3) Two blocks and a pulley made from two con- centric uniform disks are connected as...

 

Transcribed Image Text:

3) Two blocks and a pulley made from two con- centric uniform disks are connected as shown in the figure. The coefficient of kinetic friction between mi and the surface is . The masses are connected to the pulley with two separate strings each wrapped around the pulley at one end. The string connected to mi is attached to the pulley at ra and the string connected to m2 is attached to the pulley at rs. Moving m2 down causes the pulley to rotate and rotating the pul- ley drags mi toward the pulley. The pulley is constructed out of two solid disks glued together concentrically, one of mass ma for ra and one of mass mb for rb. The masses are initially at rest. Give all results in terms of k, m, m2, ma, mb, ra, rb, d, and g. m1 d a) (4 pts) Find the distance di that mass mi slides when m2 falls a distance d2. b) (4 pts) Find the moment of inertia I of the pulley about the axis through the center. ma, mb m2 d c) (8 pts) Find the velocity v2r of m2 after it has fallen a distance d2 (just before it hits the ground). You may leave "I" from part b) in the result. d) (4 pts) Once m2 hits the ground how much farther along the table does mi travel? You may as- sume it stops before it reaches the edge of the table. You may leave "I" from part b) and "v2r" from part c) in the result. 3) Two blocks and a pulley made from two con- centric uniform disks are connected as shown in the figure. The coefficient of kinetic friction between mi and the surface is . The masses are connected to the pulley with two separate strings each wrapped around the pulley at one end. The string connected to mi is attached to the pulley at ra and the string connected to m2 is attached to the pulley at rs. Moving m2 down causes the pulley to rotate and rotating the pul- ley drags mi toward the pulley. The pulley is constructed out of two solid disks glued together concentrically, one of mass ma for ra and one of mass mb for rb. The masses are initially at rest. Give all results in terms of k, m, m2, ma, mb, ra, rb, d, and g. m1 d a) (4 pts) Find the distance di that mass mi slides when m2 falls a distance d2. b) (4 pts) Find the moment of inertia I of the pulley about the axis through the center. ma, mb m2 d c) (8 pts) Find the velocity v2r of m2 after it has fallen a distance d2 (just before it hits the ground). You may leave "I" from part b) in the result. d) (4 pts) Once m2 hits the ground how much farther along the table does mi travel? You may as- sume it stops before it reaches the edge of the table. You may leave "I" from part b) and "v2r" from part c) in the result.