 Write expressions for the unknown angle I9, in terms of the known quantities m1 ,m2, M