## Write a vector formula for computing the center to center distance between two disks given their velocities, u, and their positions, r0, at a given time, t0.

Sphere and disk collisions can be expressed more compactly and computed more conveniently in vector notation. Primarily, this involves converting the procedures of Example 7.10 to use the dot product of the relative position and relative velocity. (Hint: You may find useful information in the DMD module at Etomica.org.)

(a) Write a vector formula for computing the center to center distance between two disks given their velocities, u, and their positions, r0, at a given time, t0.

(b) Write a vector formula for computing the distance of each disk from each wall. (Hint: Use unit vectors x=(1, 0) and y=(0, 1) to isolate vector components.)

(c) Noting that energy and momentum must be conserved during a collision, write a vector formula for the changes in velocity of two disks after collision.

Hints: (1) ab=abcos  . (2) A unit vector with direction of a is: a/a.

(d) Write a vector formula for the change in velocity of a disk colliding with a wall.

### design suitable bearings to support the load for at least 5E8 cycles at 1 200 rpm using deepgroove ball bearings.

The shaft shown in Figure P11-4 was designed in Problem 10-19. For the data in row (a) of Table P11-1, and the corresponding diameter of shaft found in Problem 10-19,….

### Find the minimum film thickness for a long bearing with the following data: 30-mm dia, 130 mm long, 0.0015 clearance ratio, 1 500 rpm, ISO VG 100 oil at 200°F, and supporting a load of 7 kN.

1.       A paper machine processes rolls of paper having a density of 984 kg/m3. The paper roll is 1.50-m OD X 22-cm ID X 3.23-m long and is on a simply supported, 22-cm OD, steel….

### Find the minimum film thickness for a bearing with these data: 30-mm dia, 25 mm long, 0.0015 clearance ratio, 1 500 rpm, ON = 30, ISO VG 220 oil at 200°F.

1.       Problem 7-12 estimated the volume of adhesive wear to expect from a steel shaft of 40 mm dia rotating at 250 rpm for 10 years in a plain bronze….