dynamic

ωAB ωBC

ENGR 2120 - Dynamics

Final Exam Date: 8/6/2020 Time: 105 Minutes

Problem One

A uniform rigid rod AB has a mass of M and length of L and it rests against fixed surfaces as shown. If

the rod is released from rest at θ (θ < π/2) and the kinetic friction coefficient for the rod AB and surfaces

are μ. Write, the equations of motion in terms of reaction forces at points A and B, the angular

acceleration of rotation of AB and the following parameters: M, L, gravity, μ and θ.

A

L/2

L/2

G

B θ

Problem Two

The uniform rod AB has a mass of M and is sliding on a frictionless wall at A. It is also attached to a

wheel at B and the horizontal spring as shown. If the point B is pushed by a constant force of F and is

moved to the right from rest when θ = 300. Determine, velocity of B when θ = 450. Assuming that the

wheel is rolling and M = 10 kg, L = 2 m, F = 50 N, k = 40 N/m. The wheel has a radius R = 0.1 m, and its

radius of gyration kG is 0.15 m. The spring is upstretched when θ = 30 0.

A

θ

θ

L

Datum F B k

Problem Three

In the slider mechanism shown here, the crank AB is rotating with a constant angular velocity of ωAB =10

rad/s at the instant shown. Determine velocity and acceleration of the block A. Assume AB = 1 m,

BC = 3 m, h =0. 5 m, sin φ = 1/3, and ωBC = 2.5√6 rad/s.

B

A 300

h φ

C