6. A 1 800-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 3.40 m before coming into contact with the top of the beam, and it drives the beam 14.8 cm farther into the ground before coming to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest. magnitude N

A simple accelerometer is constructed inside a car by suspending an object of mass m from a string of length L that is tied to the car's ceiling. As the car accelerates the string-object system makes a constant angle of with the vertical.

2. Find the maximum of f(x) = 4x-1.8x² +1.2 x³ -0.3x¹ using: a. Golden-Section Method b. Parabolic interpolation c. fminbnd d. For each, copy the command window with all relevant commands and results and paste them into a word document to upload to canvas.

Problem 6. (20 points) Find the center of percussion for the body shown below consisting of a slender bar of length / = 1 m and a disk each of equal mass such that m, = md = m. The radius of the disc is R = 0.1 m m R ma

3. A particle performs a simple harmonic motion given by the equation: At t=0.80 s find: (a) the position of the particle. b) the velocity of the particle. c) the acceleration of the particle. d) the kinetic, potential and total energy of the system, if the mass is 0.120 kg.

4. Consider a vertical mass-spring system. The spring constant is k = 48N/M and he mass is m = 1.0 kg. a) Find the angular frequency. The mass is pulled from equilibrium 0.10 m down. b) Write the equation for the displacement as a function of time, with a vertical x axis is pointing upward.

2. Diesel tends to wait until the rabbit is closest before starting to chase. If the rabbit is traveling across the yard in a straight line, we can assume the simulation will start when the rabbit is located at [x (0), y (0)] = [x, 0] and have a velocity of [x` (0), y` (0)] = [0, C ], where RRO RRR CR is the maximum speed at which the rabbit can run. Note, we are ignoring acceleration here, we are just assuming the rabbit has already accelerated to it's max velocity and stays there. So, the velocity vector can change direction, but not magnitude. And the rabbit will change direction, so the velocity will change direction. From my observation, it does so when Diesel gets within a certain distance of the rabbit. But to keep it simple, suppose the rabbit just turns 90 degrees to the right at a fix rate of 90 degrees/second starting at t = 2. Write the equations for the rabbit's velocity, i.e. x' (t) and y' (t). RR