Q8: The 450-kg ram of a pile driver falls 1.4 m from rest and strikes the top of a 240-kg pile embedded 0.9 m in the ground. Upon impact the ram is seen to move with the pile with no noticeable rebound. Determine the velocity u of the pile and ram imme- diately after impact. Can you justify using the principle of conservation of momentum even though the weights act during the impact? | Ans: v = 3.42 m/s 14 m www 09m

1 Problem During a particularly snowy winter in Charlotte, a child of mass m slides down a ramp starting at rest from point A and encounters the melted grassy area at B before coming to a full stop at C. Assume the ice is frictionless. The height of point A is hĄ and the distance between B and C is L. What is the coefficient of friction of the grass, k? Assume that g = 9.81 m/s², ha = 5 m, m = 20 kg, and L = 10 m. hA P JA Ice B Grass L C

A spherical bowling ball with mass m = 4.6 kg and radius R = 0.105 m is thrown down the lane with an initial speed of v = 9.5 m/s. The coefficient of static friction between the ball and the ground is 0.35 and the coefficient for kinetic friction is μ = 0.3. Once the ball begins to roll without slipping it moves with a constant velocity down the lane. 1) What is the magnitude of the angular acceleration of the bowling ball as it slides down the lane? 2) What is magnitude of the linear acceleration of the bowling ball as it slides down the lane? 3) How long does it take the bowling ball to begin rolling without slipping? 4) Once it begins to roll without slipping, what is the force of friction on the ball?

graduate who joined the Navy as a pilot is about to take off in an F-15 (WF15 = 81,000 lb) from an aircraft carrier traveling at VA = 40 mph. The jet is launched from the catapult system (a connection just below the deck that assists the aircraft) with the force (Fcp) vs time curve shown that has points of F₁ = 1,000 lb at t₁ = 2 s and F₂ = 3,000 lb at t₂ = 5 s (the plane will reach the edge of the deck at t₂). The F-15 needs to be traveling at 170 mph to take off. Determine how much constant thrust (FTR) the engines must produce during the launch to reach this speed. F2 F₁ FCP t₁ VA t₂ FTR t (s)