Question

Problem II A 15 tonne wagon travelling at 3.6 m/s is brought to rest by a buffer (spring) having a stiffness of 7.5 x 10 N/m. Assuming that the wagon comes into contact with the buffer smoothly without rebound, calculate the compression of the buffer if there is a constant rolling friction force of 800 N. 800 N 1 135 points

Answer 1

Since friction is included in this problem mechanical energy is not conserved. If x is the compression of the buffer when the wagon comes to rest, the forces acting on the wagon are the thrust of the compressed spring of the friction 800N, both acting in a direction opposite to the direction of motion. The resultant force is, - 800 k_x = - 800 - 75 times 10^5X The workdone by the forces = integral^x_0 (-7.5 times 10^5 x - 800) dr = -7.5 times 10^5 x^2/2 - 80 x The wagon comes to rest f so, remembering that 1 tonne = 10^3 kg, Equation with V = 0 4 u = 3.6 ms^-1 becomes - 7.5 times 10^5 x^2/25 - 800x = -1/2 15 times 10^3 times (3.6) ^2 Which simplifies to 750x^2 + 1.6x - 194.4 = 0 This is a Quadratic Equation whose roots are x = -1.6 plusminus squareroot(1.6) ^2 + 4 times 750 times 194.4/1500 = -1.6 plusminus 763.677/1500 \r\n = 0.508 (or) -0.510 For this Problem the negative root