VM-WB-MECH-057

VM-WB-MECH-057
Calculation of Velocity of Slider and Force by Collar

Overview

Reference:	Beer-Johnston. (2004). Vector Mechanics for Engineers: Statics & Dynamics (7th ed., Problem 13.73, p. 793). TATA McGRAW HILL.
Solver(s):	Ansys Mechanical
Analysis Type(s):	Rigid Dynamic Analysis
Element Type(s):	Multipoint Constraint Element

Test Case

A 1.2 Kg collar is attached to a spring and slides without friction along a circular rod in a vertical plane:

Figure 75: Slider and Collar Schematic

The spring has a nondeformed length of 105 mm and a constant K = 300 N/m. Knowing that the collar is at rest at C, it is given a slight push to get it moving.

Length OP = 75 mm.

Length OB = 180 mm.

Determine the force exerted by the rod on the collar as it passes through points A and B.

Material Properties

Geometric Properties

E = 2E11 Pa

ν = 0.3

Spring:

Undeformed length = 105 mm

Stiffness K = 300 N/m

Gravitational acceleration = -9.8066 m/s² (Y direction)

Results Comparison

Results	Target	Mechanical [1]	Error (%)
At point A (N)	14.88	14.992	0.7527
At point B (N)	-23.6	-23.667	0.2839

To compare these results to those obtained using explicit dynamics, see VM-EXD-MECH-010.