Question

Matt, a mechanical engineer, is intertested on the forces acting on his car as he drives along a flat road. Horizontally, the car is pushed forward by a force F(t), and the car has air resistenace acting orn Faid). Vertically, the car is supported with a spring and damper at each of its four wheels. The car's entire mass m is evenly supported by each wheel. Each spring has a stiffness of k and each damper has a damping coeficient of c. The car can only move horizontally and/or vertically, so rotational effets can be ignored. 1. Draw a large, clear Free Body Diagram of Matt's car 2. 3. If the cars top speed is 100m/s and the force the car provides at this speed is 2000N, solve for the 4 Obtain an ODE (in standard form) of the cars vertical displacement y by applying Newton's Second 5. When Matt (80kg) gets into the car, the car body lowers by 0.02m, and then remains static. Given this, Obtain an ODE (in standard form) of the cars horizontal velocity v by applying Newton's Second Law in the x-direction drag coefficient d. Law in the y-direction. solve the spring stiffness k acting at each wheel.

Answer 1

Free body diagram of matt's car Forward push = F (t), air resistance F_v = d V^2 mass of car = m: it is distributed over each wheel Each wheel is supported by F_spring = ky and F_damper = C V_y and F_weight/wheel = weight compared of car/wheel = m/4 g Y and Vy = Vertical displacement and vertical velocity respectively 2) Newton's second law of motion in X - direction: Net applied force = M_ax F (t) - dv^2 = M_ax\r\n 3) Velocity of the car at the top speed, V = 100 m/s when, the car attains top speed, there is no acceleration, Hence there is no external force acting on the car. So that, Force provided by the car = Air resistance, F_air = 2000 N But, we know that F_air = dv^2 dv^2 = 2000 d (100)^2 = 2000 Therefore d = 0.2 Newton's second law of motion in y - direction: Net applied force = M_ay