Let’s look at a simplified model of a car that’s dropped onto the ground. Model the suspension as a single linear spring and the rest of the vehicle as a single lumped mass. The car is dropped from a height of h1 = 0.9m. What is the maximum mass m for which the suspension does not bottom out? Assume a maximal allowable suspension travel of 10 cm and a spring constant of k = 2.4x10^6 N/m.

You pull on a string with a horizontal force of magnitude Fyb = 51 N that is attached to a block of mass mb = 6.3 kg, then to the axle of a solid cylinder of mass mc = 4.3 kg and radius r = 0.5 m, then to a spring of spring constant k = 190 N/m. This is all done on an inclined plane where there is friction ( μs = 0.6 and μk = 0.33 ), and the incline angle is θ = 25 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the spring stretches. What is the speed of the block and cylinder after you pulled the block 66 cm down the plane.

A forensic scientist test-fires a projectile (mass mP) at a cubic block (volume V), made from wood (density D), resting on a rough surface (static = kinetic coefficient uS). The bullet enters the block with an initial velocity vo and exits the block with a velocity v1. The friction forces on the bullet as it passes through the length of the block are unknown and are assumed to be constant. Solve these problems algebraically first: a) What is the deceleration of the bullet inside the block? How many "g" is that? b) How much time does it take the projectile to pass through the block? c) What is the velocity of the block as the bullet exits? d) How long (time) and how far (distance) does the block slide after the bullet has exited? e) Solve the above numerically for the following parameters (g =9.81m/s^2): mP = 10g, V = 0.1m^3, D = 500kg/m^3, µS = 0.8, v0 = 500m/s, v1 = 100m/s

Find the point of contraflexure solid mechanics solve the figure.

A crate of 69 kg simply stands on the moving cart with constant acceleration a. The height from the center of gravity to the cart, L, is 1.4 m, and the angle = 13°. What is the maximum acceleration a (in m/s²) the cart can have without sliding on the cart? The coefficient of static friction between the crate and the cart is μl g = 0.51. Please pay attention: the numbers may change since they are randomized. Your answer must include 3 places after the decimal point. Take g = 9.81 m/s². 0.5 m 0.5 m L Your Answer: Answer G

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Ів 00 WB WC DBC A LA WA P lc UBC Engineering A kid excitedly swings his foam cut-out hammer. If point P acts like a pin and the hammer rotates about kg that point, what is the moment of inertia of the hammer? The foam has a density of p = 150 and a uniform thickness of t = 0.5 cm. Assume each cut-out is a rectangular plate and the foam acts as a rigid body. m³ Plate A has a length 14 = 34 cm and width w₁ = 8 cm. Plate B has a length 13 = 8.5 cm and width wB = 30 cm. Plate C is identical to plate D, and has a length lc = 15 cm and width wc = 5 cm. Plate C and D are attached to plate B such that their centers line up. Ip = 0.00758 x (kg) - m²

A crate of 67 kg simply stands on the moving cart with constant acceleration a. The height from the center of gravity to the cart, L, is 1.2 m, and the angle = 12°. What is the maximum acceleration a (in m/s²) the cart can have without tipping over on the cart? The coefficient of static friction between the crate and the cart is μg = 0.55. Please pay attention: the numbers may change since they are randomized. Your answer must include 3 places after the decimal point. Take g = 9.81 m/s². 0.5 m 0.5 m L Your Answer: ● 0 Answer G

m2 Two masses connected by a massless string of length I slide without friction on two inclined planes as shown in the figure above. The motion is restricted to the x-y plane indicated in the figure. Gravity is acting in the negative y-direction. (a). Explain the term "virtual displacement". (b). State d'Alembert's principle of virtual work. (c). Write down d'Alemberts equation for this system in cartesian coordinates. Need detailed and step by step answer of all subparts with good handwriting Please I want to learn

A three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length 200mm and has a thickness of 20mm. Plywood has a density of 0.3 g/cm^3. For the purposes of finding the platform weight, W, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts M1, M2, and M3 were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. Co • F: (-75,-75) F₂: (85, -75) • F3: (15,85) -17.4319 MAT 1.338758 3.18886 7 Top View A coordinate system has been defined, such that middle of the…