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.

 

find the cost of your paper

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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.

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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.

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