3m/s and th section of the track. The coefficient of kinetic okg he mack n anc f

Question

3m/s and th section of the track. The coefficient of kinetic okg he mack n anc friction between the block and the plane is 0.3 for the first 0.5m of the plane, and zero (that is frictionless) for the rest of the track. After entering the level section of the track, the block encounters an initially uncompressed spring. It com block rebounds and heads back up the track. . A g mass is moving down a track inclined as shown. The initial speed of the mass is e mass is initially 2m above the level itm presses the spring by 0.3m before the a) Find the energy spent due to friction during the trip down the track. b) Find the speed of the block just before it hits the spring c) Find the spring constant.

Explanation / Answer

(A) N = m g cos30

and f = u N = u m g cos30

work done = - f.d = (0.3 x 10 x 9.81 x cos30) (0.5)

= -12.7 J

(A) Energy spent = 12.7 J

(b) Applying work - energy theorem,

Work done by gravity + work done by friction = change in KE

(10 x 9.81 x 2) - 12.7 = 10 (v^2 - 3^2) / 2

v = 6.76 m/s ........Ans

(c) Applying energy coservation for spring - mass system,

k (0.3^2) /2 = 10 x 6.76^2 /2

k = 5078 N/m

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