Question

Question 2 10 pts A block of mass m = 4.0 kg is dropped from height h = 74 cm onto a spring of spring constant k = 1530 N/m (See the figure below). Find the maximum distance the spring is compressed. (Your result must be in meters and include 2 digit after the decimal point. Maximum of 5% of error is accepted in your answer. Take g = 9.8 m/s 2.) pecccccee

Answer 1

Given data  :-

mass of a block (m) = 4.0 kg

Dropped from height (h) = 74 cm (or) 0.74 m

Spring constant (k) = 1530 N/m

Take g = 9.8 m/s^2

h = 0.74m K'=1530 After compression Befac compression figure After dropping of black mass onto a Spring ů stretched to a some distance & as shown facio → in figure

calculations Convelation therren Accending to Energy Initial enagy (EP)'s Final : enagy (EJ) W+ CP.£); + (k.f) (P.Et (KE) → 220 W= walk done is $ Nb cuero zarollibecause Celk done ) (:- force and in vertical dôction (K.E (kie) = f becomel So equation © (P.EE = (p.6) [:: (PF), elastic, petent enday) Cista h+ x) H 1 "Я Cht) = na kx? 1 kx² 1.kx2 x mg might ngă 2 Kxi- mgr eq e mga-mgh Substituting all values in eq x(1530) x xº - 4* (9.34 (8) – 489.8* 0.74 = 0

765x2- 39.2 x - 29.008 = 0 :: The above equation is Pin quadratic expression form in ader to find a from ax² bx + c famalac: x= -bt b²-4ac ܘܪ Here 1) 765 b=-39.2, ca-29.008 Substitute in fomulae; we get -(-39.25 + 1634.2) 4(765)(-29.008) a 2 x 765 u 39.2 I 90301-12 1530 x 39.2 + 300-501 1530 0.221m Hence, distance the The maximum a compressed Spaing % = 0.22 m