Question

2. Fig. Q2 shows a 50 kg crate sliding down a 30° incline plane and eventually stopped by a bumper with spring constant k. The kinetic coefficient of between the crate and the floor is Mk = 0.33. At the moment shown, the crate has a velocity of 2.5 m/s. 50 kg 4 = 0 33 Bumper 30° 4.3 m ww 1.5 m Fig. 22 (1) Write the work and energy equation and use it to determine the velocity of the crate when it just reaches the bumper. (ii) Determine the value of the spring constant of the bumper, k, if it is observed that the crate comes to a stop 0.4 m momentarily after impacting with the bumper. (20 marks)

Answer 1

२. Given , m = mass of crate 50 60 kg 30 - -- 1 Mk 0.33 VA Inilial Velocely . 2.5 mis ix song 1 A K 4.3m 0 - 300 2 Immal it lism Energy at point 0 1 potential energy of block & initial Kindlic Energy (1 mg x 4.3x Sin 30 + mv? 1054 - 575 Joules + X 50 X 2.5 1210.825 Joules Energy at point 2 m v² → el block where Va final velouty of lost in the Energy Energy friction due to lost plane surface inclined plane + Energy lost lost in

t ung aso Ik 4.3ml fia Friction fasce in inclined plane - 4mg coso fi 0.33 X 50 X 9.81 x COS 30 fi 140.179 N Energy lost in in inclined Plane - fix 4.3 140.179 X 4.3 U 602-77 Jade k lism f2 = Friction force the Plane Sooface f2 = img 0.33 x 50x9.81 161, 865 nl Energy lose the in Surface f2 x 105 161.865 X 1.5 242.79 Joule Total Energy lost due to friction 602.77 € 242.29

Total friction Energy lost = 845:56 Joule Applying Energy belance t Energy at point 1 = Energy al poine 2 Energy lost due to fricción 1210.825 £mv,? + 845.56 سارع 2 m V₂ 365-265 2 365.265 X 2 . Van 2 50 3.822 mis hits the bumper crode Velocity of it jusi when 3.822 mis impact after 0.4m sprung moves li ) Q maul al → Velocity of crate stard (P) X₂= 3.822 mis 0.4m 1 Velocity of of crate cet end (a) V₂ = omis

By Energy balance Kenelic energy at Starling potential Energy Energy at end + Energy lost due to friction Let spring Constant be k , then Å my? = žky (po)? at f2 x (PQ) 2 X 50 X 3.822 à x K x 0.42 + 161-865 X 0.4 K.. = 3.756 kN lm Spring constant 3.756 knim