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45 kg is released from rest from the top of a rough ramp, with Mass - coefficient of kinetic friction 0.25 between the block and the incline, of height 3.2 m and length d 5.5 m. At the bottom of the ramp, the mass slides on a horizontal, frictionless surface until it compresses a spring of spring constant k 2. 110 N/m. a. Calculate the speed of the mass at the bottom of the ramp? b. How far does the spring compress? c. How much work does gravity do on the mass when it slides down the ramp? d. How much work does the spring do on the mass during the compression? e. Calculate the work done by friction during the slide down the ramp. f. What is the total work done on the mass during the interval from the moment it is released to the moment the spring is fully compressed?

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Answer #1

Mass of the block m-45 kg 3.235.578 5.5 Angle of inclination θ sin-11- coefficient of kinetic friction μ-0.25 spring constant K-110 N/m Accelearation a g (sine - cose9.8(0.5818 -0.25x0.8133) intial velocity u -0 Velocity on reaching the bottom v-? From kineamtic relati on 3.709 m/s2 V2-0-2(3.709)(5.5) v 6.387 m/s Let x be the copression in the spring From conservati on of energy, (45)(6387) (110)x2 z 4.0854 m Work done by gravity Weygh (45)(9.8) (3.2) 141123 Work done by spring W^rng-- ^Kx* -- (0.5)(110)(4.0854) -917.977 J Work done by friction Writing cos8 d (0.25) (45)(9.8 (0.8133) (5.5)-493.1647 J Net work done W- Wrty + WrintionWgn1411.2-493.1647-917.9770

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