3. Determine the number of the degree of freedom for each of the following systems: a), b), c). 7777 C OM M k AND OM

5. In discrete modeling of a system what element is used to relate a force to velocity?

Problem 5. (20 points) An arrow of length L traveling with speed up strikes a smooth hard wall obliquely as shown below. End A doesn't penetrate, but slides downward along the wall without friction or rebound. Find the angular velocity of the arrow after impact. Treat the arrow as a slender bar. Since the impact force is so much more than the gravity force, you may ignore gravity. B L A

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

Problem 7 Bonus. (25 points) The two uniform slender bars shown below, each have a mass of 2 kg. The two bars are pinned together at P. The counter-clockwise couple Co of 150 N-m is applied to the bottom bar at t = 0 s. Upon application of the couple, find the angular accelerations of the top and bottom bars. Also, find the forces exerted on the lower bar at point P. B₁ 0.5 m 0.5 m B₂ У Р ) c.

If a man weighs 780 N on the Earth, what would he weigh on Jupiter, where the free-fall acceleration is 25.9 m/s²? KN

A toy rocket engine is securely fastened to a large puck that can glide with negligible friction over a horizontal surface, taken as the xy plane. The 4.20-kg puck has a velocity of 2.001 m/s at one instant. Eight seconds later, its velocity is (6.001 + 8.0j) m/s.

The gravitational force exerted on a baseball is 2.28 N down. A pitcher throws the ball horizontally with velocity 15.5 m/s by uniformly accelerating it along a straight horizontal line for a time interval of 185 ms. The ball starts from rest.

A brick of mass m is dropped from a sheer cliff of height h. The wind exerts a force F on the brick. Assume the wind is parallel to the face of the cliff and the ground and F is constant. (Use any variable or symbol stated above along with the following as necessary: g. For all vectors, enter the magnitude.)

In the figures, the masses are hung from an elevator ceiling. Assume the velocity of the elevator is constant. Find the tensions in the ropes (in N) for each case. Note that 0₁36.0°, 6₂ 54.0°, 055.0°, m₁5.00 kg, and m₂ 8.00 kg. (Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.)

An elevator car has two equal masses, m, attached to the ceiling as shown.

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

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.

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

Suppose an object is dropped from a height ho above the ground. Then its height after t seconds is given by h = -16t^2 + ho, where h is measured in feet. Use this information to solve the problem. If a ball is dropped from 268 ft above the ground, how long does it take to reach ground level?

1. What is the efficiency of a kettle that uses 1.0 x 10³ Watts of power to heat 0.50 kg of water from 24° C to 100° C in 4.0 minutes? (cater=4180 J/kg °C)

2. A 68.2 kg diver drops off a diving board that is 16.8m above the water surface. If the force of air resistance acting on the diver is 121 N [UP] determine: a. The work done by gravity on the diver during the jump b. The work done by air resistance on the diver during the jump c. The speed of the diver as they hit the water

3. ***A roller coaster of mass 1.35 x 10³kg rides on the track shown. It starts with a speed of 6.0 m/s at point A. a. Calculate the maximum speed (friction can be ignored) and state at what point it happens. b. Calculate the speed of the roller coaster at point E c. If the maximum speed the roller coaster can safely have at point C is 50 m/s, what is the maximum height that point A could have? (you can assume initial speed at point A is still 6.0 m/s) A Ast 100. m E D 38 m B 20. m

4. A car crashes into a brick wall at a speed of 120.0 km/h, so that the driver (mass 63 kg) travels 40.0 cm before stopping. Determine the average force applied to the driver.

28. A cyclist rides 8.0 km east for 20 minutes, then they turn and head west for 8 minutes and 3.2 km. Finally, they ride east for 16 km, which takes 40 minutes. (a) What is the final displacement of the cyclist? (b) What is their average velocity?

32. Sketch the velocity-versus-time graph from the following position-versus-time graph N x(t) (Position) Time (s)

74. A ship sets sail from Rotterdam, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0° north of east. What is the velocity of the ship relative to Earth?