Question

18. Consider the track shown in the Figure. The section AB is one quadrant of a circle of radius 2.0m and is frictionless. B to C is a horizontal span 3.0m long with a coefficient of kinetic friction uk = 0.25. The section CD under the spring is frictionless. A block of mass 1.0kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20m. Use g=10m/s2. (10 pts, total] A. Determine the velocity at point B. (2 pts] Determine the velocity of the block at point C, using work-energy relation (5pts] Determine the spring constant k for the spring [3pts] | m= 1.0 kg ΤΑΙ r= 2.0 m

Consider the track shown in the Figure. The section AB is one quadrant of a circle of radius 2.0m and is frictionless. B to C is a horizontal span 3.0m long with a coefficient of kinetic friction μk = 0.25. The section CD under the spring is frictionless. A block of mass 1.0kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20m. Use g=10m/s2.

A. Determine the velocity at point B.
B. Determine the velocity of the block at point C, using work-energy relation

C. Determine the spring constant k for the spring

Answer 1

The potential energy of the object C I a) Given that r=am Mk - 0.25 m 1.0 lg ol = 0.2mg ♡ B 9 - lom/s2 The PE of body at A is transfered to K. E of at B ie PE at A = k. E at B mgn = ²mv? There h=8= am] => 1x10x2=*1x ve V2 - 40 V340 ms 56.32 m/s Velocity at B= 6.32 m/s b) We love MK= 0.25 = funf - fic tand force => fa 0.25% mq = 0.25 x 10 = 2.5N work done by frictioné face = f.s there s- displacemed - 3 m = 2.5X 3 = 7.51 This work is done against the 209 KE it had at B ie K. E of body ate : 20-7.5 - 12:55 » % mv?= 12.5 =) < *1xV?= 12.5 V=525 - sms - Velocity of booly at cosms

Given extension of spring n= 0.2m Ke of the body, is transfeed to the PE of the spring .; PE of spring = 12.5 J We have PE = 1 kx² k-spring Const 12.5 = {K (0.2)2 K25 1 (0:2) = 625 N/m ... Spring Gestant ik of spring is 625 */ x-extenson
Summary:a)the velocity of object at B= 6.32 m/s

b) the velocity of body at C = 5m/s

c)Spring constant K of the spring =625 N/m