Question

Two blocks m1 and m2 with masses 50 kg and 100 kg respectively are connected by a string over a pulley that is frictionless with negligible mass. The 50 kg block slides on a 37 degree incline that has a coefficient of kinetic friction of 0.25. This block is also attached to a wall at the base of the incline by an ideal spring that has a spring coefficient of 100 N/m. The system is released from rest with a force of 250 N pulling down on the 100kg block. Calculate the speed of the block m1 when it has moved a distance of 2 m up the incline. Answer: 4.43 m/s (please show work in detail for solution)

Answer 1

friction force = uk mg cos(theta) since normal force is mg cos(theta)

y k=100N/m mm X 2 ne Wosk energy principle Wroug + Us = 1 (m, tm.) va room rooky - Vy Work done by sonce = 250x2=5oo] change in potential eneegy = - 100X9.842 = -1370.223 7 50x9.8x4m37° friction - 40.25x Sox 9.8% cos37°) (2) - - 195.6657 ] - Us (Spring energy) = X 100 X2²) 2003 500 + 1370.22 -195,6657 - 200 I 1 Ciso) v2 n nr 2 [V = 4.43 m/s] ) + ) = a . (berley

Spring energy = 1/2 kx^2