Question

1. (35 ps) A box ( -0.830 kg) is moving on a horizontal surface with a coeficient of Thiction of 0.108. A spring with a spring constant of 17.3 N/m is 1.95 m from the box. The box is stopped by the spring, compressing it 0.105 m A) What is the initial speed of the hox? B) How fast is the box moving when it reaches the spring? Pictorial Representation What is the System Potential Energies? Nonconservative forces ? External Forces? Is Mechanical Energy conserved?

Answer 1

m= 0.830 kg Given mass of the box I let initial velocity of box is equal to %. KE 17.3 NE smo 1.95m --p of Box 4= 0.108 AN by acceleration of box = wie - Ja Mn mg Naw, deels velocity of boxe Clet = 49 = 1.08 mise after travelling ligsme ) کہے حا - R2 = v +2 (4:08) (1.95) --fl)

0²= 4², 4:212 ) I Now applying work energy theorem, which states as work done by all forces is equal to change in kinetic energy, 80, Woriction & Wspring = K = Kg Ki we know that kg 20 and ki = 1 me? se Wfriction =- ww (1.35 +0.105) --(0.108)(8-30) (2.065) =-1.842 Jonke . Wsping = 2 x 2² = ft kh. a s-korean --(173) (0-10573 - 2 =-0.095 Joule S ) 0 1842 -0.095 - ² = 4.667 To = 2.160 misec

so, initial velocity of bon was 2.160 m (b) velocity of bore when it reaches the string we com Calentate it from equation (1) 42 43 4.212 = (2-160)2 4.212 = 4.667 - 4.212 122=0.455 v= 0.674 m see , velocity of box when it touches bon is 0.674 sec (in system =) spoing - Mass system mi im Ei systery 1 Potential Energy of spring potential energy 1 (6) Non conservative forces a friction force TO) External forces a gravitational force 1 (1) Mechanical Energy not conserved, I Converted into heat. Some Energy