ENGR216 2025 Q B2 (ENGR5004)

ENGR216 2025 Q B2Past paperOld spec ENGR2162:125 marks30 min

ENGR216 Summer 2025 Q B2[VALID] official answers

A particle (P) of mass ( $m$ ) slides in a tube with the relative velocity of $v_{rel}$ . The tube and the rod (perpendicular to the tube) rotate counterclockwise about point O with angular velocity $\omega$ and angular acceleration $\alpha$ . At the instant shown in Figure B2, the horizontal and vertical distance between O and P is $L$ and $h$ , respectively. $\mu_k$ and $\mu_s$ are the kinetic and static friction coefficients between P and the tube.

Figure B2: rod of length L pinned at O carrying a perpendicular tube; particle P at height h above the rod, moving up the tube at v_rel.

Formulas you may need

Rotating-axes acceleration: $\mathbf{a}_P = \mathbf{a}_O + (\mathbf{a}_{P/O})_{rel} + \boldsymbol\alpha\times\mathbf{r}_{P/O} + 2\boldsymbol\omega\times(\mathbf{v}_{P/O})_{rel} + \boldsymbol\omega\times(\boldsymbol\omega\times\mathbf{r}_{P/O})$ (given in the question)
Unit-vector cross products: $\mathbf{k}\times\mathbf{i} = \mathbf{j}$ , $\mathbf{k}\times\mathbf{j} = -\mathbf{i}$ (learn this)
Newton's second law for a particle: $\sum\mathbf{F} = m\mathbf{a}$ , in components (learn this)
Kinetic friction $F = \mu_k N$ , opposing the relative sliding; static $F \le \mu_s N$ only when there is no sliding (learn this)

(a)
Draw the free-body and kinetic diagrams of the particle P. State appropriate coordinate systems.
[10]
(b)
Determine the acceleration of the particle P. Hint: use the following equation: $a_P = a_O + (a_{P/O})_{rel} + \alpha \times r_{P/O} + 2\omega \times (v_{P/O})_{rel} + \omega \times (\omega \times r_{P/O}).$
[10]
(c)
Determine the normal force and friction force of the particle P.
[5]2:2